Merge branch 'main' of github.com:joeycastillo/Sensor-Watch into mars-clock

29 files changed, 5097 insertions, 17 deletions

diff --git a/movement/lib/astrolib/LICENSE.txt b/movement/lib/astrolib/LICENSE.txt
new file mode 100755
index 00000000..26356b05
--- /dev/null
+++ b/movement/lib/astrolib/LICENSE.txt
@@ -0,0 +1,9 @@
+Public domain

+

+THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE

+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER

+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,

+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE

+SOFTWARE.

diff --git a/movement/lib/astrolib/README.md b/movement/lib/astrolib/README.md
new file mode 100644
index 00000000..d63bc463
--- /dev/null
+++ b/movement/lib/astrolib/README.md
@@ -0,0 +1,9 @@
+# Astrolib
+
+This is a relatively straightforward C port of Greg Miller's [JavaScript astro library](https://github.com/gmiller123456/astrogreg), done by Joey Castillo, for the Sensor Watch Astronomy watch face.
+
+He released his work into the public domain and so I release this into the public domain as well.
+
+I have tested the output of this library against [NASA's Horizons system](https://ssd.jpl.nasa.gov/horizons/app.html#/) and found the results to match (within reason, as we're using a truncated version of VSOP87). Moon calculations still seem a bit iffy, but it doesn't surprise me seeing as there are three calculations involved and the error could stack up.
+
+THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
diff --git a/movement/lib/astrolib/astrolib.c b/movement/lib/astrolib/astrolib.c
new file mode 100644
index 00000000..f1bacc55
--- /dev/null
+++ b/movement/lib/astrolib/astrolib.c
@@ -0,0 +1,555 @@
+/*
+ * Partial C port of Greg Miller's public domain astro library (gmiller@gregmiller.net) 2019
+ * https://github.com/gmiller123456/astrogreg
+ * 
+ * Ported by Joey Castillo for Sensor Watch
+ * https://github.com/joeycastillo/Sensor-Watch/
+ *
+ * Public Domain
+ *
+ * THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include <stdbool.h>
+#include <stdio.h>
+#include "astrolib.h"
+#include "vsop87a_milli.h"
+
+double astro_convert_utc_to_tt(double jd) ;
+double astro_get_GMST(double ut1);
+astro_cartesian_coordinates_t astro_subtract_cartesian(astro_cartesian_coordinates_t a, astro_cartesian_coordinates_t b);
+astro_cartesian_coordinates_t astro_rotate_from_vsop_to_J2000(astro_cartesian_coordinates_t c);
+astro_matrix_t astro_get_x_rotation_matrix(double r);
+astro_matrix_t astro_get_y_rotation_matrix(double r);
+astro_matrix_t astro_get_z_rotation_matrix(double r);
+astro_matrix_t astro_transpose_matrix(astro_matrix_t m);
+astro_matrix_t astro_dot_product(astro_matrix_t a, astro_matrix_t b);
+astro_matrix_t astro_get_precession_matrix(double jd);
+astro_cartesian_coordinates_t astro_matrix_multiply(astro_cartesian_coordinates_t v, astro_matrix_t m);
+astro_cartesian_coordinates_t astro_convert_geodedic_latlon_to_ITRF_XYZ(double lat, double lon, double height);
+astro_cartesian_coordinates_t astro_convert_ITRF_to_GCRS(astro_cartesian_coordinates_t r, double ut1);
+astro_cartesian_coordinates_t astro_convert_coordinates_from_meters_to_AU(astro_cartesian_coordinates_t c);
+astro_cartesian_coordinates_t astro_get_observer_geocentric_coords(double jd, double lat, double lon);
+astro_cartesian_coordinates_t astro_get_body_coordinates(astro_body_t bodyNum, double et);
+astro_cartesian_coordinates_t astro_get_body_coordinates_light_time_adjusted(astro_body_t body, astro_cartesian_coordinates_t origin, double t);
+astro_equatorial_coordinates_t astro_convert_cartesian_to_polar(astro_cartesian_coordinates_t xyz);
+
+//Special "Math.floor()" function used by convertDateToJulianDate()
+static double _astro_special_floor(double d) {
+    if(d > 0) {
+        return floor(d);
+    }
+    return floor(d) - 1;
+}
+
+double astro_convert_date_to_julian_date(uint16_t year, uint8_t month, uint8_t day, uint8_t hour, uint8_t minute, uint8_t second) {
+    if (month < 3){
+        year = year - 1;
+        month = month + 12;
+    }
+
+    double b = 0;
+    if (!(year < 1582 || (year == 1582 && (month < 10 || (month == 10 && day < 5))))) {
+        double a = _astro_special_floor(year / 100.0);
+        b = 2 - a + _astro_special_floor(a / 4.0);
+    }
+
+    double jd = _astro_special_floor(365.25 * (year + 4716)) + _astro_special_floor(30.6001 * (month + 1)) + day + b - 1524.5;
+    jd += hour / 24.0;
+    jd += minute / 24.0 / 60.0;
+    jd += second / 24.0 / 60.0 / 60.0;
+
+    return jd;
+}
+
+//Return all values in radians.
+//The positions are adjusted for the parallax of the Earth, and the offset of the observer from the Earth's center
+//All input and output angles are in radians!
+astro_equatorial_coordinates_t astro_get_ra_dec(double jd, astro_body_t body, double lat, double lon, bool calculate_precession) {
+    double jdTT = astro_convert_utc_to_tt(jd);
+    double t = astro_convert_jd_to_julian_millenia_since_j2000(jdTT);
+    
+    // Get current position of Earth and the target body
+    astro_cartesian_coordinates_t earth_coords = astro_get_body_coordinates(ASTRO_BODY_EARTH, t);
+    astro_cartesian_coordinates_t body_coords = astro_get_body_coordinates_light_time_adjusted(body, earth_coords, t);
+
+    // Convert to Geocentric coordinate
+    body_coords = astro_subtract_cartesian(body_coords, earth_coords);
+
+    //Rotate ecliptic coordinates to J2000 coordinates
+    body_coords = astro_rotate_from_vsop_to_J2000(body_coords);
+
+    astro_matrix_t precession;
+    // TODO: rotate body for precession, nutation and bias
+    if(calculate_precession) {
+        precession = astro_get_precession_matrix(jdTT);
+        body_coords = astro_matrix_multiply(body_coords, precession);
+    }
+
+    //Convert to topocentric
+    astro_cartesian_coordinates_t observerXYZ = astro_get_observer_geocentric_coords(jdTT, lat, lon);
+
+    if(calculate_precession) {
+        //TODO: rotate observerXYZ for precession, nutation and bias
+        astro_matrix_t precessionInv = astro_transpose_matrix(precession);
+        observerXYZ = astro_matrix_multiply(observerXYZ, precessionInv);
+    }
+
+    body_coords = astro_subtract_cartesian(body_coords, observerXYZ);
+
+    //Convert to topocentric RA DEC by converting from cartesian coordinates to polar coordinates
+    astro_equatorial_coordinates_t retval = astro_convert_cartesian_to_polar(body_coords);
+    
+    retval.declination = M_PI/2.0 - retval.declination;  //Dec.  Offset to make 0 the equator, and the poles +/-90 deg
+    if(retval.right_ascension < 0) retval.right_ascension += 2*M_PI; //Ensure RA is positive
+    
+    return retval;
+}
+
+//Converts a Julian Date in UTC to Terrestrial Time (TT)
+double astro_convert_utc_to_tt(double jd) {
+    //Leap seconds are hard coded, should be updated from the IERS website for other times
+    
+    //TAI = UTC + leap seconds (e.g. 32)
+    //TT=TAI + 32.184
+
+    //return jd + (32.0 + 32.184) / 24.0 / 60.0 / 60.0;
+    return jd + (37.0 + 32.184) / 24.0 / 60.0 / 60.0;
+
+    /*
+    https://data.iana.org/time-zones/tzdb-2018a/leap-seconds.list
+    2272060800  10  # 1 Jan 1972
+    2287785600  11  # 1 Jul 1972
+    2303683200  12  # 1 Jan 1973
+    2335219200  13  # 1 Jan 1974
+    2366755200  14  # 1 Jan 1975
+    2398291200  15  # 1 Jan 1976
+    2429913600  16  # 1 Jan 1977
+    2461449600  17  # 1 Jan 1978
+    2492985600  18  # 1 Jan 1979
+    2524521600  19  # 1 Jan 1980
+    2571782400  20  # 1 Jul 1981
+    2603318400  21  # 1 Jul 1982
+    2634854400  22  # 1 Jul 1983
+    2698012800  23  # 1 Jul 1985
+    2776982400  24  # 1 Jan 1988
+    2840140800  25  # 1 Jan 1990
+    2871676800  26  # 1 Jan 1991
+    2918937600  27  # 1 Jul 1992
+    2950473600  28  # 1 Jul 1993
+    2982009600  29  # 1 Jul 1994
+    3029443200  30  # 1 Jan 1996
+    3076704000  31  # 1 Jul 1997
+    3124137600  32  # 1 Jan 1999
+    3345062400  33  # 1 Jan 2006
+    3439756800  34  # 1 Jan 2009
+    3550089600  35  # 1 Jul 2012
+    3644697600  36  # 1 Jul 2015
+    3692217600  37  # 1 Jan 2017
+    */
+}
+
+double astro_convert_jd_to_julian_millenia_since_j2000(double jd) {
+    return (jd - 2451545.0) / 365250.0;
+}
+
+astro_cartesian_coordinates_t astro_subtract_cartesian(astro_cartesian_coordinates_t a, astro_cartesian_coordinates_t b) {
+    astro_cartesian_coordinates_t retval;
+
+    retval.x = a.x - b.x;
+    retval.y = a.y - b.y;
+    retval.z = a.z - b.z;
+
+    return retval;
+}
+
+// Performs the rotation from ecliptic coordinates to J2000 coordinates for the given vector x
+astro_cartesian_coordinates_t astro_rotate_from_vsop_to_J2000(astro_cartesian_coordinates_t c) {
+    /* From VSOP87.doc
+        X        +1.000000000000  +0.000000440360  -0.000000190919   X
+        Y     =  -0.000000479966  +0.917482137087  -0.397776982902   Y
+        Z FK5     0.000000000000  +0.397776982902  +0.917482137087   Z VSOP87A
+    */
+    astro_cartesian_coordinates_t t;
+    t.x = c.x + c.y * 0.000000440360 + c.z * -0.000000190919;
+    t.y = c.x * -0.000000479966 + c.y * 0.917482137087 + c.z * -0.397776982902;
+    t.z = c.y * 0.397776982902 + c.z * 0.917482137087;
+
+    return t;
+}
+
+double astro_get_GMST(double ut1) {
+    double D = ut1 - 2451545.0;
+    double T = D/36525.0;
+    double gmst = fmod((280.46061837 + 360.98564736629*D + 0.000387933*T*T - T*T*T/38710000.0), 360.0);
+
+    if(gmst<0) {
+        gmst+=360;
+    }
+
+    return gmst/15;
+}
+
+static astro_matrix_t _astro_get_empty_matrix() {
+    astro_matrix_t t;
+    for(uint8_t i = 0; i < 3 ; i++) {
+        for(uint8_t j = 0 ; j < 3 ; j++) {
+            t.elements[i][j] = 0;
+        }
+    }
+    return t;
+}
+
+//Gets a rotation matrix about the x axis.  Angle R is in radians
+astro_matrix_t astro_get_x_rotation_matrix(double r) {
+    astro_matrix_t t = _astro_get_empty_matrix();
+
+    t.elements[0][0]=1;
+    t.elements[0][1]=0;
+    t.elements[0][2]=0;
+    t.elements[1][0]=0;
+    t.elements[1][1]=cos(r);
+    t.elements[1][2]=sin(r);
+    t.elements[2][0]=0;
+    t.elements[2][1]=-sin(r);
+    t.elements[2][2]=cos(r);
+
+    return t;
+}
+
+//Gets a rotation matrix about the y axis.  Angle R is in radians
+astro_matrix_t astro_get_y_rotation_matrix(double r) {
+    astro_matrix_t t = _astro_get_empty_matrix();
+
+    t.elements[0][0]=cos(r);
+    t.elements[0][1]=0;
+    t.elements[0][2]=-sin(r);
+    t.elements[1][0]=0;
+    t.elements[1][1]=1;
+    t.elements[1][2]=0;
+    t.elements[2][0]=sin(r);
+    t.elements[2][1]=0;
+    t.elements[2][2]=cos(r);
+
+    return t;
+}
+
+//Gets a rotation matrix about the z axis.  Angle R is in radians
+astro_matrix_t astro_get_z_rotation_matrix(double r) {
+    astro_matrix_t t = _astro_get_empty_matrix();
+
+    t.elements[0][0]=cos(r);
+    t.elements[0][1]=sin(r);
+    t.elements[0][2]=0;
+    t.elements[1][0]=-sin(r);
+    t.elements[1][1]=cos(r);
+    t.elements[1][2]=0;
+    t.elements[2][0]=0;
+    t.elements[2][1]=0;
+    t.elements[2][2]=1;
+
+    return t;
+}
+
+void astro_print_matrix(char * title, astro_matrix_t matrix);
+void astro_print_matrix(char * title, astro_matrix_t matrix) {
+    printf("%s\n", title);
+    for(uint8_t i = 0; i < 3 ; i++) {
+        printf("\t");
+        for(uint8_t j = 0 ; j < 3 ; j++) {
+            printf("%12f", matrix.elements[i][j]);
+        }
+        printf("\n");
+    }
+    printf("\n");
+}
+
+astro_matrix_t astro_dot_product(astro_matrix_t a, astro_matrix_t b) {
+    astro_matrix_t retval;
+
+    for(uint8_t i = 0; i < 3 ; i++) {
+        for(uint8_t j = 0 ; j < 3 ; j++) {
+            double temp = 0;
+            for(uint8_t k = 0; k < 3 ; k++) {
+                temp += a.elements[i][k] * b.elements[k][j];
+            }
+            retval.elements[i][j]=temp;
+        }
+    }
+
+    return retval;
+}
+
+astro_matrix_t astro_transpose_matrix(astro_matrix_t m) {
+    astro_matrix_t retval;
+    for(uint8_t i = 0; i < 3 ; i++) {
+        for(uint8_t j = 0 ; j < 3 ; j++) {
+            retval.elements[i][j] = m.elements[j][i];
+        }
+    }
+    return retval;
+}
+
+astro_matrix_t astro_get_precession_matrix(double jd) {
+    //2006 IAU Precession.  Implemented from IERS Technical Note No 36 ch5.
+    //https://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote36/tn36_043.pdf?__blob=publicationFile&v=1
+
+    double t = (jd - 2451545.0) / 36525.0;  //5.2
+    const double Arcsec2Radians = M_PI/180.0/60.0/60.0; //Converts arc seconds used in equations below to radians
+
+    double e0 = 84381.406 * Arcsec2Radians; //5.6.4
+    double omegaA = e0 + ((-0.025754 + (0.0512623 +	(-0.00772503 + (-0.000000467 + 0.0000003337*t) * t) * t) * t) * t) * Arcsec2Radians; //5.39
+    double psiA = ((5038.481507 +	(-1.0790069 + (-0.00114045 + (0.000132851 - 0.0000000951*t) * t) * t) * t) * t) * Arcsec2Radians; //5.39
+    double chiA = ((10.556403 + (-2.3814292 + (-0.00121197 + (0.000170663 - 0.0000000560*t) * t) * t) * t) * t) * Arcsec2Radians; //5.40
+    //Rotation matrix from 5.4.5
+    //(R1(−e0) · R3(psiA) · R1(omegaA) · R3(−chiA))
+    //Above eq rotates from "of date" to J2000, so we reverse the signs to go from J2000 to "of date"
+    astro_matrix_t m1 = astro_get_x_rotation_matrix(e0);
+    astro_matrix_t m2 = astro_get_z_rotation_matrix(-psiA);
+    astro_matrix_t m3 = astro_get_x_rotation_matrix(-omegaA);
+    astro_matrix_t m4 = astro_get_z_rotation_matrix(chiA);
+
+    astro_matrix_t m5 = astro_dot_product(m4, m3);
+    astro_matrix_t m6 = astro_dot_product(m5, m2);
+    astro_matrix_t precessionMatrix = astro_dot_product(m6, m1);
+
+    return precessionMatrix;
+}
+
+astro_cartesian_coordinates_t astro_matrix_multiply(astro_cartesian_coordinates_t v, astro_matrix_t m) {
+    astro_cartesian_coordinates_t t;
+
+    t.x = v.x*m.elements[0][0] + v.y*m.elements[0][1] + v.z*m.elements[0][2];
+    t.y = v.x*m.elements[1][0] + v.y*m.elements[1][1] + v.z*m.elements[1][2];
+    t.z = v.x*m.elements[2][0] + v.y*m.elements[2][1] + v.z*m.elements[2][2];
+
+    return t;
+}
+
+//Converts cartesian XYZ coordinates to polar (e.g. J2000 xyz to Right Accention and Declication)
+astro_equatorial_coordinates_t astro_convert_cartesian_to_polar(astro_cartesian_coordinates_t xyz) {
+    astro_equatorial_coordinates_t t;
+
+    t.distance = sqrt(xyz.x * xyz.x + xyz.y * xyz.y + xyz.z * xyz.z);
+    t.declination = acos(xyz.z / t.distance);
+    t.right_ascension = atan2(xyz.y, xyz.x);
+
+    if(t.declination < 0) t.declination += 2 * M_PI;
+
+    if(t.right_ascension < 0) t.right_ascension += 2 * M_PI;
+
+    return t;
+}
+
+//Convert Geodedic Lat Lon to geocentric XYZ position vector
+//All angles are input as radians
+astro_cartesian_coordinates_t astro_convert_geodedic_latlon_to_ITRF_XYZ(double lat, double lon, double height) {
+    //Algorithm from Explanatory Supplement to the Astronomical Almanac 3rd ed. P294
+    const double a = 6378136.6;
+    const double f = 1 / 298.25642;
+
+    const double C = sqrt(((cos(lat)*cos(lat)) + (1.0-f)*(1.0-f) * (sin(lat)*sin(lat))));
+
+    const double S = (1-f)*(1-f)*C;
+    
+    double h = height;
+
+    astro_cartesian_coordinates_t r;
+    r.x = (a*C+h) * cos(lat) * cos(lon);
+    r.y = (a*C+h) * cos(lat) * sin(lon);
+    r.z = (a*S+h) * sin(lat);
+    
+    return r;
+}
+
+//Convert position vector to celestial "of date" system.
+//g(t)=R3(-GAST) r
+//(Remember to use UT1 for GAST, not ET)
+//All angles are input and output as radians
+astro_cartesian_coordinates_t astro_convert_ITRF_to_GCRS(astro_cartesian_coordinates_t r, double ut1) {
+    //This is a simple rotation matrix implemenation about the Z axis, rotation angle is -GMST
+
+    double GMST = astro_get_GMST(ut1);
+    GMST =- GMST * 15.0 * M_PI / 180.0;
+
+    astro_matrix_t m = astro_get_z_rotation_matrix(GMST);
+    astro_cartesian_coordinates_t t = astro_matrix_multiply(r, m);
+
+    return t;
+}
+
+astro_cartesian_coordinates_t astro_convert_coordinates_from_meters_to_AU(astro_cartesian_coordinates_t c) {
+    astro_cartesian_coordinates_t t;
+    
+    t.x = c.x / 1.49597870691E+11;
+    t.y = c.y / 1.49597870691E+11;
+    t.z = c.z / 1.49597870691E+11;
+    
+    return t;
+}
+
+astro_cartesian_coordinates_t astro_get_observer_geocentric_coords(double jd, double lat, double lon) {
+    astro_cartesian_coordinates_t r = astro_convert_geodedic_latlon_to_ITRF_XYZ(lat, lon,0);
+    r = astro_convert_ITRF_to_GCRS(r, jd);
+    r = astro_convert_coordinates_from_meters_to_AU(r);
+    
+    return r;
+}
+
+//Returns a body's cartesian coordinates centered on the Sun.
+//Requires vsop87a_milli_js, if you wish to use a different version of VSOP87, replace the class name vsop87a_milli below
+astro_cartesian_coordinates_t astro_get_body_coordinates(astro_body_t body, double et) {
+    astro_cartesian_coordinates_t retval = {0};
+    double coords[3];
+    switch(body) {
+        case ASTRO_BODY_SUN: 
+            return retval; //Sun is at the center for vsop87a
+        case ASTRO_BODY_MERCURY:
+             vsop87a_milli_getMercury(et, coords);
+             break;
+        case ASTRO_BODY_VENUS:
+             vsop87a_milli_getVenus(et, coords);
+             break;
+        case ASTRO_BODY_EARTH:
+             vsop87a_milli_getEarth(et, coords);
+             break;
+        case ASTRO_BODY_MARS:
+             vsop87a_milli_getMars(et, coords);
+             break;
+        case ASTRO_BODY_JUPITER:
+             vsop87a_milli_getJupiter(et, coords);
+             break;
+        case ASTRO_BODY_SATURN:
+             vsop87a_milli_getSaturn(et, coords);
+             break;
+        case ASTRO_BODY_URANUS:
+             vsop87a_milli_getUranus(et, coords);
+             break;
+        case ASTRO_BODY_NEPTUNE:
+             vsop87a_milli_getNeptune(et, coords);
+             break;
+        case ASTRO_BODY_EMB:
+             vsop87a_milli_getEmb(et, coords);
+             break;
+        case ASTRO_BODY_MOON:
+            {
+                double earth_coords[3];
+                double emb_coords[3];
+                vsop87a_milli_getEarth(et, earth_coords);
+                vsop87a_milli_getEmb(et, emb_coords);
+                vsop87a_milli_getMoon(earth_coords, emb_coords, coords);
+            }
+             break;
+    }
+
+    retval.x = coords[0];
+    retval.y = coords[1];
+    retval.z = coords[2];
+
+    return retval;
+}
+
+astro_cartesian_coordinates_t astro_get_body_coordinates_light_time_adjusted(astro_body_t body, astro_cartesian_coordinates_t origin, double t) {
+    //Get current position of body
+    astro_cartesian_coordinates_t body_coords = astro_get_body_coordinates(body, t);
+
+    double newT = t;
+
+    for(uint8_t i = 0 ; i < 2 ; i++) {
+        //Calculate light time to body
+        body_coords = astro_subtract_cartesian(body_coords, origin);
+        double distance = sqrt(body_coords.x*body_coords.x + body_coords.y*body_coords.y + body_coords.z*body_coords.z);
+        distance *= 1.496e+11; //Convert from AU to meters
+        double lightTime = distance / 299792458.0;
+
+        //Convert light time to Julian Millenia, and subtract it from the original value of t
+        newT -= lightTime / 24.0 / 60.0 / 60.0 / 365250.0;  
+        //Recalculate body position adjusted for light time
+        body_coords = astro_get_body_coordinates(body, newT);
+    }
+
+    return body_coords;
+}
+
+astro_horizontal_coordinates_t astro_ra_dec_to_alt_az(double jd, double lat, double lon, double ra, double dec) {
+    double GMST = astro_get_GMST(jd) * M_PI/180.0 * 15.0;
+    double h = GMST + lon - ra;
+
+    double sina = sin(dec)*sin(lat) + cos(dec)*cos(h)*cos(lat);
+    double a = asin(sina);
+
+    double cosAz = (sin(dec)*cos(lat) - cos(dec)*cos(h)*sin(lat)) / cos(a);
+    double Az = acos(cosAz);
+
+    if(sin(h) > 0) Az = 2.0*M_PI - Az;
+
+    astro_horizontal_coordinates_t retval;
+    retval.altitude = a;
+    retval.azimuth = Az;
+
+    return retval;
+}
+
+double astro_degrees_to_radians(double degrees) {
+    return degrees * M_PI / 180;
+}
+
+double astro_radians_to_degrees(double radians) {
+    return radians * 180.0 / M_PI;
+}
+
+astro_angle_dms_t astro_radians_to_dms(double radians) {
+    astro_angle_dms_t retval;
+    int8_t sign = (radians < 0) ? -1 : 1;
+    double degrees = fabs(astro_radians_to_degrees(radians));
+
+    retval.degrees = (uint16_t)degrees;
+    double temp = 60.0 * (degrees - retval.degrees);
+    retval.minutes = (uint8_t)temp;
+    retval.seconds = (uint8_t)round(60.0 * (temp - retval.minutes));
+
+    if (retval.seconds > 59) {
+        retval.seconds = 0.0;
+        retval.minutes++;
+    }
+
+    if (retval.minutes > 59) {
+        retval.minutes = 0;
+        retval.degrees++;
+    }
+
+    degrees *= sign;
+
+    return retval;
+}
+
+astro_angle_hms_t astro_radians_to_hms(double radians) {
+    astro_angle_hms_t retval;
+    double degrees = astro_radians_to_degrees(radians);
+    double temp = degrees / 15.0;
+
+    retval.hours = (uint8_t)temp;
+    temp = 60.0 * (temp - retval.hours);
+    retval.minutes = (uint8_t)temp;
+    retval.seconds = (uint8_t)round(60.0 * (temp - retval.minutes));
+
+    if (retval.seconds > 59) {
+        retval.seconds = 0;
+        retval.minutes++;
+    }
+
+    if (retval.minutes > 59) {
+        retval.minutes = 0;
+        retval.hours++;
+    }
+
+    return retval;
+}
diff --git a/movement/lib/astrolib/astrolib.h b/movement/lib/astrolib/astrolib.h
new file mode 100644
index 00000000..2523ead3
--- /dev/null
+++ b/movement/lib/astrolib/astrolib.h
@@ -0,0 +1,87 @@
+/*
+ * Partial C port of Greg Miller's public domain astro library (gmiller@gregmiller.net) 2019
+ * https://github.com/gmiller123456/astrogreg
+ *
+ * Ported by Joey Castillo for Sensor Watch
+ * https://github.com/joeycastillo/Sensor-Watch/
+ *
+ * Public Domain
+ *
+ * THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#ifndef ASTROLIB_H_
+#define ASTROLIB_H_
+
+typedef enum {
+    ASTRO_BODY_SUN = 0,
+    ASTRO_BODY_MERCURY,
+    ASTRO_BODY_VENUS,
+    ASTRO_BODY_EARTH,
+    ASTRO_BODY_MARS,
+    ASTRO_BODY_JUPITER,
+    ASTRO_BODY_SATURN,
+    ASTRO_BODY_URANUS,
+    ASTRO_BODY_NEPTUNE,
+    ASTRO_BODY_EMB,
+    ASTRO_BODY_MOON
+} astro_body_t;
+
+typedef struct {
+    double elements[3][3];
+} astro_matrix_t;
+
+typedef struct {
+    double x;
+    double y;
+    double z;
+} astro_cartesian_coordinates_t;
+
+typedef struct {
+    double right_ascension;
+    double declination;
+    double distance;
+} astro_equatorial_coordinates_t;
+
+typedef struct {
+    double altitude;
+    double azimuth;
+} astro_horizontal_coordinates_t;
+
+typedef struct {
+    int16_t degrees;
+    uint8_t minutes;
+    uint8_t seconds; // you may want this to be a float, watch just can't display any more digits
+} astro_angle_dms_t;
+
+typedef struct {
+    uint8_t hours;
+    uint8_t minutes;
+    uint8_t seconds; // you may want this to be a float, watch just can't display any more digits
+} astro_angle_hms_t;
+
+// Convert a date to a julian date. Must be in UTC+0 time zone!
+double astro_convert_date_to_julian_date(uint16_t year, uint8_t month, uint8_t day, uint8_t hour, uint8_t minute, uint8_t second);
+
+// Converts a Julan Date to Julian Millenia since J2000, which is what VSOP87 expects as input.
+double astro_convert_jd_to_julian_millenia_since_j2000(double jd);
+
+// Get right ascension / declination for a given body in the list above.
+astro_equatorial_coordinates_t astro_get_ra_dec(double jd, astro_body_t bodyNum, double lat, double lon, bool calculate_precession);
+
+// Convert right ascension / declination to altitude/azimuth for a given location.
+astro_horizontal_coordinates_t astro_ra_dec_to_alt_az(double jd, double lat, double lon, double ra, double dec);
+
+// these are self-explanatory
+double astro_degrees_to_radians(double degrees);
+double astro_radians_to_degrees(double radians);
+astro_angle_dms_t astro_radians_to_dms(double radians);
+astro_angle_hms_t astro_radians_to_hms(double radians);
+
+#endif // ASTROLIB_H_
diff --git a/movement/lib/sunriset/sunriset.c b/movement/lib/sunriset/sunriset.c
index 9126c3bc..178f2ff5 100644
--- a/movement/lib/sunriset/sunriset.c
+++ b/movement/lib/sunriset/sunriset.c
@@ -17,6 +17,7 @@ Released to the public domain by Paul Schlyter, December 1992
 #include <math.h>
 #include "sunriset.h"
 
+static void sunpos( double d, double *lon, double *r );
 
 /* A macro to compute the number of days elapsed since 2000 Jan 0.0 */
 /* (which is equal to 1999 Dec 31, 0h UT)                           */
@@ -199,7 +200,7 @@ double __daylen__( int year, int month, int day, double lon, double lat,
 
 /* This function computes the Sun's position at any instant */
 
-void sunpos( double d, double *lon, double *r )
+static void sunpos( double d, double *lon, double *r )
 /******************************************************/
 /* Computes the Sun's ecliptic longitude and distance */
 /* at an instant given in d, number of days since     */
diff --git a/movement/lib/sunriset/sunriset.h b/movement/lib/sunriset/sunriset.h
index f8b97e32..7b2b6c83 100644
--- a/movement/lib/sunriset/sunriset.h
+++ b/movement/lib/sunriset/sunriset.h
@@ -24,8 +24,6 @@ double __daylen__( int year, int month, int day, double lon, double lat,
 int __sunriset__( int year, int month, int day, double lon, double lat,
                   double altit, int upper_limb, double *rise, double *set );
 
-void sunpos( double d, double *lon, double *r );
-
 void sun_RA_dec( double d, double *RA, double *dec, double *r );
 
 double revolution( double x );
diff --git a/movement/lib/vsop87/LICENSE.txt b/movement/lib/vsop87/LICENSE.txt
new file mode 100755
index 00000000..cc8be278
--- /dev/null
+++ b/movement/lib/vsop87/LICENSE.txt
@@ -0,0 +1,5 @@
+Author: Greg A Miller (gmiller@gregmiller.net)

+I release all of my work in this project to the public domain.

+

+Note, though, not everything here can be considered my work.  The VSOP87 theory is the work of

+Bureau des Longitudes.
\ No newline at end of file
diff --git a/movement/lib/vsop87/README.md b/movement/lib/vsop87/README.md
new file mode 100755
index 00000000..6ec7cbb3
--- /dev/null
+++ b/movement/lib/vsop87/README.md
@@ -0,0 +1,143 @@
+# Example

+

+An example in JavaScript showing computations is available at http://www.celestialprogramming.com/vsop87-multilang/

+

+### Current Stauts

+Versions for many different languages and environments have been created.  These have passed all test cases provided by the

+VSOP87 authors, a validation program is also included for each language.  They are ready for use. See the "Languages" directory for the status

+of each language.

+

+Still to come: more languages, documentation, and examples.

+

+# About this Project

+The purpose of this project is to create versions of VSOP87 in many different languages.  The plan is to generate a initial version in C# truncated to different

+precisions, then convert the resulting files into other languages.  This project was inspired by the [Neoprogrammics Source Code Generator Tool](http://www.neoprogrammics.com/vsop87/source_code_generator_tool/).

+The goal of this project is to provide easier to use (readymade source files), include all data (e.g. the Moon and velocities), are truncated to different accuracy levels,

+, for more languages, and have a more permissive license (public domain).  It will provide tests against the original VSOP87 test data for each programming language to validate correctness, as well as examples to show common useage.

+

+# Language Status

+

+Below is a list of the planned languages and their current status.

+

+

+Language     |Inline|JSON|CSV|CSV Low Mem|Validation Tests|Alt Az Reduction Example

+-------------|------|----|---|-----------|----------------|--------------

+Java         |Yes   |    |Yes|           |Pass            |

+C            |Yes   |    |   |Yes        |Pass            |

+C#           |Yes   |    |Yes|           |Pass            |

+Python       |Yes   |Yes |Yes|           |Pass            |

+C++          |Yes   |    |   |           |Pass            |

+VB.Net       |Yes   |    |   |           |Pass            |

+JavaScript   |Yes   |Yes |   |           |Pass            |Yes

+PHP          |Yes   |    |   |           |Pass            |

+Ruby         |Yes   |    |   |           |Pass            |

+Swift        |Yes   |    |   |           |Pass            |

+Matlab/Octave|Yes   |    |   |           |Pass            |

+Groovy       |      |    |Yes|           |Pass            |

+Go           |Yes   |    |   |           |Pass            |

+Pascal       |Yes   |    |   |           |0.000009au      |

+Perl         |Yes   |    |   |Yes        |Pass            |

+R            |Fail! |    |   |           |Fail!           |

+Cobol        |      |    |   |           |                |

+Fortran      |      |    |   |           |                |

+Rust         |Yes   |    |   |           |Pass            |

+Arduino      |Yes   |    |   |           |0.000009au      |

+

+# What is VSOP87? Why use it?

+VSOP87 is one of many solutions available for predicting the positions of the planets (plus the Sun and the Moon) in our solar system.  The actual name is

+Variations S�culaires des Orbites Plan�taires, and it was published in 1987 by the Bureau des Longitudes.  Even though there have been many other methods

+developed before and after VSOP87, it remains one of the most popular methods among amatuers.  It provides better accuracy than most amatuers require (.1 arcseconds)

+over a period of a few thousand years before and after the year 2000.

+

+# Implementation Types

+There are a few different types of implementations: Inline, JSON, CSV, and CSV Low Memory.  The inline versions are generally the easiest to use as they will have no

+external requirements, they are also the easiest to generate, so they're available for more languages.  The JSON versions require a JSON file (located in the 

+languages/JSON folder) which is loaded into memory.  The advantages of the JSON versions are you can compute the velocities with the same data the positions

+are generated from, and you can load and dispose of the memory used by the data when you need it.  The CSV implementations are similar to the JSON implementations, 

+but, obviously, read from a CSV file (located in the languages/CSV folder). And the Low Memory CSV implementations read the same CSV files, but the

+data is not retained in memory.  The JSON versions are located in the Languages/JSON directory, as well as the required JSON files, and the CSV implementations

+are in the languages/CSV folder.

+

+# Which Version Should I Use?

+For the overwhelming majority of users, the VSOP87A_full version will be all that you need.  This is the full version, but should still be fast enough and small enough

+for most use cases.  Using the full version eliminates any questions of whether it will be accurate enough.  If, after trying the full version, the computation isn't

+fast enough, from there you should experiment with truncated versions.  The VSOP87A versions are the only versions which include both the Earth and Moon.  VSOP87A doesn't include the moon directly, but does include the Earth and the Earth-Moon Barrycenter, and all provided code for the VSOP87A versions include a function to compute the Moon's position from the Earth and EMB.  Using the versions that provide the velocities is necessary if you want to account for relativistic effects do to the motion of the observer.

+

+There are several versions of the main theory.  The first is just called VSOP87, the remainder of them are appended with the letters A, B, C, D, E.  Each version

+provides the data in a slightly different form.

+

+Version|Mercury|Venus|Earth|EMB|Mars|Jupiter|Saturn|Uranus|Neptune|Sun|Coordinates

+-------|-------|-----|-----|---|----|-------|------|------|-------|---|-----------

+VSOP87|Yes|Yes|No|Yes|Yes|Yes|Yes|Yes|Yes|No|Keperian Orbital Elements

+VSOP87A|Yes|Yes|Yes|Yes|Yes|Yes|Yes|Yes|Yes|No|Heliocentric J2000 Ecliptic Rectangular XYZ

+VSOP87B|Yes|Yes|Yes|No|Yes|Yes|Yes|Yes|Yes|No|Heliocentric J2000 Ecliptic Spherical LBR

+VSOP87C|Yes|Yes|Yes|No|Yes|Yes|Yes|Yes|Yes|No|Heliocentric Ecliptic of date Rectangular XYZ

+VSOP87D|Yes|Yes|Yes|No|Yes|Yes|Yes|Yes|Yes|No|Heliocentric Ecliptic of date Spherical LBR

+VSOP87E|Yes|Yes|Yes|No|Yes|Yes|Yes|Yes|Yes|Yes|Barycentric J2000 Ecliptic Rectangular XYZ

+

+# Truncated versions

+Since the full VSOP87 provides more accuracy than most amateurs require, the algorithm can be shortened by eliminating terms.  This speeds up the computations, and

+reduces the overall size of the code at the cost of accuracy.  For each programming language, this project supplies VSOP87 truncated at ten different levels.  The

+effects of accuracy are detailed in the graphs below.  Each level of truncation eliminates any terms with a coefficient 1/10 the previous truncation level.

+

+Trunaction Level|Total Terms|Skipped Terms|Percent Skipped

+----------------|-----------|-------------|---------------

+full 	 |269949|0     |0 %

+xx large |269949|20998 |7.7 %

+x large  |269949|67848 |25.1 %

+large 	 |269949|145031|53.7 %

+small 	 |269949|218559|80.9 %

+x small  |269949|250204|92.6 %

+milli 	 |269949|262369|97.1 %

+micro 	 |269949|266975|98.8 %

+nano 	 |269949|268686|99.5 %

+pico 	 |269949|269464|99.8 %

+

+# Accuracy

+

+Accuracy graphs are below.  They show the error in degrees of each body as viewed from Earth.  Each graph shows the error for one body for all truncated versions of

+VSOP87.  The error is vs. the full version of VSOP87, so the inherent error in VSOP87 also has to be added.  Some bodies appear twice, to zoom in on the lower portion

+of the graph, as the error of the pico version makes it difficult to see errors amongst the larger versions.  The Python script and data to reproduce the graphs is

+in the Accuracy folder, by regenerating them you can use the Matplotlib interface to explore the graphs further.

+

+Since the error is computed from the geocenter, the Earth does not appear in the graphs below, nor does the Sun.  Graphs are also not present for the Moon, but graphs

+are available for the Earth-Moon Barrycenter (EMB), the error for the Moon will be a linear function of the EMB error.

+

+The full VSOP87 accuracy is .1 arcseconds for Saturn, and better for all others.  For more details on accuracy of the full theory consult

+[Planetary theories in rectangular and spherical variables - VSOP 87 solutions](http://articles.adsabs.harvard.edu/full/1988A%26A...202..309B).

+

+### Mercury

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/mercury.png)

+

+### Venus

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/venus.png)

+

+### Earth-Moon Barrycenter

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/emb.png)

+

+### Earth-Moon Barrycenter (zoomed)

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/emb2.png)

+

+### Mars

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/mars.png)

+

+### Jupiter

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/jupiter.png)

+

+### Saturn

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/saturn.png)

+

+### Saturn (zoomed)

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/saturn2.png)

+

+### Uranus

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/uranus.png)

+

+### Uranus (zoomed)

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/uranus2.png)

+

+### Neptune

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/neptune.png)

+

+### Neptune (zoomed)

+![Mercury](https://raw.githubusercontent.com/gmiller123456/vsop87-multilang/master/utility/Accuracy/neptune2.png)

diff --git a/movement/lib/vsop87/vsop87a_micro.c b/movement/lib/vsop87/vsop87a_micro.c
new file mode 100755
index 00000000..7e69feac
--- /dev/null
+++ b/movement/lib/vsop87/vsop87a_micro.c
@@ -0,0 +1,1019 @@
+//VSOP87-Multilang http://www.astrogreg.com/vsop87-multilang/index.html

+//Greg Miller (gmiller@gregmiller.net) 2019.  Released as Public Domain

+

+#include <math.h>

+#include "vsop87a_micro.h"

+double vsop87a_micro_earth_x(double t);

+double vsop87a_micro_earth_y(double t);

+double vsop87a_micro_earth_z(double t);

+double vsop87a_micro_emb_x(double t);

+double vsop87a_micro_emb_y(double t);

+double vsop87a_micro_emb_z(double t);

+double vsop87a_micro_jupiter_x(double t);

+double vsop87a_micro_jupiter_y(double t);

+double vsop87a_micro_jupiter_z(double t);

+double vsop87a_micro_mars_x(double t);

+double vsop87a_micro_mars_y(double t);

+double vsop87a_micro_mars_z(double t);

+double vsop87a_micro_mercury_x(double t);

+double vsop87a_micro_mercury_y(double t);

+double vsop87a_micro_mercury_z(double t);

+double vsop87a_micro_neptune_x(double t);

+double vsop87a_micro_neptune_y(double t);

+double vsop87a_micro_neptune_z(double t);

+double vsop87a_micro_saturn_x(double t);

+double vsop87a_micro_saturn_y(double t);

+double vsop87a_micro_saturn_z(double t);

+double vsop87a_micro_uranus_x(double t);

+double vsop87a_micro_uranus_y(double t);

+double vsop87a_micro_uranus_z(double t);

+double vsop87a_micro_venus_x(double t);

+double vsop87a_micro_venus_y(double t);

+double vsop87a_micro_venus_z(double t);

+

+

+void vsop87a_micro_getEarth(double t,double temp[]){

+   temp[0]=vsop87a_micro_earth_x(t);

+   temp[1]=vsop87a_micro_earth_y(t);

+   temp[2]=vsop87a_micro_earth_z(t);

+}

+

+void vsop87a_micro_getEmb(double t,double temp[]){

+   temp[0]=vsop87a_micro_emb_x(t);

+   temp[1]=vsop87a_micro_emb_y(t);

+   temp[2]=vsop87a_micro_emb_z(t);

+}

+

+void vsop87a_micro_getJupiter(double t,double temp[]){

+   temp[0]=vsop87a_micro_jupiter_x(t);

+   temp[1]=vsop87a_micro_jupiter_y(t);

+   temp[2]=vsop87a_micro_jupiter_z(t);

+}

+

+void vsop87a_micro_getMars(double t,double temp[]){

+   temp[0]=vsop87a_micro_mars_x(t);

+   temp[1]=vsop87a_micro_mars_y(t);

+   temp[2]=vsop87a_micro_mars_z(t);

+}

+

+void vsop87a_micro_getMercury(double t,double temp[]){

+   temp[0]=vsop87a_micro_mercury_x(t);

+   temp[1]=vsop87a_micro_mercury_y(t);

+   temp[2]=vsop87a_micro_mercury_z(t);

+}

+

+void vsop87a_micro_getNeptune(double t,double temp[]){

+   temp[0]=vsop87a_micro_neptune_x(t);

+   temp[1]=vsop87a_micro_neptune_y(t);

+   temp[2]=vsop87a_micro_neptune_z(t);

+}

+

+void vsop87a_micro_getSaturn(double t,double temp[]){

+   temp[0]=vsop87a_micro_saturn_x(t);

+   temp[1]=vsop87a_micro_saturn_y(t);

+   temp[2]=vsop87a_micro_saturn_z(t);

+}

+

+void vsop87a_micro_getUranus(double t,double temp[]){

+   temp[0]=vsop87a_micro_uranus_x(t);

+   temp[1]=vsop87a_micro_uranus_y(t);

+   temp[2]=vsop87a_micro_uranus_z(t);

+}

+

+void vsop87a_micro_getVenus(double t,double temp[]){

+   temp[0]=vsop87a_micro_venus_x(t);

+   temp[1]=vsop87a_micro_venus_y(t);

+   temp[2]=vsop87a_micro_venus_z(t);

+}

+

+void vsop87a_micro_getMoon(double earth[], double emb[],double temp[]){

+   temp[0]=(emb[0]-earth[0])*(1 + 1 / 0.01230073677);

+   temp[1]=(emb[1]-earth[1])*(1 + 1 / 0.01230073677);

+   temp[2]=(emb[2]-earth[2])*(1 + 1 / 0.01230073677);

+   temp[0]=temp[0]+earth[0];

+   temp[1]=temp[1]+earth[1];

+   temp[2]=temp[2]+earth[2];

+}

+

+double vsop87a_micro_earth_x(double t){

+   double earth_x_0=0.0;

+   earth_x_0+=     0.99982928844 * cos( 1.75348568475 +     6283.07584999140*t);

+   earth_x_0+=     0.00835257300 * cos( 1.71034539450 +    12566.15169998280*t);

+   earth_x_0+=     0.00561144206 * cos( 0.00000000000 +        0.00000000000*t);

+   earth_x_0+=     0.00010466628 * cos( 1.66722645223 +    18849.22754997420*t);

+

+   double earth_x_1=0.0;

+   earth_x_1+=     0.00123403056 * cos( 0.00000000000 +        0.00000000000*t);

+   earth_x_1+=     0.00051500156 * cos( 6.00266267204 +    12566.15169998280*t);

+   earth_x_1=earth_x_1 * t;

+

+   return earth_x_0+earth_x_1;

+}

+

+double vsop87a_micro_earth_y(double t){

+   double earth_y_0=0.0;

+   earth_y_0+=     0.99989211030 * cos( 0.18265890456 +     6283.07584999140*t);

+   earth_y_0+=     0.02442699036 * cos( 3.14159265359 +        0.00000000000*t);

+   earth_y_0+=     0.00835292314 * cos( 0.13952878991 +    12566.15169998280*t);

+   earth_y_0+=     0.00010466965 * cos( 0.09641690558 +    18849.22754997420*t);

+

+   double earth_y_1=0.0;

+   earth_y_1+=     0.00093046324 * cos( 0.00000000000 +        0.00000000000*t);

+   earth_y_1+=     0.00051506609 * cos( 4.43180499286 +    12566.15169998280*t);

+   earth_y_1=earth_y_1 * t;

+

+   return earth_y_0+earth_y_1;

+}

+

+double vsop87a_micro_earth_z(double t){

+   double earth_z_1=0.0;

+   earth_z_1+=     0.00227822442 * cos( 3.41372504278 +     6283.07584999140*t);

+   earth_z_1=earth_z_1 * t;

+

+   return earth_z_1;

+}

+

+double vsop87a_micro_emb_x(double t){

+   double emb_x_0=0.0;

+   emb_x_0+=     0.99982927460 * cos( 1.75348568475 +     6283.07584999140*t);

+   emb_x_0+=     0.00835257300 * cos( 1.71034539450 +    12566.15169998280*t);

+   emb_x_0+=     0.00561144161 * cos( 0.00000000000 +        0.00000000000*t);

+   emb_x_0+=     0.00010466628 * cos( 1.66722645223 +    18849.22754997420*t);

+

+   double emb_x_1=0.0;

+   emb_x_1+=     0.00123403046 * cos( 0.00000000000 +        0.00000000000*t);

+   emb_x_1+=     0.00051500156 * cos( 6.00266267204 +    12566.15169998280*t);

+   emb_x_1=emb_x_1 * t;

+

+   return emb_x_0+emb_x_1;

+}

+

+double vsop87a_micro_emb_y(double t){

+   double emb_y_0=0.0;

+   emb_y_0+=     0.99989209645 * cos( 0.18265890456 +     6283.07584999140*t);

+   emb_y_0+=     0.02442698841 * cos( 3.14159265359 +        0.00000000000*t);

+   emb_y_0+=     0.00835292314 * cos( 0.13952878991 +    12566.15169998280*t);

+   emb_y_0+=     0.00010466965 * cos( 0.09641690558 +    18849.22754997420*t);

+

+   double emb_y_1=0.0;

+   emb_y_1+=     0.00093046317 * cos( 0.00000000000 +        0.00000000000*t);

+   emb_y_1+=     0.00051506609 * cos( 4.43180499286 +    12566.15169998280*t);

+   emb_y_1=emb_y_1 * t;

+

+   return emb_y_0+emb_y_1;

+}

+

+double vsop87a_micro_emb_z(double t){

+   double emb_z_1=0.0;

+   emb_z_1+=     0.00227822442 * cos( 3.41372504278 +     6283.07584999140*t);

+   emb_z_1=emb_z_1 * t;

+

+   return emb_z_1;

+}

+

+double vsop87a_micro_jupiter_x(double t){

+   double jupiter_x_0=0.0;

+   jupiter_x_0+=     5.19663470114 * cos( 0.59945082355 +      529.69096509460*t);

+   jupiter_x_0+=     0.36662642320 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_x_0+=     0.12593937922 * cos( 0.94911583701 +     1059.38193018920*t);

+   jupiter_x_0+=     0.01500672056 * cos( 0.73175134610 +      522.57741809380*t);

+   jupiter_x_0+=     0.01476224578 * cos( 3.61736921122 +      536.80451209540*t);

+   jupiter_x_0+=     0.00457752736 * cos( 1.29883700755 +     1589.07289528380*t);

+   jupiter_x_0+=     0.00301689798 * cos( 5.17372551148 +        7.11354700080*t);

+   jupiter_x_0+=     0.00385975375 * cos( 2.01229910687 +      103.09277421860*t);

+   jupiter_x_0+=     0.00194025405 * cos( 5.02580363996 +      426.59819087600*t);

+   jupiter_x_0+=     0.00150678793 * cos( 6.12003027739 +      110.20632121940*t);

+   jupiter_x_0+=     0.00144867641 * cos( 5.55980577080 +      632.78373931320*t);

+   jupiter_x_0+=     0.00134226996 * cos( 0.87648567011 +      213.29909543800*t);

+   jupiter_x_0+=     0.00103494641 * cos( 6.19324769120 +     1052.26838318840*t);

+   jupiter_x_0+=     0.00114201562 * cos( 0.01567084269 +     1162.47470440780*t);

+   jupiter_x_0+=     0.00072095575 * cos( 3.96117430643 +     1066.49547719000*t);

+   jupiter_x_0+=     0.00059486083 * cos( 4.45769374358 +      949.17560896980*t);

+   jupiter_x_0+=     0.00068284021 * cos( 3.44051122631 +      846.08283475120*t);

+   jupiter_x_0+=     0.00047092251 * cos( 1.44612636451 +      419.48464387520*t);

+   jupiter_x_0+=     0.00030623417 * cos( 2.99132321427 +      206.18554843720*t);

+   jupiter_x_0+=     0.00026613459 * cos( 4.85169906494 +      323.50541665740*t);

+   jupiter_x_0+=     0.00019727457 * cos( 1.64891626213 +     2118.76386037840*t);

+   jupiter_x_0+=     0.00016481594 * cos( 1.95150056568 +      316.39186965660*t);

+   jupiter_x_0+=     0.00016101974 * cos( 0.87973155980 +      515.46387109300*t);

+   jupiter_x_0+=     0.00014209487 * cos( 2.07769621413 +      742.99006053260*t);

+   jupiter_x_0+=     0.00015192516 * cos( 6.25820127906 +      735.87651353180*t);

+   jupiter_x_0+=     0.00011423199 * cos( 3.48146108929 +      543.91805909620*t);

+   jupiter_x_0+=     0.00012155285 * cos( 3.75229924999 +      525.75881183150*t);

+   jupiter_x_0+=     0.00011996271 * cos( 0.58568573729 +      533.62311835770*t);

+

+   double jupiter_x_1=0.0;

+   jupiter_x_1+=     0.00882389251 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_x_1+=     0.00635297172 * cos( 0.10662156868 +     1059.38193018920*t);

+   jupiter_x_1+=     0.00599720482 * cos( 2.42996678275 +      522.57741809380*t);

+   jupiter_x_1+=     0.00589157060 * cos( 1.91556314637 +      536.80451209540*t);

+   jupiter_x_1+=     0.00081697204 * cos( 3.46668108797 +        7.11354700080*t);

+   jupiter_x_1+=     0.00046201898 * cos( 0.45714214032 +     1589.07289528380*t);

+   jupiter_x_1+=     0.00032508590 * cos( 1.74648849928 +     1052.26838318840*t);

+   jupiter_x_1+=     0.00033891193 * cos( 4.10113482752 +      529.69096509460*t);

+   jupiter_x_1+=     0.00031234303 * cos( 2.34698051502 +     1066.49547719000*t);

+   jupiter_x_1+=     0.00021244363 * cos( 4.36576178953 +      110.20632121940*t);

+   jupiter_x_1+=     0.00018156701 * cos( 4.00572238779 +      426.59819087600*t);

+   jupiter_x_1+=     0.00013577576 * cos( 0.30008010246 +      632.78373931320*t);

+   jupiter_x_1+=     0.00012889505 * cos( 2.57489294062 +      515.46387109300*t);

+   jupiter_x_1=jupiter_x_1 * t;

+

+   double jupiter_x_2=0.0;

+   jupiter_x_2+=     0.00123864644 * cos( 4.13563277513 +      522.57741809380*t);

+   jupiter_x_2+=     0.00121521296 * cos( 0.21155109275 +      536.80451209540*t);

+   jupiter_x_2+=     0.00085355503 * cos( 0.00000000000 +        0.00000000000*t);

+   jupiter_x_2+=     0.00077685547 * cos( 5.29776154458 +      529.69096509460*t);

+   jupiter_x_2+=     0.00041410887 * cos( 5.12291589939 +     1059.38193018920*t);

+   jupiter_x_2+=     0.00011423070 * cos( 1.72917878238 +        7.11354700080*t);

+   jupiter_x_2=jupiter_x_2 * t * t;

+

+   double jupiter_x_3=0.0;

+   jupiter_x_3+=     0.00017071323 * cos( 5.86133022278 +      522.57741809380*t);

+   jupiter_x_3+=     0.00016713548 * cos( 4.77458794485 +      536.80451209540*t);

+   jupiter_x_3=jupiter_x_3 * t * t * t;

+

+   return jupiter_x_0+jupiter_x_1+jupiter_x_2+jupiter_x_3;

+}

+

+double vsop87a_micro_jupiter_y(double t){

+   double jupiter_y_0=0.0;

+   jupiter_y_0+=     5.19520046589 * cos( 5.31203162731 +      529.69096509460*t);

+   jupiter_y_0+=     0.12592862602 * cos( 5.66160227728 +     1059.38193018920*t);

+   jupiter_y_0+=     0.09363670616 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_y_0+=     0.01508275299 * cos( 5.43934968102 +      522.57741809380*t);

+   jupiter_y_0+=     0.01475809370 * cos( 2.04679566495 +      536.80451209540*t);

+   jupiter_y_0+=     0.00457750806 * cos( 6.01129093501 +     1589.07289528380*t);

+   jupiter_y_0+=     0.00300686679 * cos( 3.60948050740 +        7.11354700080*t);

+   jupiter_y_0+=     0.00378285578 * cos( 3.53006782383 +      103.09277421860*t);

+   jupiter_y_0+=     0.00192333128 * cos( 3.45690564771 +      426.59819087600*t);

+   jupiter_y_0+=     0.00146104656 * cos( 4.62267224431 +      110.20632121940*t);

+   jupiter_y_0+=     0.00139480058 * cos( 4.00075307706 +      632.78373931320*t);

+   jupiter_y_0+=     0.00132696764 * cos( 5.62184581859 +      213.29909543800*t);

+   jupiter_y_0+=     0.00101999807 * cos( 4.57594598884 +     1052.26838318840*t);

+   jupiter_y_0+=     0.00114043110 * cos( 4.72982262969 +     1162.47470440780*t);

+   jupiter_y_0+=     0.00072091178 * cos( 2.39048659148 +     1066.49547719000*t);

+   jupiter_y_0+=     0.00059051769 * cos( 2.89529070968 +      949.17560896980*t);

+   jupiter_y_0+=     0.00068374489 * cos( 1.86537074374 +      846.08283475120*t);

+   jupiter_y_0+=     0.00029807369 * cos( 4.52105772740 +      206.18554843720*t);

+   jupiter_y_0+=     0.00026933579 * cos( 3.86233956827 +      419.48464387520*t);

+   jupiter_y_0+=     0.00026619714 * cos( 3.28203174951 +      323.50541665740*t);

+   jupiter_y_0+=     0.00020873780 * cos( 3.79369881757 +      735.87651353180*t);

+   jupiter_y_0+=     0.00019727397 * cos( 0.07818534532 +     2118.76386037840*t);

+   jupiter_y_0+=     0.00018639846 * cos( 0.38751972138 +      316.39186965660*t);

+   jupiter_y_0+=     0.00016355726 * cos( 5.56997881604 +      515.46387109300*t);

+   jupiter_y_0+=     0.00014606858 * cos( 0.47759399145 +      742.99006053260*t);

+   jupiter_y_0+=     0.00011419853 * cos( 1.91089341468 +      543.91805909620*t);

+   jupiter_y_0+=     0.00012153427 * cos( 2.18151972499 +      525.75881183150*t);

+   jupiter_y_0+=     0.00011988875 * cos( 5.29687602089 +      533.62311835770*t);

+

+   double jupiter_y_1=0.0;

+   jupiter_y_1+=     0.01694798253 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_y_1+=     0.00634859798 * cos( 4.81903199650 +     1059.38193018920*t);

+   jupiter_y_1+=     0.00601160431 * cos( 0.85811249940 +      522.57741809380*t);

+   jupiter_y_1+=     0.00588928504 * cos( 0.34491576890 +      536.80451209540*t);

+   jupiter_y_1+=     0.00081187145 * cos( 1.90914316532 +        7.11354700080*t);

+   jupiter_y_1+=     0.00046888090 * cos( 1.91294535618 +      529.69096509460*t);

+   jupiter_y_1+=     0.00046194129 * cos( 5.16955994561 +     1589.07289528380*t);

+   jupiter_y_1+=     0.00032503453 * cos( 0.17640743623 +     1052.26838318840*t);

+   jupiter_y_1+=     0.00031231694 * cos( 0.77623645597 +     1066.49547719000*t);

+   jupiter_y_1+=     0.00019462096 * cos( 3.00957119470 +      110.20632121940*t);

+   jupiter_y_1+=     0.00017738615 * cos( 2.46531787101 +      426.59819087600*t);

+   jupiter_y_1+=     0.00013701692 * cos( 5.02070197804 +      632.78373931320*t);

+   jupiter_y_1+=     0.00013034616 * cos( 0.98979834442 +      515.46387109300*t);

+   jupiter_y_1=jupiter_y_1 * t;

+

+   double jupiter_y_2=0.0;

+   jupiter_y_2+=     0.00124032509 * cos( 2.56495576833 +      522.57741809380*t);

+   jupiter_y_2+=     0.00121455991 * cos( 4.92398766380 +      536.80451209540*t);

+   jupiter_y_2+=     0.00076523263 * cos( 3.75913371793 +      529.69096509460*t);

+   jupiter_y_2+=     0.00076943042 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_y_2+=     0.00041357600 * cos( 3.55228440457 +     1059.38193018920*t);

+   jupiter_y_2+=     0.00011277667 * cos( 0.18559902389 +        7.11354700080*t);

+   jupiter_y_2=jupiter_y_2 * t * t;

+

+   double jupiter_y_3=0.0;

+   jupiter_y_3+=     0.00017085516 * cos( 4.29096904063 +      522.57741809380*t);

+   jupiter_y_3+=     0.00016701353 * cos( 3.20365737109 +      536.80451209540*t);

+   jupiter_y_3=jupiter_y_3 * t * t * t;

+

+   return jupiter_y_0+jupiter_y_1+jupiter_y_2+jupiter_y_3;

+}

+

+double vsop87a_micro_jupiter_z(double t){

+   double jupiter_z_0=0.0;

+   jupiter_z_0+=     0.11823100489 * cos( 3.55844646343 +      529.69096509460*t);

+   jupiter_z_0+=     0.00859031952 * cos( 0.00000000000 +        0.00000000000*t);

+   jupiter_z_0+=     0.00286562094 * cos( 3.90812238338 +     1059.38193018920*t);

+   jupiter_z_0+=     0.00042388592 * cos( 3.60144191032 +      522.57741809380*t);

+   jupiter_z_0+=     0.00033295491 * cos( 0.30297050585 +      536.80451209540*t);

+   jupiter_z_0+=     0.00010416160 * cos( 4.25764593061 +     1589.07289528380*t);

+

+   double jupiter_z_1=0.0;

+   jupiter_z_1+=     0.00407072175 * cos( 1.52699353482 +      529.69096509460*t);

+   jupiter_z_1+=     0.00020307341 * cos( 2.59878269248 +     1059.38193018920*t);

+   jupiter_z_1+=     0.00014424953 * cos( 4.85400155025 +      536.80451209540*t);

+   jupiter_z_1+=     0.00015474611 * cos( 0.00000000000 +        0.00000000000*t);

+   jupiter_z_1+=     0.00012730364 * cos( 5.45536715732 +      522.57741809380*t);

+   jupiter_z_1=jupiter_z_1 * t;

+

+   double jupiter_z_2=0.0;

+   jupiter_z_2+=     0.00028635326 * cos( 3.01374166973 +      529.69096509460*t);

+   jupiter_z_2=jupiter_z_2 * t * t;

+

+   return jupiter_z_0+jupiter_z_1+jupiter_z_2;

+}

+

+double vsop87a_micro_mars_x(double t){

+   double mars_x_0=0.0;

+   mars_x_0+=     1.51769936383 * cos( 6.20403346548 +     3340.61242669980*t);

+   mars_x_0+=     0.19502945246 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_x_0+=     0.07070919655 * cos( 0.25870338558 +     6681.22485339960*t);

+   mars_x_0+=     0.00494196914 * cos( 0.59669127768 +    10021.83728009940*t);

+   mars_x_0+=     0.00040938237 * cos( 0.93473307419 +    13362.44970679920*t);

+   mars_x_0+=     0.00021067199 * cos( 1.80435656154 +     3337.08930835080*t);

+   mars_x_0+=     0.00021041626 * cos( 1.17895619474 +     3344.13554504880*t);

+   mars_x_0+=     0.00011370375 * cos( 4.83265211109 +     1059.38193018920*t);

+   mars_x_0+=     0.00013527976 * cos( 0.63010765169 +      529.69096509460*t);

+

+   double mars_x_1=0.0;

+   mars_x_1+=     0.00861441374 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_x_1+=     0.00552437949 * cos( 5.09565872891 +     6681.22485339960*t);

+   mars_x_1+=     0.00077184977 * cos( 5.43315636209 +    10021.83728009940*t);

+   mars_x_1+=     0.00020467294 * cos( 5.57051812369 +     3340.61242669980*t);

+   mars_x_1=mars_x_1 * t;

+

+   double mars_x_2=0.0;

+   mars_x_2+=     0.00056323939 * cos( 0.00000000000 +        0.00000000000*t);

+   mars_x_2+=     0.00022122528 * cos( 3.54372113272 +     6681.22485339960*t);

+   mars_x_2=mars_x_2 * t * t;

+

+   return mars_x_0+mars_x_1+mars_x_2;

+}

+

+double vsop87a_micro_mars_y(double t){

+   double mars_y_0=0.0;

+   mars_y_0+=     1.51558976277 * cos( 4.63212206588 +     3340.61242669980*t);

+   mars_y_0+=     0.07064550239 * cos( 4.97051892902 +     6681.22485339960*t);

+   mars_y_0+=     0.08655481102 * cos( 0.00000000000 +        0.00000000000*t);

+   mars_y_0+=     0.00493872848 * cos( 5.30877806694 +    10021.83728009940*t);

+   mars_y_0+=     0.00040917422 * cos( 5.64698263703 +    13362.44970679920*t);

+   mars_y_0+=     0.00021036784 * cos( 0.23240270955 +     3337.08930835080*t);

+   mars_y_0+=     0.00021012921 * cos( 5.89022773653 +     3344.13554504880*t);

+   mars_y_0+=     0.00011370034 * cos( 3.26131408801 +     1059.38193018920*t);

+   mars_y_0+=     0.00013324177 * cos( 5.34259389724 +      529.69096509460*t);

+

+   double mars_y_1=0.0;

+   mars_y_1+=     0.01427324210 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_y_1+=     0.00551063753 * cos( 3.52128320402 +     6681.22485339960*t);

+   mars_y_1+=     0.00077091913 * cos( 3.86082685753 +    10021.83728009940*t);

+   mars_y_1+=     0.00037310491 * cos( 1.16016958445 +     3340.61242669980*t);

+   mars_y_1=mars_y_1 * t;

+

+   double mars_y_2=0.0;

+   mars_y_2+=     0.00035396765 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_y_2+=     0.00021950759 * cos( 1.96291594946 +     6681.22485339960*t);

+   mars_y_2=mars_y_2 * t * t;

+

+   return mars_y_0+mars_y_1+mars_y_2;

+}

+

+double vsop87a_micro_mars_z(double t){

+   double mars_z_0=0.0;

+   mars_z_0+=     0.04901207220 * cos( 3.76712324286 +     3340.61242669980*t);

+   mars_z_0+=     0.00660669541 * cos( 0.00000000000 +        0.00000000000*t);

+   mars_z_0+=     0.00228333904 * cos( 4.10544022266 +     6681.22485339960*t);

+   mars_z_0+=     0.00015958402 * cos( 4.44367058261 +    10021.83728009940*t);

+

+   double mars_z_1=0.0;

+   mars_z_1+=     0.00331842958 * cos( 6.05027773492 +     3340.61242669980*t);

+   mars_z_1+=     0.00047930411 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_z_1=mars_z_1 * t;

+

+   double mars_z_2=0.0;

+   mars_z_2+=     0.00013705360 * cos( 1.04212852598 +     3340.61242669980*t);

+   mars_z_2=mars_z_2 * t * t;

+

+   return mars_z_0+mars_z_1+mars_z_2;

+}

+

+double vsop87a_micro_mercury_x(double t){

+   double mercury_x_0=0.0;

+   mercury_x_0+=     0.37546291728 * cos( 4.39651506942 +    26087.90314157420*t);

+   mercury_x_0+=     0.03825746672 * cos( 1.16485604339 +    52175.80628314840*t);

+   mercury_x_0+=     0.02625615963 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_x_0+=     0.00584261333 * cos( 4.21599394757 +    78263.70942472259*t);

+   mercury_x_0+=     0.00105716695 * cos( 0.98379033182 +   104351.61256629678*t);

+   mercury_x_0+=     0.00021011730 * cos( 4.03469353923 +   130439.51570787099*t);

+

+   double mercury_x_1=0.0;

+   mercury_x_1+=     0.00318848034 * cos( 0.00000000000 +        0.00000000000*t);

+   mercury_x_1+=     0.00105289019 * cos( 5.91600475006 +    52175.80628314840*t);

+   mercury_x_1+=     0.00032316001 * cos( 2.68247273347 +    78263.70942472259*t);

+   mercury_x_1+=     0.00011992889 * cos( 5.81575112963 +    26087.90314157420*t);

+   mercury_x_1=mercury_x_1 * t;

+

+   return mercury_x_0+mercury_x_1;

+}

+

+double vsop87a_micro_mercury_y(double t){

+   double mercury_y_0=0.0;

+   mercury_y_0+=     0.37953642888 * cos( 2.83780617820 +    26087.90314157420*t);

+   mercury_y_0+=     0.11626131831 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_y_0+=     0.03854668215 * cos( 5.88780608966 +    52175.80628314840*t);

+   mercury_y_0+=     0.00587711268 * cos( 2.65498896201 +    78263.70942472259*t);

+   mercury_y_0+=     0.00106235493 * cos( 5.70550616735 +   104351.61256629678*t);

+   mercury_y_0+=     0.00021100828 * cos( 2.47291315849 +   130439.51570787099*t);

+

+   double mercury_y_1=0.0;

+   mercury_y_1+=     0.00107803852 * cos( 4.34964793883 +    52175.80628314840*t);

+   mercury_y_1+=     0.00080651544 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_y_1+=     0.00032715354 * cos( 1.11763734425 +    78263.70942472259*t);

+   mercury_y_1+=     0.00011914709 * cos( 1.22139986340 +    26087.90314157420*t);

+   mercury_y_1=mercury_y_1 * t;

+

+   return mercury_y_0+mercury_y_1;

+}

+

+double vsop87a_micro_mercury_z(double t){

+   double mercury_z_0=0.0;

+   mercury_z_0+=     0.04607665326 * cos( 1.99295081967 +    26087.90314157420*t);

+   mercury_z_0+=     0.00708734365 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_z_0+=     0.00469171617 * cos( 5.04215742764 +    52175.80628314840*t);

+   mercury_z_0+=     0.00071626395 * cos( 1.80894256071 +    78263.70942472259*t);

+   mercury_z_0+=     0.00012957446 * cos( 4.85922032010 +   104351.61256629678*t);

+

+   double mercury_z_1=0.0;

+   mercury_z_1+=     0.00108722177 * cos( 3.91134750825 +    26087.90314157420*t);

+   mercury_z_1+=     0.00057826621 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_z_1=mercury_z_1 * t;

+

+   return mercury_z_0+mercury_z_1;

+}

+

+double vsop87a_micro_neptune_x(double t){

+   double neptune_x_0=0.0;

+   neptune_x_0+=    30.05890004476 * cos( 5.31211340029 +       38.13303563780*t);

+   neptune_x_0+=     0.27080164222 * cos( 3.14159265359 +        0.00000000000*t);

+   neptune_x_0+=     0.13505661755 * cos( 3.50078975634 +       76.26607127560*t);

+   neptune_x_0+=     0.15726094556 * cos( 0.11319072675 +       36.64856292950*t);

+   neptune_x_0+=     0.14935120126 * cos( 1.08499403018 +       39.61750834610*t);

+   neptune_x_0+=     0.02597313814 * cos( 1.99590301412 +        1.48447270830*t);

+   neptune_x_0+=     0.01074040708 * cos( 5.38502938672 +       74.78159856730*t);

+   neptune_x_0+=     0.00823793287 * cos( 1.43221581862 +       35.16409022120*t);

+   neptune_x_0+=     0.00817588813 * cos( 0.78180174031 +        2.96894541660*t);

+   neptune_x_0+=     0.00565534918 * cos( 5.98964907613 +       41.10198105440*t);

+   neptune_x_0+=     0.00495719107 * cos( 0.59948143567 +      529.69096509460*t);

+   neptune_x_0+=     0.00307525907 * cos( 0.40023311011 +       73.29712585900*t);

+   neptune_x_0+=     0.00272253551 * cos( 0.87443494387 +      213.29909543800*t);

+   neptune_x_0+=     0.00135887219 * cos( 5.54676577816 +       77.75054398390*t);

+   neptune_x_0+=     0.00090965704 * cos( 1.68910246115 +      114.39910691340*t);

+   neptune_x_0+=     0.00069040539 * cos( 5.83469123520 +        4.45341812490*t);

+   neptune_x_0+=     0.00060813556 * cos( 2.62589958380 +       33.67961751290*t);

+   neptune_x_0+=     0.00054690827 * cos( 1.55799996661 +       71.81265315070*t);

+   neptune_x_0+=     0.00028889260 * cos( 4.78966826027 +       42.58645376270*t);

+   neptune_x_0+=     0.00012614732 * cos( 3.57002516434 +      112.91463420510*t);

+   neptune_x_0+=     0.00012749153 * cos( 2.73719269645 +      111.43016149680*t);

+   neptune_x_0+=     0.00012013994 * cos( 0.94912933496 +     1059.38193018920*t);

+

+   double neptune_x_1=0.0;

+   neptune_x_1+=     0.00255840261 * cos( 2.01935686795 +       36.64856292950*t);

+   neptune_x_1+=     0.00243125299 * cos( 5.46214902873 +       39.61750834610*t);

+   neptune_x_1+=     0.00118398168 * cos( 2.88251845061 +       76.26607127560*t);

+   neptune_x_1+=     0.00037965449 * cos( 3.14159265359 +        0.00000000000*t);

+   neptune_x_1+=     0.00021924705 * cos( 3.20156164152 +       35.16409022120*t);

+   neptune_x_1+=     0.00017459808 * cos( 4.26349398817 +       41.10198105440*t);

+   neptune_x_1+=     0.00013130617 * cos( 5.36424961848 +        2.96894541660*t);

+   neptune_x_1=neptune_x_1 * t;

+

+   return neptune_x_0+neptune_x_1;

+}

+

+double vsop87a_micro_neptune_y(double t){

+   double neptune_y_0=0.0;

+   neptune_y_0+=    30.06056351665 * cos( 3.74086294714 +       38.13303563780*t);

+   neptune_y_0+=     0.30205857683 * cos( 3.14159265359 +        0.00000000000*t);

+   neptune_y_0+=     0.13506391797 * cos( 1.92953034883 +       76.26607127560*t);

+   neptune_y_0+=     0.15706589373 * cos( 4.82539970129 +       36.64856292950*t);

+   neptune_y_0+=     0.14936165806 * cos( 5.79694900665 +       39.61750834610*t);

+   neptune_y_0+=     0.02584250749 * cos( 0.42549700754 +        1.48447270830*t);

+   neptune_y_0+=     0.01073739772 * cos( 3.81371728533 +       74.78159856730*t);

+   neptune_y_0+=     0.00815187583 * cos( 5.49429775826 +        2.96894541660*t);

+   neptune_y_0+=     0.00582199295 * cos( 6.19633718936 +       35.16409022120*t);

+   neptune_y_0+=     0.00565576412 * cos( 4.41843009015 +       41.10198105440*t);

+   neptune_y_0+=     0.00495581047 * cos( 5.31205825784 +      529.69096509460*t);

+   neptune_y_0+=     0.00304525203 * cos( 5.11048113661 +       73.29712585900*t);

+   neptune_y_0+=     0.00272640298 * cos( 5.58603690785 +      213.29909543800*t);

+   neptune_y_0+=     0.00135897385 * cos( 3.97553750964 +       77.75054398390*t);

+   neptune_y_0+=     0.00090970871 * cos( 0.11783619888 +      114.39910691340*t);

+   neptune_y_0+=     0.00068790261 * cos( 4.26391997151 +        4.45341812490*t);

+   neptune_y_0+=     0.00028893355 * cos( 3.21848975032 +       42.58645376270*t);

+   neptune_y_0+=     0.00020081559 * cos( 1.19787916085 +       33.67961751290*t);

+   neptune_y_0+=     0.00012613583 * cos( 1.99777332934 +      112.91463420510*t);

+   neptune_y_0+=     0.00012828708 * cos( 1.16740053443 +      111.43016149680*t);

+   neptune_y_0+=     0.00012012961 * cos( 5.66157563804 +     1059.38193018920*t);

+

+   double neptune_y_1=0.0;

+   neptune_y_1+=     0.00352947493 * cos( 3.14159265359 +        0.00000000000*t);

+   neptune_y_1+=     0.00256125493 * cos( 0.44757496817 +       36.64856292950*t);

+   neptune_y_1+=     0.00243147725 * cos( 3.89099798696 +       39.61750834610*t);

+   neptune_y_1+=     0.00118427205 * cos( 1.31128027037 +       76.26607127560*t);

+   neptune_y_1+=     0.00021936702 * cos( 1.63124087591 +       35.16409022120*t);

+   neptune_y_1+=     0.00017462332 * cos( 2.69229902966 +       41.10198105440*t);

+   neptune_y_1+=     0.00012992380 * cos( 3.79578633002 +        2.96894541660*t);

+   neptune_y_1=neptune_y_1 * t;

+

+   return neptune_y_0+neptune_y_1;

+}

+

+double vsop87a_micro_neptune_z(double t){

+   double neptune_z_0=0.0;

+   neptune_z_0+=     0.92866054405 * cos( 1.44103930278 +       38.13303563780*t);

+   neptune_z_0+=     0.01245978462 * cos( 0.00000000000 +        0.00000000000*t);

+   neptune_z_0+=     0.00474333567 * cos( 2.52218774238 +       36.64856292950*t);

+   neptune_z_0+=     0.00451987936 * cos( 3.50949720541 +       39.61750834610*t);

+   neptune_z_0+=     0.00417558068 * cos( 5.91310695421 +       76.26607127560*t);

+   neptune_z_0+=     0.00084104329 * cos( 4.38928900096 +        1.48447270830*t);

+   neptune_z_0+=     0.00032704958 * cos( 1.52048692001 +       74.78159856730*t);

+   neptune_z_0+=     0.00030873335 * cos( 3.29017611456 +       35.16409022120*t);

+   neptune_z_0+=     0.00025812584 * cos( 3.19303128782 +        2.96894541660*t);

+   neptune_z_0+=     0.00016865319 * cos( 2.13251104425 +       41.10198105440*t);

+   neptune_z_0+=     0.00011789909 * cos( 3.60001877675 +      213.29909543800*t);

+   neptune_z_0+=     0.00011279680 * cos( 3.55816676334 +      529.69096509460*t);

+

+   double neptune_z_1=0.0;

+   neptune_z_1+=     0.00154885971 * cos( 2.14239039664 +       38.13303563780*t);

+   neptune_z_1=neptune_z_1 * t;

+

+   return neptune_z_0+neptune_z_1;

+}

+

+double vsop87a_micro_saturn_x(double t){

+   double saturn_x_0=0.0;

+   saturn_x_0+=     9.51638335797 * cos( 0.87441380794 +      213.29909543800*t);

+   saturn_x_0+=     0.26412374238 * cos( 0.12390892620 +      426.59819087600*t);

+   saturn_x_0+=     0.06760430339 * cos( 4.16767145778 +      206.18554843720*t);

+   saturn_x_0+=     0.06624260115 * cos( 0.75094737780 +      220.41264243880*t);

+   saturn_x_0+=     0.04244797817 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_x_0+=     0.02336340488 * cos( 2.02227784673 +        7.11354700080*t);

+   saturn_x_0+=     0.01255372247 * cos( 2.17338917731 +      110.20632121940*t);

+   saturn_x_0+=     0.01115684467 * cos( 3.15686878377 +      419.48464387520*t);

+   saturn_x_0+=     0.01097683232 * cos( 5.65753337256 +      639.89728631400*t);

+   saturn_x_0+=     0.00716328481 * cos( 2.71149993708 +      316.39186965660*t);

+   saturn_x_0+=     0.00509313365 * cos( 4.95865624780 +      103.09277421860*t);

+   saturn_x_0+=     0.00433994439 * cos( 0.72012820974 +      529.69096509460*t);

+   saturn_x_0+=     0.00372894461 * cos( 0.00137195497 +      433.71173787680*t);

+   saturn_x_0+=     0.00097843523 * cos( 1.01485750417 +      323.50541665740*t);

+   saturn_x_0+=     0.00080600536 * cos( 5.62103979796 +       11.04570026390*t);

+   saturn_x_0+=     0.00083782316 * cos( 0.62038893702 +      227.52618943960*t);

+   saturn_x_0+=     0.00074150224 * cos( 2.38206066655 +      632.78373931320*t);

+   saturn_x_0+=     0.00070219382 * cos( 0.88789752415 +      209.36694217490*t);

+   saturn_x_0+=     0.00068855792 * cos( 4.01788097627 +      217.23124870110*t);

+   saturn_x_0+=     0.00065620467 * cos( 2.69728593339 +      202.25339517410*t);

+   saturn_x_0+=     0.00058297911 * cos( 2.16155251399 +      224.34479570190*t);

+   saturn_x_0+=     0.00054022837 * cos( 4.90928184374 +      853.19638175200*t);

+   saturn_x_0+=     0.00045550446 * cos( 1.88235037830 +       14.22709400160*t);

+   saturn_x_0+=     0.00038345667 * cos( 4.39815501478 +      199.07200143640*t);

+   saturn_x_0+=     0.00044551703 * cos( 5.60763553535 +       63.73589830340*t);

+   saturn_x_0+=     0.00025165185 * cos( 0.37800582257 +      216.48048917570*t);

+   saturn_x_0+=     0.00024554499 * cos( 4.53150598095 +      210.11770170030*t);

+   saturn_x_0+=     0.00024673219 * cos( 5.90891573850 +      522.57741809380*t);

+   saturn_x_0+=     0.00024677050 * cos( 5.60389382420 +      415.55249061210*t);

+   saturn_x_0+=     0.00025491374 * cos( 1.63922423181 +      117.31986822020*t);

+   saturn_x_0+=     0.00031253049 * cos( 4.62976601833 +      735.87651353180*t);

+   saturn_x_0+=     0.00023372467 * cos( 5.53491987276 +      647.01083331480*t);

+   saturn_x_0+=     0.00023355468 * cos( 0.18791490124 +      149.56319713460*t);

+   saturn_x_0+=     0.00024805815 * cos( 5.50327676733 +       74.78159856730*t);

+   saturn_x_0+=     0.00014731703 * cos( 4.67981909838 +      277.03499374140*t);

+   saturn_x_0+=     0.00012427525 * cos( 1.02995545746 +     1059.38193018920*t);

+   saturn_x_0+=     0.00012393514 * cos( 4.19747622821 +      490.33408917940*t);

+   saturn_x_0+=     0.00012026472 * cos( 5.66372282839 +      351.81659230870*t);

+

+   double saturn_x_1=0.0;

+   saturn_x_1+=     0.07575103962 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_x_1+=     0.03085041716 * cos( 4.27565749128 +      426.59819087600*t);

+   saturn_x_1+=     0.02714918399 * cos( 5.85229412397 +      206.18554843720*t);

+   saturn_x_1+=     0.02643100909 * cos( 5.33291950584 +      220.41264243880*t);

+   saturn_x_1+=     0.00627104520 * cos( 0.32898307969 +        7.11354700080*t);

+   saturn_x_1+=     0.00256560953 * cos( 3.52478934343 +      639.89728631400*t);

+   saturn_x_1+=     0.00312356512 * cos( 4.83001724941 +      419.48464387520*t);

+   saturn_x_1+=     0.00189196274 * cos( 4.48642453552 +      433.71173787680*t);

+   saturn_x_1+=     0.00203646570 * cos( 1.10998681782 +      213.29909543800*t);

+   saturn_x_1+=     0.00119531145 * cos( 1.14735096078 +      110.20632121940*t);

+   saturn_x_1+=     0.00066764238 * cos( 3.72346596928 +      316.39186965660*t);

+   saturn_x_1+=     0.00066901225 * cos( 5.20257500380 +      227.52618943960*t);

+   saturn_x_1+=     0.00031000840 * cos( 6.06067919437 +      199.07200143640*t);

+   saturn_x_1+=     0.00030418100 * cos( 0.18746903351 +       14.22709400160*t);

+   saturn_x_1+=     0.00022275210 * cos( 6.19530878014 +      103.09277421860*t);

+   saturn_x_1+=     0.00018939377 * cos( 2.77618306725 +      853.19638175200*t);

+   saturn_x_1+=     0.00018093009 * cos( 5.09162723865 +      209.36694217490*t);

+   saturn_x_1+=     0.00017777854 * cos( 6.10381593351 +      217.23124870110*t);

+   saturn_x_1+=     0.00016296201 * cos( 4.86945681437 +      216.48048917570*t);

+   saturn_x_1+=     0.00017120250 * cos( 4.59611664188 +      632.78373931320*t);

+   saturn_x_1+=     0.00015894491 * cos( 0.03653502304 +      210.11770170030*t);

+   saturn_x_1+=     0.00016192653 * cos( 5.60798014450 +      323.50541665740*t);

+   saturn_x_1+=     0.00014466010 * cos( 3.67449380090 +      647.01083331480*t);

+   saturn_x_1+=     0.00011061528 * cos( 0.03163071461 +      117.31986822020*t);

+   saturn_x_1=saturn_x_1 * t;

+

+   double saturn_x_2=0.0;

+   saturn_x_2+=     0.00560746334 * cos( 1.26401632282 +      206.18554843720*t);

+   saturn_x_2+=     0.00545834518 * cos( 3.62343709657 +      220.41264243880*t);

+   saturn_x_2+=     0.00443342186 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_x_2+=     0.00336109713 * cos( 2.42547432460 +      213.29909543800*t);

+   saturn_x_2+=     0.00224302269 * cos( 2.49151203519 +      426.59819087600*t);

+   saturn_x_2+=     0.00087170924 * cos( 4.89048951691 +        7.11354700080*t);

+   saturn_x_2+=     0.00050028094 * cos( 2.70119046081 +      433.71173787680*t);

+   saturn_x_2+=     0.00045122590 * cos( 0.36735068943 +      419.48464387520*t);

+   saturn_x_2+=     0.00032847824 * cos( 1.59210153669 +      639.89728631400*t);

+   saturn_x_2+=     0.00027153555 * cos( 3.49804002218 +      227.52618943960*t);

+   saturn_x_2+=     0.00012676167 * cos( 1.45465729530 +      199.07200143640*t);

+   saturn_x_2+=     0.00010330738 * cos( 4.76949531290 +       14.22709400160*t);

+   saturn_x_2=saturn_x_2 * t * t;

+

+   double saturn_x_3=0.0;

+   saturn_x_3+=     0.00077115952 * cos( 2.97714385362 +      206.18554843720*t);

+   saturn_x_3+=     0.00075340436 * cos( 1.89208005248 +      220.41264243880*t);

+   saturn_x_3+=     0.00018450895 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_x_3+=     0.00010527244 * cos( 0.66368256891 +      426.59819087600*t);

+   saturn_x_3=saturn_x_3 * t * t * t;

+

+   return saturn_x_0+saturn_x_1+saturn_x_2+saturn_x_3;

+}

+

+double vsop87a_micro_saturn_y(double t){

+   double saturn_y_0=0.0;

+   saturn_y_0+=     9.52986882699 * cos( 5.58600556665 +      213.29909543800*t);

+   saturn_y_0+=     0.79387988806 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_y_0+=     0.26441781302 * cos( 4.83528061849 +      426.59819087600*t);

+   saturn_y_0+=     0.06916653915 * cos( 2.55279408706 +      206.18554843720*t);

+   saturn_y_0+=     0.06633570703 * cos( 5.46258848288 +      220.41264243880*t);

+   saturn_y_0+=     0.02345609742 * cos( 0.44652132519 +        7.11354700080*t);

+   saturn_y_0+=     0.01183874652 * cos( 1.34638298371 +      419.48464387520*t);

+   saturn_y_0+=     0.01245790434 * cos( 0.60367177975 +      110.20632121940*t);

+   saturn_y_0+=     0.01098751131 * cos( 4.08608782813 +      639.89728631400*t);

+   saturn_y_0+=     0.00700849336 * cos( 1.13611298025 +      316.39186965660*t);

+   saturn_y_0+=     0.00434466176 * cos( 5.42474696262 +      529.69096509460*t);

+   saturn_y_0+=     0.00373327342 * cos( 4.71308726958 +      433.71173787680*t);

+   saturn_y_0+=     0.00335162363 * cos( 0.66422253983 +      103.09277421860*t);

+   saturn_y_0+=     0.00097837745 * cos( 5.72844290173 +      323.50541665740*t);

+   saturn_y_0+=     0.00080571808 * cos( 4.05295449910 +       11.04570026390*t);

+   saturn_y_0+=     0.00083899691 * cos( 5.33204070267 +      227.52618943960*t);

+   saturn_y_0+=     0.00070158491 * cos( 5.59777963629 +      209.36694217490*t);

+   saturn_y_0+=     0.00065937657 * cos( 1.25969608208 +      202.25339517410*t);

+   saturn_y_0+=     0.00070957225 * cos( 0.88888207567 +      632.78373931320*t);

+   saturn_y_0+=     0.00068985859 * cos( 2.44460312617 +      217.23124870110*t);

+   saturn_y_0+=     0.00058382264 * cos( 0.58978766922 +      224.34479570190*t);

+   saturn_y_0+=     0.00054049836 * cos( 3.33757904879 +      853.19638175200*t);

+   saturn_y_0+=     0.00045790930 * cos( 0.30331527632 +       14.22709400160*t);

+   saturn_y_0+=     0.00041976402 * cos( 2.62591355948 +      199.07200143640*t);

+   saturn_y_0+=     0.00044697175 * cos( 0.90661238256 +       63.73589830340*t);

+   saturn_y_0+=     0.00025199575 * cos( 5.08963506006 +      216.48048917570*t);

+   saturn_y_0+=     0.00024640836 * cos( 2.95445247282 +      210.11770170030*t);

+   saturn_y_0+=     0.00024835151 * cos( 4.02630190571 +      415.55249061210*t);

+   saturn_y_0+=     0.00025545907 * cos( 0.06626229252 +      117.31986822020*t);

+   saturn_y_0+=     0.00029666833 * cos( 6.09910638345 +      735.87651353180*t);

+   saturn_y_0+=     0.00023396742 * cos( 3.96337393635 +      647.01083331480*t);

+   saturn_y_0+=     0.00023380691 * cos( 4.90051072276 +      149.56319713460*t);

+   saturn_y_0+=     0.00020272215 * cos( 2.34319548198 +      309.27832265580*t);

+   saturn_y_0+=     0.00020099552 * cos( 0.98365186365 +      522.57741809380*t);

+   saturn_y_0+=     0.00024827950 * cos( 3.92681428900 +       74.78159856730*t);

+   saturn_y_0+=     0.00015383927 * cos( 3.10227822627 +      277.03499374140*t);

+   saturn_y_0+=     0.00011629210 * cos( 5.74108283772 +     1059.38193018920*t);

+   saturn_y_0+=     0.00012422966 * cos( 2.62557865743 +      490.33408917940*t);

+   saturn_y_0+=     0.00012048048 * cos( 4.09265980116 +      351.81659230870*t);

+

+   double saturn_y_1=0.0;

+   saturn_y_1+=     0.05373889135 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_y_1+=     0.03090575152 * cos( 2.70346890906 +      426.59819087600*t);

+   saturn_y_1+=     0.02741594312 * cos( 4.26667636015 +      206.18554843720*t);

+   saturn_y_1+=     0.02647489677 * cos( 3.76132298889 +      220.41264243880*t);

+   saturn_y_1+=     0.00631520527 * cos( 5.03245505280 +        7.11354700080*t);

+   saturn_y_1+=     0.00256799701 * cos( 1.95351819758 +      639.89728631400*t);

+   saturn_y_1+=     0.00312271930 * cos( 3.25850205023 +      419.48464387520*t);

+   saturn_y_1+=     0.00189433319 * cos( 2.91501840819 +      433.71173787680*t);

+   saturn_y_1+=     0.00164133553 * cos( 5.29239290066 +      213.29909543800*t);

+   saturn_y_1+=     0.00116791227 * cos( 5.89146675760 +      110.20632121940*t);

+   saturn_y_1+=     0.00067210919 * cos( 2.17042636344 +      316.39186965660*t);

+   saturn_y_1+=     0.00067003292 * cos( 3.63101075514 +      227.52618943960*t);

+   saturn_y_1+=     0.00033002406 * cos( 4.35527405801 +      199.07200143640*t);

+   saturn_y_1+=     0.00030628998 * cos( 4.88861760772 +       14.22709400160*t);

+   saturn_y_1+=     0.00022234714 * cos( 4.62212779231 +      103.09277421860*t);

+   saturn_y_1+=     0.00018945004 * cos( 1.20412493845 +      853.19638175200*t);

+   saturn_y_1+=     0.00018079959 * cos( 3.51566153251 +      209.36694217490*t);

+   saturn_y_1+=     0.00017791543 * cos( 4.53214140649 +      217.23124870110*t);

+   saturn_y_1+=     0.00016320701 * cos( 3.29784030970 +      216.48048917570*t);

+   saturn_y_1+=     0.00015944258 * cos( 4.74503265169 +      210.11770170030*t);

+   saturn_y_1+=     0.00016717122 * cos( 3.00270792752 +      632.78373931320*t);

+   saturn_y_1+=     0.00016149947 * cos( 4.04186432517 +      323.50541665740*t);

+   saturn_y_1+=     0.00014481431 * cos( 2.10298298650 +      647.01083331480*t);

+   saturn_y_1+=     0.00011084040 * cos( 4.74073871754 +      117.31986822020*t);

+   saturn_y_1=saturn_y_1 * t;

+

+   double saturn_y_2=0.0;

+   saturn_y_2+=     0.00563706537 * cos( 5.97115878242 +      206.18554843720*t);

+   saturn_y_2+=     0.00547012116 * cos( 2.05154973426 +      220.41264243880*t);

+   saturn_y_2+=     0.00458518613 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_y_2+=     0.00362294249 * cos( 0.89540100509 +      213.29909543800*t);

+   saturn_y_2+=     0.00225521642 * cos( 0.91699821445 +      426.59819087600*t);

+   saturn_y_2+=     0.00088390611 * cos( 3.30289449917 +        7.11354700080*t);

+   saturn_y_2+=     0.00050101314 * cos( 1.12976163835 +      433.71173787680*t);

+   saturn_y_2+=     0.00045516403 * cos( 5.07669466539 +      419.48464387520*t);

+   saturn_y_2+=     0.00032896745 * cos( 0.02089057938 +      639.89728631400*t);

+   saturn_y_2+=     0.00027199743 * cos( 1.92638417640 +      227.52618943960*t);

+   saturn_y_2+=     0.00013251505 * cos( 6.07693099404 +      199.07200143640*t);

+   saturn_y_2+=     0.00010425984 * cos( 3.18246869028 +       14.22709400160*t);

+   saturn_y_2=saturn_y_2 * t * t;

+

+   double saturn_y_3=0.0;

+   saturn_y_3+=     0.00077376615 * cos( 1.40391048961 +      206.18554843720*t);

+   saturn_y_3+=     0.00075564351 * cos( 0.31962896379 +      220.41264243880*t);

+   saturn_y_3+=     0.00022843837 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_y_3+=     0.00010672263 * cos( 5.36495663820 +      426.59819087600*t);

+   saturn_y_3=saturn_y_3 * t * t * t;

+

+   return saturn_y_0+saturn_y_1+saturn_y_2+saturn_y_3;

+}

+

+double vsop87a_micro_saturn_z(double t){

+   double saturn_z_0=0.0;

+   saturn_z_0+=     0.41356950940 * cos( 3.60234142982 +      213.29909543800*t);

+   saturn_z_0+=     0.01148283576 * cos( 2.85128367469 +      426.59819087600*t);

+   saturn_z_0+=     0.01214249867 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_z_0+=     0.00329280791 * cos( 0.57121407104 +      206.18554843720*t);

+   saturn_z_0+=     0.00286934048 * cos( 3.48073526693 +      220.41264243880*t);

+   saturn_z_0+=     0.00099076584 * cos( 4.73369511264 +        7.11354700080*t);

+   saturn_z_0+=     0.00057361820 * cos( 4.92611225093 +      110.20632121940*t);

+   saturn_z_0+=     0.00047738127 * cos( 2.10039779728 +      639.89728631400*t);

+   saturn_z_0+=     0.00043458803 * cos( 5.84904978051 +      419.48464387520*t);

+   saturn_z_0+=     0.00034565673 * cos( 5.42614229590 +      316.39186965660*t);

+   saturn_z_0+=     0.00016185391 * cos( 2.72987173675 +      433.71173787680*t);

+   saturn_z_0+=     0.00011433574 * cos( 3.71662021072 +      529.69096509460*t);

+

+   double saturn_z_1=0.0;

+   saturn_z_1+=     0.01906503283 * cos( 4.94544746116 +      213.29909543800*t);

+   saturn_z_1+=     0.00528301265 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_z_1+=     0.00130262284 * cos( 2.26140980879 +      206.18554843720*t);

+   saturn_z_1+=     0.00101466332 * cos( 1.79095829545 +      220.41264243880*t);

+   saturn_z_1+=     0.00085947578 * cos( 0.51612788497 +      426.59819087600*t);

+   saturn_z_1+=     0.00022257446 * cos( 3.07684015656 +        7.11354700080*t);

+   saturn_z_1+=     0.00016179946 * cos( 1.19987517506 +      419.48464387520*t);

+   saturn_z_1=saturn_z_1 * t;

+

+   double saturn_z_2=0.0;

+   saturn_z_2+=     0.00131275155 * cos( 0.08868998101 +      213.29909543800*t);

+   saturn_z_2+=     0.00030147649 * cos( 3.91396203887 +      206.18554843720*t);

+   saturn_z_2+=     0.00019322173 * cos( 0.09228748624 +      220.41264243880*t);

+   saturn_z_2=saturn_z_2 * t * t;

+

+   return saturn_z_0+saturn_z_1+saturn_z_2;

+}

+

+double vsop87a_micro_uranus_x(double t){

+   double uranus_x_0=0.0;

+   uranus_x_0+=    19.17370730359 * cos( 5.48133416489 +       74.78159856730*t);

+   uranus_x_0+=     1.32272523872 * cos( 0.00000000000 +        0.00000000000*t);

+   uranus_x_0+=     0.44402496796 * cos( 1.65967519586 +      149.56319713460*t);

+   uranus_x_0+=     0.14668209481 * cos( 3.42395862804 +       73.29712585900*t);

+   uranus_x_0+=     0.14130269479 * cos( 4.39572927934 +       76.26607127560*t);

+   uranus_x_0+=     0.06201106178 * cos( 5.14043574125 +        1.48447270830*t);

+   uranus_x_0+=     0.01542951343 * cos( 4.12121838072 +      224.34479570190*t);

+   uranus_x_0+=     0.01444216660 * cos( 2.65117115201 +      148.07872442630*t);

+   uranus_x_0+=     0.00944995563 * cos( 1.65869338757 +       11.04570026390*t);

+   uranus_x_0+=     0.00657524815 * cos( 0.57595170636 +      151.04766984290*t);

+   uranus_x_0+=     0.00621624676 * cos( 3.05882246638 +       77.75054398390*t);

+   uranus_x_0+=     0.00585182542 * cos( 4.79934779678 +       71.81265315070*t);

+   uranus_x_0+=     0.00634000270 * cos( 4.09556589724 +       63.73589830340*t);

+   uranus_x_0+=     0.00547699056 * cos( 3.63127725056 +       85.82729883120*t);

+   uranus_x_0+=     0.00458219984 * cos( 3.90788284112 +        2.96894541660*t);

+   uranus_x_0+=     0.00496087649 * cos( 0.59947400861 +      529.69096509460*t);

+   uranus_x_0+=     0.00383625535 * cos( 6.18762010576 +      138.51749687070*t);

+   uranus_x_0+=     0.00267938156 * cos( 0.96885660137 +      213.29909543800*t);

+   uranus_x_0+=     0.00215368005 * cos( 5.30877641428 +       38.13303563780*t);

+   uranus_x_0+=     0.00145505389 * cos( 2.31759757085 +       70.84944530420*t);

+   uranus_x_0+=     0.00135340032 * cos( 5.51062460816 +       78.71375183040*t);

+   uranus_x_0+=     0.00119593859 * cos( 4.10138544267 +       39.61750834610*t);

+   uranus_x_0+=     0.00125105686 * cos( 2.51455273063 +      111.43016149680*t);

+   uranus_x_0+=     0.00111260244 * cos( 5.12252784325 +      222.86032299360*t);

+   uranus_x_0+=     0.00104619827 * cos( 3.90538916334 +      146.59425171800*t);

+   uranus_x_0+=     0.00110125387 * cos( 4.45473528724 +       35.16409022120*t);

+   uranus_x_0+=     0.00063584588 * cos( 0.29966233158 +      299.12639426920*t);

+   uranus_x_0+=     0.00053904041 * cos( 3.92590422507 +        3.93215326310*t);

+   uranus_x_0+=     0.00065066905 * cos( 3.73008452906 +      109.94568878850*t);

+   uranus_x_0+=     0.00039181662 * cos( 2.68841280769 +        4.45341812490*t);

+   uranus_x_0+=     0.00034341683 * cos( 3.03781661928 +      225.82926841020*t);

+   uranus_x_0+=     0.00033134636 * cos( 2.54201591218 +       65.22037101170*t);

+   uranus_x_0+=     0.00034555652 * cos( 1.84699329257 +       79.23501669220*t);

+   uranus_x_0+=     0.00033867050 * cos( 5.98418436103 +       70.32818044240*t);

+   uranus_x_0+=     0.00028371614 * cos( 2.58026657123 +      127.47179660680*t);

+   uranus_x_0+=     0.00035943348 * cos( 4.08754543016 +      202.25339517410*t);

+   uranus_x_0+=     0.00025208833 * cos( 5.30272144657 +        9.56122755560*t);

+   uranus_x_0+=     0.00023467802 * cos( 4.09729860322 +      145.63104387150*t);

+   uranus_x_0+=     0.00022963939 * cos( 5.51475073655 +       84.34282612290*t);

+   uranus_x_0+=     0.00031823951 * cos( 5.53948583244 +      152.53214255120*t);

+   uranus_x_0+=     0.00028384953 * cos( 6.01785430306 +      184.72728735580*t);

+   uranus_x_0+=     0.00026657176 * cos( 6.11027939727 +      160.60889739850*t);

+   uranus_x_0+=     0.00019676762 * cos( 5.53431398332 +       74.66972398270*t);

+   uranus_x_0+=     0.00019653873 * cos( 2.28660913421 +       74.89347315190*t);

+   uranus_x_0+=     0.00019954280 * cos( 0.57450958037 +       12.53017297220*t);

+   uranus_x_0+=     0.00018565067 * cos( 0.62225019017 +       52.69019803950*t);

+   uranus_x_0+=     0.00020084756 * cos( 4.47297488471 +       22.09140052780*t);

+   uranus_x_0+=     0.00019926329 * cos( 1.39878194708 +      112.91463420510*t);

+   uranus_x_0+=     0.00018575632 * cos( 5.70217475790 +       33.67961751290*t);

+   uranus_x_0+=     0.00016587870 * cos( 4.86920309163 +      108.46121608020*t);

+   uranus_x_0+=     0.00015171194 * cos( 2.88415453399 +       41.10198105440*t);

+   uranus_x_0+=     0.00011245800 * cos( 6.11597016146 +       71.60020482960*t);

+   uranus_x_0+=     0.00013948521 * cos( 6.27545694160 +      221.37585028530*t);

+   uranus_x_0+=     0.00010798350 * cos( 1.70031857078 +       77.96299230500*t);

+   uranus_x_0+=     0.00013593955 * cos( 2.55407820633 +       87.31177153950*t);

+   uranus_x_0+=     0.00011997848 * cos( 0.94875212305 +     1059.38193018920*t);

+   uranus_x_0+=     0.00012884351 * cos( 5.08737999470 +      145.10977900970*t);

+   uranus_x_0+=     0.00012394786 * cos( 6.21892878850 +       72.33391801250*t);

+   uranus_x_0+=     0.00012253318 * cos( 0.19452856525 +       36.64856292950*t);

+   uranus_x_0+=     0.00011538642 * cos( 1.77241794539 +       77.22927912210*t);

+

+   double uranus_x_1=0.0;

+   uranus_x_1+=     0.00739730021 * cos( 6.01067825116 +      149.56319713460*t);

+   uranus_x_1+=     0.00526878306 * cos( 3.14159265359 +        0.00000000000*t);

+   uranus_x_1+=     0.00239840801 * cos( 5.33657762707 +       73.29712585900*t);

+   uranus_x_1+=     0.00229676787 * cos( 2.48204455775 +       76.26607127560*t);

+   uranus_x_1+=     0.00111045158 * cos( 5.57157235960 +       11.04570026390*t);

+   uranus_x_1+=     0.00096352822 * cos( 0.35070389084 +       63.73589830340*t);

+   uranus_x_1+=     0.00081511870 * cos( 1.21058618039 +       85.82729883120*t);

+   uranus_x_1+=     0.00045687564 * cos( 2.29216583843 +      138.51749687070*t);

+   uranus_x_1+=     0.00051382501 * cos( 2.18935125260 +      224.34479570190*t);

+   uranus_x_1+=     0.00038844330 * cos( 0.30724575951 +       70.84944530420*t);

+   uranus_x_1+=     0.00036158493 * cos( 1.23634798757 +       78.71375183040*t);

+   uranus_x_1+=     0.00032333094 * cos( 5.06666556704 +       74.78159856730*t);

+   uranus_x_1+=     0.00021685656 * cos( 4.93710968392 +      151.04766984290*t);

+   uranus_x_1+=     0.00019441970 * cos( 1.30617490304 +       77.75054398390*t);

+   uranus_x_1+=     0.00017376241 * cos( 0.24607221230 +       71.81265315070*t);

+   uranus_x_1+=     0.00015211071 * cos( 5.53141633140 +        3.93215326310*t);

+   uranus_x_1=uranus_x_1 * t;

+

+   double uranus_x_2=0.0;

+   uranus_x_2+=     0.00016015732 * cos( 3.83700026619 +       74.78159856730*t);

+   uranus_x_2+=     0.00010915299 * cos( 3.02987776270 +      149.56319713460*t);

+   uranus_x_2=uranus_x_2 * t * t;

+

+   return uranus_x_0+uranus_x_1+uranus_x_2;

+}

+

+double vsop87a_micro_uranus_y(double t){

+   double uranus_y_0=0.0;

+   uranus_y_0+=    19.16518231584 * cos( 3.91045677002 +       74.78159856730*t);

+   uranus_y_0+=     0.44390465203 * cos( 0.08884111329 +      149.56319713460*t);

+   uranus_y_0+=     0.16256125476 * cos( 3.14159265359 +        0.00000000000*t);

+   uranus_y_0+=     0.14755940186 * cos( 1.85423280679 +       73.29712585900*t);

+   uranus_y_0+=     0.14123958128 * cos( 2.82486076549 +       76.26607127560*t);

+   uranus_y_0+=     0.06250078231 * cos( 3.56960243857 +        1.48447270830*t);

+   uranus_y_0+=     0.01542668264 * cos( 2.55040539213 +      224.34479570190*t);

+   uranus_y_0+=     0.01442356575 * cos( 1.08004542712 +      148.07872442630*t);

+   uranus_y_0+=     0.00938975501 * cos( 0.09275714761 +       11.04570026390*t);

+   uranus_y_0+=     0.00650331846 * cos( 2.76142680222 +       63.73589830340*t);

+   uranus_y_0+=     0.00657343120 * cos( 5.28830704469 +      151.04766984290*t);

+   uranus_y_0+=     0.00621326770 * cos( 1.48795811387 +       77.75054398390*t);

+   uranus_y_0+=     0.00541961958 * cos( 3.24476486661 +       71.81265315070*t);

+   uranus_y_0+=     0.00547472694 * cos( 2.06037924573 +       85.82729883120*t);

+   uranus_y_0+=     0.00459589120 * cos( 2.33745536070 +        2.96894541660*t);

+   uranus_y_0+=     0.00495936105 * cos( 5.31205753740 +      529.69096509460*t);

+   uranus_y_0+=     0.00387922853 * cos( 4.62026923885 +      138.51749687070*t);

+   uranus_y_0+=     0.00268363417 * cos( 5.68085299020 +      213.29909543800*t);

+   uranus_y_0+=     0.00216239629 * cos( 3.73800767580 +       38.13303563780*t);

+   uranus_y_0+=     0.00144032475 * cos( 0.75015700920 +       70.84944530420*t);

+   uranus_y_0+=     0.00135290820 * cos( 3.93970260616 +       78.71375183040*t);

+   uranus_y_0+=     0.00119670613 * cos( 2.53058783780 +       39.61750834610*t);

+   uranus_y_0+=     0.00124868545 * cos( 0.94315917319 +      111.43016149680*t);

+   uranus_y_0+=     0.00111204860 * cos( 3.55163219419 +      222.86032299360*t);

+   uranus_y_0+=     0.00104507929 * cos( 2.33345675603 +      146.59425171800*t);

+   uranus_y_0+=     0.00108584454 * cos( 6.02234848388 +       35.16409022120*t);

+   uranus_y_0+=     0.00063573747 * cos( 5.01204967920 +      299.12639426920*t);

+   uranus_y_0+=     0.00053289771 * cos( 2.38437587876 +        3.93215326310*t);

+   uranus_y_0+=     0.00063774261 * cos( 2.15607602904 +      109.94568878850*t);

+   uranus_y_0+=     0.00039218598 * cos( 1.11841109252 +        4.45341812490*t);

+   uranus_y_0+=     0.00034205426 * cos( 0.92405922576 +       65.22037101170*t);

+   uranus_y_0+=     0.00034334377 * cos( 1.46696169843 +      225.82926841020*t);

+   uranus_y_0+=     0.00034538316 * cos( 0.27613780697 +       79.23501669220*t);

+   uranus_y_0+=     0.00039256771 * cos( 5.75956853703 +      202.25339517410*t);

+   uranus_y_0+=     0.00026157754 * cos( 3.74097610798 +        9.56122755560*t);

+   uranus_y_0+=     0.00023427328 * cos( 2.52740125551 +      145.63104387150*t);

+   uranus_y_0+=     0.00022933138 * cos( 3.94455540350 +       84.34282612290*t);

+   uranus_y_0+=     0.00031816303 * cos( 3.96860170484 +      152.53214255120*t);

+   uranus_y_0+=     0.00025237176 * cos( 4.45141413666 +       70.32818044240*t);

+   uranus_y_0+=     0.00028372491 * cos( 4.44714627097 +      184.72728735580*t);

+   uranus_y_0+=     0.00026652859 * cos( 4.53944395347 +      160.60889739850*t);

+   uranus_y_0+=     0.00019666208 * cos( 3.96350065335 +       74.66972398270*t);

+   uranus_y_0+=     0.00019643845 * cos( 0.71577796385 +       74.89347315190*t);

+   uranus_y_0+=     0.00019838981 * cos( 5.29113397354 +       12.53017297220*t);

+   uranus_y_0+=     0.00021523908 * cos( 4.93565132068 +       36.64856292950*t);

+   uranus_y_0+=     0.00015537967 * cos( 1.87863275460 +       52.69019803950*t);

+   uranus_y_0+=     0.00020115100 * cos( 3.45473780762 +      127.47179660680*t);

+   uranus_y_0+=     0.00020051641 * cos( 2.90386352937 +       22.09140052780*t);

+   uranus_y_0+=     0.00019901477 * cos( 6.11075402434 +      112.91463420510*t);

+   uranus_y_0+=     0.00018126776 * cos( 0.98478853787 +       33.67961751290*t);

+   uranus_y_0+=     0.00015174962 * cos( 1.31314034959 +       41.10198105440*t);

+   uranus_y_0+=     0.00011239020 * cos( 4.54508334011 +       71.60020482960*t);

+   uranus_y_0+=     0.00013948849 * cos( 4.70474945682 +      221.37585028530*t);

+   uranus_y_0+=     0.00010819728 * cos( 0.12807029856 +       77.96299230500*t);

+   uranus_y_0+=     0.00013589665 * cos( 0.98313719930 +       87.31177153950*t);

+   uranus_y_0+=     0.00011996772 * cos( 5.66129275335 +     1059.38193018920*t);

+   uranus_y_0+=     0.00012407787 * cos( 4.64945783340 +       72.33391801250*t);

+   uranus_y_0+=     0.00011531140 * cos( 0.20190074645 +       77.22927912210*t);

+

+   double uranus_y_1=0.0;

+   uranus_y_1+=     0.02157896385 * cos( 0.00000000000 +        0.00000000000*t);

+   uranus_y_1+=     0.00739227349 * cos( 4.43963890935 +      149.56319713460*t);

+   uranus_y_1+=     0.00238545685 * cos( 3.76882493145 +       73.29712585900*t);

+   uranus_y_1+=     0.00229396424 * cos( 0.91090183978 +       76.26607127560*t);

+   uranus_y_1+=     0.00110137111 * cos( 4.00844441616 +       11.04570026390*t);

+   uranus_y_1+=     0.00094979054 * cos( 5.07141537066 +       63.73589830340*t);

+   uranus_y_1+=     0.00081474163 * cos( 5.92275367106 +       85.82729883120*t);

+   uranus_y_1+=     0.00045457174 * cos( 0.73292241207 +      138.51749687070*t);

+   uranus_y_1+=     0.00051366974 * cos( 0.61844114994 +      224.34479570190*t);

+   uranus_y_1+=     0.00038296005 * cos( 5.01873578671 +       70.84944530420*t);

+   uranus_y_1+=     0.00036146116 * cos( 5.94859452787 +       78.71375183040*t);

+   uranus_y_1+=     0.00032420558 * cos( 4.32617271732 +       74.78159856730*t);

+   uranus_y_1+=     0.00021673269 * cos( 3.36607263522 +      151.04766984290*t);

+   uranus_y_1+=     0.00019425087 * cos( 6.01842187783 +       77.75054398390*t);

+   uranus_y_1+=     0.00017393206 * cos( 4.96098895488 +       71.81265315070*t);

+   uranus_y_1+=     0.00014991169 * cos( 3.97176856758 +        3.93215326310*t);

+   uranus_y_1=uranus_y_1 * t;

+

+   double uranus_y_2=0.0;

+   uranus_y_2+=     0.00034812647 * cos( 3.14159265359 +        0.00000000000*t);

+   uranus_y_2+=     0.00016589194 * cos( 2.29556740620 +       74.78159856730*t);

+   uranus_y_2+=     0.00010905147 * cos( 1.45737963668 +      149.56319713460*t);

+   uranus_y_2=uranus_y_2 * t * t;

+

+   return uranus_y_0+uranus_y_1+uranus_y_2;

+}

+

+double vsop87a_micro_uranus_z(double t){

+   double uranus_z_0=0.0;

+   uranus_z_0+=     0.25878127698 * cos( 2.61861272578 +       74.78159856730*t);

+   uranus_z_0+=     0.01774318778 * cos( 3.14159265359 +        0.00000000000*t);

+   uranus_z_0+=     0.00599316131 * cos( 5.08119500585 +      149.56319713460*t);

+   uranus_z_0+=     0.00190281890 * cos( 1.61643841193 +       76.26607127560*t);

+   uranus_z_0+=     0.00190881685 * cos( 0.57869575952 +       73.29712585900*t);

+   uranus_z_0+=     0.00084626761 * cos( 2.26030150166 +        1.48447270830*t);

+   uranus_z_0+=     0.00030734257 * cos( 0.23571721555 +       63.73589830340*t);

+   uranus_z_0+=     0.00020842052 * cos( 1.26054208091 +      224.34479570190*t);

+   uranus_z_0+=     0.00019734273 * cos( 6.04314677688 +      148.07872442630*t);

+   uranus_z_0+=     0.00012537530 * cos( 5.17169051466 +       11.04570026390*t);

+   uranus_z_0+=     0.00014582864 * cos( 6.14852037212 +       71.81265315070*t);

+   uranus_z_0+=     0.00010407529 * cos( 3.65320417038 +      213.29909543800*t);

+   uranus_z_0+=     0.00011261541 * cos( 3.55973769686 +      529.69096509460*t);

+

+   double uranus_z_1=0.0;

+   uranus_z_1+=     0.00655916626 * cos( 0.01271947660 +       74.78159856730*t);

+   uranus_z_1+=     0.00049648951 * cos( 0.00000000000 +        0.00000000000*t);

+   uranus_z_1+=     0.00023874178 * cos( 2.73870491220 +      149.56319713460*t);

+   uranus_z_1=uranus_z_1 * t;

+

+   double uranus_z_2=0.0;

+   uranus_z_2+=     0.00014697858 * cos( 1.75149165003 +       74.78159856730*t);

+   uranus_z_2=uranus_z_2 * t * t;

+

+   return uranus_z_0+uranus_z_1+uranus_z_2;

+}

+

+double vsop87a_micro_venus_x(double t){

+   double venus_x_0=0.0;

+   venus_x_0+=     0.72211281391 * cos( 3.17575836361 +    10213.28554621100*t);

+   venus_x_0+=     0.00486448018 * cos( 0.00000000000 +        0.00000000000*t);

+   venus_x_0+=     0.00244500474 * cos( 4.05566613861 +    20426.57109242200*t);

+

+   double venus_x_1=0.0;

+   venus_x_1+=     0.00033862636 * cos( 3.14159265359 +        0.00000000000*t);

+   venus_x_1+=     0.00017234992 * cos( 0.92721124604 +    20426.57109242200*t);

+   venus_x_1=venus_x_1 * t;

+

+   return venus_x_0+venus_x_1;

+}

+

+double vsop87a_micro_venus_y(double t){

+   double venus_y_0=0.0;

+   venus_y_0+=     0.72324820731 * cos( 1.60573808356 +    10213.28554621100*t);

+   venus_y_0+=     0.00549506273 * cos( 3.14159265359 +        0.00000000000*t);

+   venus_y_0+=     0.00244884790 * cos( 2.48564954004 +    20426.57109242200*t);

+

+   double venus_y_1=0.0;

+   venus_y_1+=     0.00039231430 * cos( 0.00000000000 +        0.00000000000*t);

+   venus_y_1+=     0.00017282326 * cos( 5.63824735900 +    20426.57109242200*t);

+   venus_y_1=venus_y_1 * t;

+

+   return venus_y_0+venus_y_1;

+}

+

+double vsop87a_micro_venus_z(double t){

+   double venus_z_0=0.0;

+   venus_z_0+=     0.04282990302 * cos( 0.26703856476 +    10213.28554621100*t);

+   venus_z_0+=     0.00035588343 * cos( 3.14159265359 +        0.00000000000*t);

+   venus_z_0+=     0.00014501879 * cos( 1.14696911390 +    20426.57109242200*t);

+

+   double venus_z_1=0.0;

+   venus_z_1+=     0.00208096402 * cos( 1.88967278742 +    10213.28554621100*t);

+   venus_z_1=venus_z_1 * t;

+

+   return venus_z_0+venus_z_1;

+}

+

diff --git a/movement/lib/vsop87/vsop87a_micro.h b/movement/lib/vsop87/vsop87a_micro.h
new file mode 100755
index 00000000..87515f5f
--- /dev/null
+++ b/movement/lib/vsop87/vsop87a_micro.h
@@ -0,0 +1,17 @@
+//VSOP87-Multilang http://www.astrogreg.com/vsop87-multilang/index.html

+//Greg Miller (gmiller@gregmiller.net) 2019.  Released as Public Domain

+

+#ifndef VSOP87A_MICRO

+#define VSOP87A_MICRO

+

+   void vsop87a_micro_getEarth(double t,double temp[]);

+   void vsop87a_micro_getEmb(double t,double temp[]);

+   void vsop87a_micro_getJupiter(double t,double temp[]);

+   void vsop87a_micro_getMars(double t,double temp[]);

+   void vsop87a_micro_getMercury(double t,double temp[]);

+   void vsop87a_micro_getNeptune(double t,double temp[]);

+   void vsop87a_micro_getSaturn(double t,double temp[]);

+   void vsop87a_micro_getUranus(double t,double temp[]);

+   void vsop87a_micro_getVenus(double t,double temp[]);

+   void vsop87a_micro_getMoon(double earth[], double emb[],double temp[]);

+#endif

diff --git a/movement/lib/vsop87/vsop87a_milli.c b/movement/lib/vsop87/vsop87a_milli.c
new file mode 100755
index 00000000..b1875721
--- /dev/null
+++ b/movement/lib/vsop87/vsop87a_milli.c
@@ -0,0 +1,2048 @@
+//VSOP87-Multilang http://www.astrogreg.com/vsop87-multilang/index.html

+//Greg Miller (gmiller@gregmiller.net) 2019.  Released as Public Domain

+

+#include <math.h>

+#include "vsop87a_milli.h"

+double vsop87a_milli_earth_x(double t);

+double vsop87a_milli_earth_y(double t);

+double vsop87a_milli_earth_z(double t);

+double vsop87a_milli_emb_x(double t);

+double vsop87a_milli_emb_y(double t);

+double vsop87a_milli_emb_z(double t);

+double vsop87a_milli_jupiter_x(double t);

+double vsop87a_milli_jupiter_y(double t);

+double vsop87a_milli_jupiter_z(double t);

+double vsop87a_milli_mars_x(double t);

+double vsop87a_milli_mars_y(double t);

+double vsop87a_milli_mars_z(double t);

+double vsop87a_milli_mercury_x(double t);

+double vsop87a_milli_mercury_y(double t);

+double vsop87a_milli_mercury_z(double t);

+double vsop87a_milli_neptune_x(double t);

+double vsop87a_milli_neptune_y(double t);

+double vsop87a_milli_neptune_z(double t);

+double vsop87a_milli_saturn_x(double t);

+double vsop87a_milli_saturn_y(double t);

+double vsop87a_milli_saturn_z(double t);

+double vsop87a_milli_uranus_x(double t);

+double vsop87a_milli_uranus_y(double t);

+double vsop87a_milli_uranus_z(double t);

+double vsop87a_milli_venus_x(double t);

+double vsop87a_milli_venus_y(double t);

+double vsop87a_milli_venus_z(double t);

+

+

+void vsop87a_milli_getEarth(double t,double temp[]){

+   temp[0]=vsop87a_milli_earth_x(t);

+   temp[1]=vsop87a_milli_earth_y(t);

+   temp[2]=vsop87a_milli_earth_z(t);

+}

+

+void vsop87a_milli_getEmb(double t,double temp[]){

+   temp[0]=vsop87a_milli_emb_x(t);

+   temp[1]=vsop87a_milli_emb_y(t);

+   temp[2]=vsop87a_milli_emb_z(t);

+}

+

+void vsop87a_milli_getJupiter(double t,double temp[]){

+   temp[0]=vsop87a_milli_jupiter_x(t);

+   temp[1]=vsop87a_milli_jupiter_y(t);

+   temp[2]=vsop87a_milli_jupiter_z(t);

+}

+

+void vsop87a_milli_getMars(double t,double temp[]){

+   temp[0]=vsop87a_milli_mars_x(t);

+   temp[1]=vsop87a_milli_mars_y(t);

+   temp[2]=vsop87a_milli_mars_z(t);

+}

+

+void vsop87a_milli_getMercury(double t,double temp[]){

+   temp[0]=vsop87a_milli_mercury_x(t);

+   temp[1]=vsop87a_milli_mercury_y(t);

+   temp[2]=vsop87a_milli_mercury_z(t);

+}

+

+void vsop87a_milli_getNeptune(double t,double temp[]){

+   temp[0]=vsop87a_milli_neptune_x(t);

+   temp[1]=vsop87a_milli_neptune_y(t);

+   temp[2]=vsop87a_milli_neptune_z(t);

+}

+

+void vsop87a_milli_getSaturn(double t,double temp[]){

+   temp[0]=vsop87a_milli_saturn_x(t);

+   temp[1]=vsop87a_milli_saturn_y(t);

+   temp[2]=vsop87a_milli_saturn_z(t);

+}

+

+void vsop87a_milli_getUranus(double t,double temp[]){

+   temp[0]=vsop87a_milli_uranus_x(t);

+   temp[1]=vsop87a_milli_uranus_y(t);

+   temp[2]=vsop87a_milli_uranus_z(t);

+}

+

+void vsop87a_milli_getVenus(double t,double temp[]){

+   temp[0]=vsop87a_milli_venus_x(t);

+   temp[1]=vsop87a_milli_venus_y(t);

+   temp[2]=vsop87a_milli_venus_z(t);

+}

+

+void vsop87a_milli_getMoon(double earth[], double emb[],double temp[]){

+   temp[0]=(emb[0]-earth[0])*(1 + 1 / 0.01230073677);

+   temp[1]=(emb[1]-earth[1])*(1 + 1 / 0.01230073677);

+   temp[2]=(emb[2]-earth[2])*(1 + 1 / 0.01230073677);

+   temp[0]=temp[0]+earth[0];

+   temp[1]=temp[1]+earth[1];

+   temp[2]=temp[2]+earth[2];

+}

+

+double vsop87a_milli_earth_x(double t){

+   double earth_x_0=0.0;

+   earth_x_0+=     0.99982928844 * cos( 1.75348568475 +     6283.07584999140*t);

+   earth_x_0+=     0.00835257300 * cos( 1.71034539450 +    12566.15169998280*t);

+   earth_x_0+=     0.00561144206 * cos( 0.00000000000 +        0.00000000000*t);

+   earth_x_0+=     0.00010466628 * cos( 1.66722645223 +    18849.22754997420*t);

+   earth_x_0+=     0.00003110838 * cos( 0.66875185215 +    83996.84731811189*t);

+   earth_x_0+=     0.00002552498 * cos( 0.58310207301 +      529.69096509460*t);

+   earth_x_0+=     0.00002137256 * cos( 1.09235189672 +     1577.34354244780*t);

+   earth_x_0+=     0.00001709103 * cos( 0.49540223397 +     6279.55273164240*t);

+   earth_x_0+=     0.00001707882 * cos( 6.15315547484 +     6286.59896834040*t);

+   earth_x_0+=     0.00001445242 * cos( 3.47272783760 +     2352.86615377180*t);

+   earth_x_0+=     0.00001091006 * cos( 3.68984782465 +     5223.69391980220*t);

+

+   double earth_x_1=0.0;

+   earth_x_1+=     0.00123403056 * cos( 0.00000000000 +        0.00000000000*t);

+   earth_x_1+=     0.00051500156 * cos( 6.00266267204 +    12566.15169998280*t);

+   earth_x_1+=     0.00001290726 * cos( 5.95943124583 +    18849.22754997420*t);

+   earth_x_1+=     0.00001068627 * cos( 2.01554176551 +     6283.07584999140*t);

+   earth_x_1=earth_x_1 * t;

+

+   double earth_x_2=0.0;

+   earth_x_2+=     0.00004143217 * cos( 3.14159265359 +        0.00000000000*t);

+   earth_x_2+=     0.00002175695 * cos( 4.39999849572 +    12566.15169998280*t);

+   earth_x_2=earth_x_2 * t * t;

+

+   return earth_x_0+earth_x_1+earth_x_2;

+}

+

+double vsop87a_milli_earth_y(double t){

+   double earth_y_0=0.0;

+   earth_y_0+=     0.99989211030 * cos( 0.18265890456 +     6283.07584999140*t);

+   earth_y_0+=     0.02442699036 * cos( 3.14159265359 +        0.00000000000*t);

+   earth_y_0+=     0.00835292314 * cos( 0.13952878991 +    12566.15169998280*t);

+   earth_y_0+=     0.00010466965 * cos( 0.09641690558 +    18849.22754997420*t);

+   earth_y_0+=     0.00003110838 * cos( 5.38114091484 +    83996.84731811189*t);

+   earth_y_0+=     0.00002570338 * cos( 5.30103973360 +      529.69096509460*t);

+   earth_y_0+=     0.00002147473 * cos( 2.66253538905 +     1577.34354244780*t);

+   earth_y_0+=     0.00001709219 * cos( 5.20780401071 +     6279.55273164240*t);

+   earth_y_0+=     0.00001707987 * cos( 4.58232858766 +     6286.59896834040*t);

+   earth_y_0+=     0.00001440265 * cos( 1.90068164664 +     2352.86615377180*t);

+   earth_y_0+=     0.00001135092 * cos( 5.27313415220 +     5223.69391980220*t);

+

+   double earth_y_1=0.0;

+   earth_y_1+=     0.00093046324 * cos( 0.00000000000 +        0.00000000000*t);

+   earth_y_1+=     0.00051506609 * cos( 4.43180499286 +    12566.15169998280*t);

+   earth_y_1+=     0.00001290800 * cos( 4.38860548540 +    18849.22754997420*t);

+   earth_y_1=earth_y_1 * t;

+

+   double earth_y_2=0.0;

+   earth_y_2+=     0.00005080208 * cos( 0.00000000000 +        0.00000000000*t);

+   earth_y_2+=     0.00002178016 * cos( 2.82957544235 +    12566.15169998280*t);

+   earth_y_2+=     0.00001020487 * cos( 4.63746718598 +     6283.07584999140*t);

+   earth_y_2=earth_y_2 * t * t;

+

+   return earth_y_0+earth_y_1+earth_y_2;

+}

+

+double vsop87a_milli_earth_z(double t){

+   double earth_z_1=0.0;

+   earth_z_1+=     0.00227822442 * cos( 3.41372504278 +     6283.07584999140*t);

+   earth_z_1+=     0.00005429282 * cos( 0.00000000000 +        0.00000000000*t);

+   earth_z_1+=     0.00001903183 * cos( 3.37061270964 +    12566.15169998280*t);

+   earth_z_1=earth_z_1 * t;

+

+   double earth_z_2=0.0;

+   earth_z_2+=     0.00009721989 * cos( 5.15233725915 +     6283.07584999140*t);

+   earth_z_2=earth_z_2 * t * t;

+

+   return earth_z_1+earth_z_2;

+}

+

+double vsop87a_milli_emb_x(double t){

+   double emb_x_0=0.0;

+   emb_x_0+=     0.99982927460 * cos( 1.75348568475 +     6283.07584999140*t);

+   emb_x_0+=     0.00835257300 * cos( 1.71034539450 +    12566.15169998280*t);

+   emb_x_0+=     0.00561144161 * cos( 0.00000000000 +        0.00000000000*t);

+   emb_x_0+=     0.00010466628 * cos( 1.66722645223 +    18849.22754997420*t);

+   emb_x_0+=     0.00002552498 * cos( 0.58310207301 +      529.69096509460*t);

+   emb_x_0+=     0.00002137256 * cos( 1.09235189672 +     1577.34354244780*t);

+   emb_x_0+=     0.00001709103 * cos( 0.49540223397 +     6279.55273164240*t);

+   emb_x_0+=     0.00001707882 * cos( 6.15315547484 +     6286.59896834040*t);

+   emb_x_0+=     0.00001445242 * cos( 3.47272783760 +     2352.86615377180*t);

+   emb_x_0+=     0.00001091006 * cos( 3.68984782465 +     5223.69391980220*t);

+

+   double emb_x_1=0.0;

+   emb_x_1+=     0.00123403046 * cos( 0.00000000000 +        0.00000000000*t);

+   emb_x_1+=     0.00051500156 * cos( 6.00266267204 +    12566.15169998280*t);

+   emb_x_1+=     0.00001290726 * cos( 5.95943124583 +    18849.22754997420*t);

+   emb_x_1+=     0.00001068627 * cos( 2.01554176551 +     6283.07584999140*t);

+   emb_x_1=emb_x_1 * t;

+

+   double emb_x_2=0.0;

+   emb_x_2+=     0.00004143217 * cos( 3.14159265359 +        0.00000000000*t);

+   emb_x_2+=     0.00002175695 * cos( 4.39999849572 +    12566.15169998280*t);

+   emb_x_2=emb_x_2 * t * t;

+

+   return emb_x_0+emb_x_1+emb_x_2;

+}

+

+double vsop87a_milli_emb_y(double t){

+   double emb_y_0=0.0;

+   emb_y_0+=     0.99989209645 * cos( 0.18265890456 +     6283.07584999140*t);

+   emb_y_0+=     0.02442698841 * cos( 3.14159265359 +        0.00000000000*t);

+   emb_y_0+=     0.00835292314 * cos( 0.13952878991 +    12566.15169998280*t);

+   emb_y_0+=     0.00010466965 * cos( 0.09641690558 +    18849.22754997420*t);

+   emb_y_0+=     0.00002570338 * cos( 5.30103973360 +      529.69096509460*t);

+   emb_y_0+=     0.00002147473 * cos( 2.66253538905 +     1577.34354244780*t);

+   emb_y_0+=     0.00001709219 * cos( 5.20780401071 +     6279.55273164240*t);

+   emb_y_0+=     0.00001707987 * cos( 4.58232858766 +     6286.59896834040*t);

+   emb_y_0+=     0.00001440265 * cos( 1.90068164664 +     2352.86615377180*t);

+   emb_y_0+=     0.00001135092 * cos( 5.27313415220 +     5223.69391980220*t);

+

+   double emb_y_1=0.0;

+   emb_y_1+=     0.00093046317 * cos( 0.00000000000 +        0.00000000000*t);

+   emb_y_1+=     0.00051506609 * cos( 4.43180499286 +    12566.15169998280*t);

+   emb_y_1+=     0.00001290800 * cos( 4.38860548540 +    18849.22754997420*t);

+   emb_y_1=emb_y_1 * t;

+

+   double emb_y_2=0.0;

+   emb_y_2+=     0.00005080208 * cos( 0.00000000000 +        0.00000000000*t);

+   emb_y_2+=     0.00002178016 * cos( 2.82957544235 +    12566.15169998280*t);

+   emb_y_2+=     0.00001020487 * cos( 4.63746718598 +     6283.07584999140*t);

+   emb_y_2=emb_y_2 * t * t;

+

+   return emb_y_0+emb_y_1+emb_y_2;

+}

+

+double vsop87a_milli_emb_z(double t){

+   double emb_z_1=0.0;

+   emb_z_1+=     0.00227822442 * cos( 3.41372504278 +     6283.07584999140*t);

+   emb_z_1+=     0.00005429282 * cos( 0.00000000000 +        0.00000000000*t);

+   emb_z_1+=     0.00001903183 * cos( 3.37061270964 +    12566.15169998280*t);

+   emb_z_1=emb_z_1 * t;

+

+   double emb_z_2=0.0;

+   emb_z_2+=     0.00009721989 * cos( 5.15233725915 +     6283.07584999140*t);

+   emb_z_2=emb_z_2 * t * t;

+

+   return emb_z_1+emb_z_2;

+}

+

+double vsop87a_milli_jupiter_x(double t){

+   double jupiter_x_0=0.0;

+   jupiter_x_0+=     5.19663470114 * cos( 0.59945082355 +      529.69096509460*t);

+   jupiter_x_0+=     0.36662642320 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_x_0+=     0.12593937922 * cos( 0.94911583701 +     1059.38193018920*t);

+   jupiter_x_0+=     0.01500672056 * cos( 0.73175134610 +      522.57741809380*t);

+   jupiter_x_0+=     0.01476224578 * cos( 3.61736921122 +      536.80451209540*t);

+   jupiter_x_0+=     0.00457752736 * cos( 1.29883700755 +     1589.07289528380*t);

+   jupiter_x_0+=     0.00301689798 * cos( 5.17372551148 +        7.11354700080*t);

+   jupiter_x_0+=     0.00385975375 * cos( 2.01229910687 +      103.09277421860*t);

+   jupiter_x_0+=     0.00194025405 * cos( 5.02580363996 +      426.59819087600*t);

+   jupiter_x_0+=     0.00150678793 * cos( 6.12003027739 +      110.20632121940*t);

+   jupiter_x_0+=     0.00144867641 * cos( 5.55980577080 +      632.78373931320*t);

+   jupiter_x_0+=     0.00134226996 * cos( 0.87648567011 +      213.29909543800*t);

+   jupiter_x_0+=     0.00103494641 * cos( 6.19324769120 +     1052.26838318840*t);

+   jupiter_x_0+=     0.00114201562 * cos( 0.01567084269 +     1162.47470440780*t);

+   jupiter_x_0+=     0.00072095575 * cos( 3.96117430643 +     1066.49547719000*t);

+   jupiter_x_0+=     0.00059486083 * cos( 4.45769374358 +      949.17560896980*t);

+   jupiter_x_0+=     0.00068284021 * cos( 3.44051122631 +      846.08283475120*t);

+   jupiter_x_0+=     0.00047092251 * cos( 1.44612636451 +      419.48464387520*t);

+   jupiter_x_0+=     0.00030623417 * cos( 2.99132321427 +      206.18554843720*t);

+   jupiter_x_0+=     0.00026613459 * cos( 4.85169906494 +      323.50541665740*t);

+   jupiter_x_0+=     0.00019727457 * cos( 1.64891626213 +     2118.76386037840*t);

+   jupiter_x_0+=     0.00016481594 * cos( 1.95150056568 +      316.39186965660*t);

+   jupiter_x_0+=     0.00016101974 * cos( 0.87973155980 +      515.46387109300*t);

+   jupiter_x_0+=     0.00014209487 * cos( 2.07769621413 +      742.99006053260*t);

+   jupiter_x_0+=     0.00015192516 * cos( 6.25820127906 +      735.87651353180*t);

+   jupiter_x_0+=     0.00011423199 * cos( 3.48146108929 +      543.91805909620*t);

+   jupiter_x_0+=     0.00012155285 * cos( 3.75229924999 +      525.75881183150*t);

+   jupiter_x_0+=     0.00011996271 * cos( 0.58568573729 +      533.62311835770*t);

+   jupiter_x_0+=     0.00008468556 * cos( 3.47248751739 +      639.89728631400*t);

+   jupiter_x_0+=     0.00008223302 * cos( 5.56680447143 +     1478.86657406440*t);

+   jupiter_x_0+=     0.00008694124 * cos( 0.38262009411 +     1692.16566950240*t);

+   jupiter_x_0+=     0.00007427517 * cos( 5.98380751196 +      956.28915597060*t);

+   jupiter_x_0+=     0.00007516470 * cos( 0.92896448412 +     1265.56747862640*t);

+   jupiter_x_0+=     0.00007655867 * cos( 0.14178789086 +     1581.95934828300*t);

+   jupiter_x_0+=     0.00005318791 * cos( 1.10494016349 +      526.50957135690*t);

+   jupiter_x_0+=     0.00005218492 * cos( 3.23235129224 +      532.87235883230*t);

+   jupiter_x_0+=     0.00005777311 * cos( 5.03726165628 +       14.22709400160*t);

+   jupiter_x_0+=     0.00004622685 * cos( 3.75817086099 +     1375.77379984580*t);

+   jupiter_x_0+=     0.00003939864 * cos( 4.30892687511 +     1596.18644228460*t);

+   jupiter_x_0+=     0.00004569444 * cos( 2.15087281710 +       95.97922721780*t);

+   jupiter_x_0+=     0.00002952712 * cos( 3.85988483947 +      309.27832265580*t);

+   jupiter_x_0+=     0.00002857935 * cos( 6.01118473739 +      117.31986822020*t);

+   jupiter_x_0+=     0.00002440094 * cos( 4.23995765702 +      433.71173787680*t);

+   jupiter_x_0+=     0.00002438257 * cos( 3.88808463822 +      220.41264243880*t);

+   jupiter_x_0+=     0.00002675112 * cos( 3.18723449094 +     1169.58825140860*t);

+   jupiter_x_0+=     0.00002386425 * cos( 5.96354994324 +     1045.15483618760*t);

+   jupiter_x_0+=     0.00001870097 * cos( 0.52019313301 +     1155.36115740700*t);

+   jupiter_x_0+=     0.00001939060 * cos( 5.91883412864 +      625.67019231240*t);

+   jupiter_x_0+=     0.00001631500 * cos( 4.41910383466 +      942.06206196900*t);

+   jupiter_x_0+=     0.00001451667 * cos( 5.76112706040 +      853.19638175200*t);

+   jupiter_x_0+=     0.00001361286 * cos( 1.34792748837 +     1368.66025284500*t);

+   jupiter_x_0+=     0.00001663331 * cos( 1.94010629194 +      838.96928775040*t);

+   jupiter_x_0+=     0.00001611229 * cos( 5.49324974845 +       74.78159856730*t);

+   jupiter_x_0+=     0.00001033570 * cos( 0.08907208789 +     1795.25844372100*t);

+   jupiter_x_0+=     0.00001088284 * cos( 1.13406104190 +      527.24328453980*t);

+   jupiter_x_0+=     0.00001080643 * cos( 3.20528362573 +      532.13864564940*t);

+

+   double jupiter_x_1=0.0;

+   jupiter_x_1+=     0.00882389251 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_x_1+=     0.00635297172 * cos( 0.10662156868 +     1059.38193018920*t);

+   jupiter_x_1+=     0.00599720482 * cos( 2.42996678275 +      522.57741809380*t);

+   jupiter_x_1+=     0.00589157060 * cos( 1.91556314637 +      536.80451209540*t);

+   jupiter_x_1+=     0.00081697204 * cos( 3.46668108797 +        7.11354700080*t);

+   jupiter_x_1+=     0.00046201898 * cos( 0.45714214032 +     1589.07289528380*t);

+   jupiter_x_1+=     0.00032508590 * cos( 1.74648849928 +     1052.26838318840*t);

+   jupiter_x_1+=     0.00033891193 * cos( 4.10113482752 +      529.69096509460*t);

+   jupiter_x_1+=     0.00031234303 * cos( 2.34698051502 +     1066.49547719000*t);

+   jupiter_x_1+=     0.00021244363 * cos( 4.36576178953 +      110.20632121940*t);

+   jupiter_x_1+=     0.00018156701 * cos( 4.00572238779 +      426.59819087600*t);

+   jupiter_x_1+=     0.00013577576 * cos( 0.30008010246 +      632.78373931320*t);

+   jupiter_x_1+=     0.00012889505 * cos( 2.57489294062 +      515.46387109300*t);

+   jupiter_x_1+=     0.00009125875 * cos( 1.78082469962 +      543.91805909620*t);

+   jupiter_x_1+=     0.00008085991 * cos( 6.16136518902 +      949.17560896980*t);

+   jupiter_x_1+=     0.00007142547 * cos( 3.17267801203 +      323.50541665740*t);

+   jupiter_x_1+=     0.00004292240 * cos( 4.74970626655 +      206.18554843720*t);

+   jupiter_x_1+=     0.00004393977 * cos( 1.14770788063 +      735.87651353180*t);

+   jupiter_x_1+=     0.00003399164 * cos( 2.90091450747 +      526.50957135690*t);

+   jupiter_x_1+=     0.00003333344 * cos( 1.43691652967 +      532.87235883230*t);

+   jupiter_x_1+=     0.00003873467 * cos( 3.33648870101 +       14.22709400160*t);

+   jupiter_x_1+=     0.00003044408 * cos( 1.65428048669 +      525.75881183150*t);

+   jupiter_x_1+=     0.00003001874 * cos( 2.68376982746 +      533.62311835770*t);

+   jupiter_x_1+=     0.00002933359 * cos( 2.61899855005 +      419.48464387520*t);

+   jupiter_x_1+=     0.00002438199 * cos( 3.60655644537 +      316.39186965660*t);

+   jupiter_x_1+=     0.00002804218 * cos( 4.89742591320 +      103.09277421860*t);

+   jupiter_x_1+=     0.00002990245 * cos( 0.80692155639 +     2118.76386037840*t);

+   jupiter_x_1+=     0.00001977572 * cos( 5.08915489088 +      956.28915597060*t);

+   jupiter_x_1+=     0.00001853679 * cos( 2.76941001747 +     1596.18644228460*t);

+   jupiter_x_1+=     0.00001772800 * cos( 0.72631739446 +      742.99006053260*t);

+   jupiter_x_1+=     0.00001812965 * cos( 3.84602148747 +       95.97922721780*t);

+   jupiter_x_1+=     0.00001532945 * cos( 4.31556714501 +      117.31986822020*t);

+   jupiter_x_1+=     0.00001904067 * cos( 1.85937873703 +     1581.95934828300*t);

+   jupiter_x_1+=     0.00001539212 * cos( 1.47899172821 +      639.89728631400*t);

+   jupiter_x_1+=     0.00001632362 * cos( 1.41504212408 +     1045.15483618760*t);

+   jupiter_x_1+=     0.00001023812 * cos( 2.57182697715 +      433.71173787680*t);

+   jupiter_x_1+=     0.00001055422 * cos( 2.50844222977 +     1265.56747862640*t);

+   jupiter_x_1=jupiter_x_1 * t;

+

+   double jupiter_x_2=0.0;

+   jupiter_x_2+=     0.00123864644 * cos( 4.13563277513 +      522.57741809380*t);

+   jupiter_x_2+=     0.00121521296 * cos( 0.21155109275 +      536.80451209540*t);

+   jupiter_x_2+=     0.00085355503 * cos( 0.00000000000 +        0.00000000000*t);

+   jupiter_x_2+=     0.00077685547 * cos( 5.29776154458 +      529.69096509460*t);

+   jupiter_x_2+=     0.00041410887 * cos( 5.12291589939 +     1059.38193018920*t);

+   jupiter_x_2+=     0.00011423070 * cos( 1.72917878238 +        7.11354700080*t);

+   jupiter_x_2+=     0.00007051587 * cos( 0.74163703419 +     1066.49547719000*t);

+   jupiter_x_2+=     0.00005711029 * cos( 3.63172846494 +     1052.26838318840*t);

+   jupiter_x_2+=     0.00005242644 * cos( 4.27482379441 +      515.46387109300*t);

+   jupiter_x_2+=     0.00004039540 * cos( 5.58417732117 +     1589.07289528380*t);

+   jupiter_x_2+=     0.00003706457 * cos( 0.07769981349 +      543.91805909620*t);

+   jupiter_x_2+=     0.00001698817 * cos( 2.44284418066 +      110.20632121940*t);

+   jupiter_x_2+=     0.00001134598 * cos( 2.35807061809 +      426.59819087600*t);

+   jupiter_x_2+=     0.00001322673 * cos( 1.63142549980 +       14.22709400160*t);

+   jupiter_x_2=jupiter_x_2 * t * t;

+

+   double jupiter_x_3=0.0;

+   jupiter_x_3+=     0.00017071323 * cos( 5.86133022278 +      522.57741809380*t);

+   jupiter_x_3+=     0.00016713548 * cos( 4.77458794485 +      536.80451209540*t);

+   jupiter_x_3+=     0.00003348610 * cos( 0.00000000000 +        0.00000000000*t);

+   jupiter_x_3+=     0.00001787838 * cos( 3.56550298031 +     1059.38193018920*t);

+   jupiter_x_3+=     0.00001435449 * cos( 5.98502036587 +      515.46387109300*t);

+   jupiter_x_3+=     0.00001080194 * cos( 5.42530305914 +     1066.49547719000*t);

+   jupiter_x_3+=     0.00001014206 * cos( 4.64773902077 +      543.91805909620*t);

+   jupiter_x_3+=     0.00001073175 * cos( 6.22314467964 +        7.11354700080*t);

+   jupiter_x_3=jupiter_x_3 * t * t * t;

+

+   double jupiter_x_4=0.0;

+   jupiter_x_4+=     0.00001762402 * cos( 1.32863039757 +      522.57741809380*t);

+   jupiter_x_4+=     0.00001717846 * cos( 3.03331531843 +      536.80451209540*t);

+   jupiter_x_4=jupiter_x_4 * t * t * t * t;

+

+   return jupiter_x_0+jupiter_x_1+jupiter_x_2+jupiter_x_3+jupiter_x_4;

+}

+

+double vsop87a_milli_jupiter_y(double t){

+   double jupiter_y_0=0.0;

+   jupiter_y_0+=     5.19520046589 * cos( 5.31203162731 +      529.69096509460*t);

+   jupiter_y_0+=     0.12592862602 * cos( 5.66160227728 +     1059.38193018920*t);

+   jupiter_y_0+=     0.09363670616 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_y_0+=     0.01508275299 * cos( 5.43934968102 +      522.57741809380*t);

+   jupiter_y_0+=     0.01475809370 * cos( 2.04679566495 +      536.80451209540*t);

+   jupiter_y_0+=     0.00457750806 * cos( 6.01129093501 +     1589.07289528380*t);

+   jupiter_y_0+=     0.00300686679 * cos( 3.60948050740 +        7.11354700080*t);

+   jupiter_y_0+=     0.00378285578 * cos( 3.53006782383 +      103.09277421860*t);

+   jupiter_y_0+=     0.00192333128 * cos( 3.45690564771 +      426.59819087600*t);

+   jupiter_y_0+=     0.00146104656 * cos( 4.62267224431 +      110.20632121940*t);

+   jupiter_y_0+=     0.00139480058 * cos( 4.00075307706 +      632.78373931320*t);

+   jupiter_y_0+=     0.00132696764 * cos( 5.62184581859 +      213.29909543800*t);

+   jupiter_y_0+=     0.00101999807 * cos( 4.57594598884 +     1052.26838318840*t);

+   jupiter_y_0+=     0.00114043110 * cos( 4.72982262969 +     1162.47470440780*t);

+   jupiter_y_0+=     0.00072091178 * cos( 2.39048659148 +     1066.49547719000*t);

+   jupiter_y_0+=     0.00059051769 * cos( 2.89529070968 +      949.17560896980*t);

+   jupiter_y_0+=     0.00068374489 * cos( 1.86537074374 +      846.08283475120*t);

+   jupiter_y_0+=     0.00029807369 * cos( 4.52105772740 +      206.18554843720*t);

+   jupiter_y_0+=     0.00026933579 * cos( 3.86233956827 +      419.48464387520*t);

+   jupiter_y_0+=     0.00026619714 * cos( 3.28203174951 +      323.50541665740*t);

+   jupiter_y_0+=     0.00020873780 * cos( 3.79369881757 +      735.87651353180*t);

+   jupiter_y_0+=     0.00019727397 * cos( 0.07818534532 +     2118.76386037840*t);

+   jupiter_y_0+=     0.00018639846 * cos( 0.38751972138 +      316.39186965660*t);

+   jupiter_y_0+=     0.00016355726 * cos( 5.56997881604 +      515.46387109300*t);

+   jupiter_y_0+=     0.00014606858 * cos( 0.47759399145 +      742.99006053260*t);

+   jupiter_y_0+=     0.00011419853 * cos( 1.91089341468 +      543.91805909620*t);

+   jupiter_y_0+=     0.00012153427 * cos( 2.18151972499 +      525.75881183150*t);

+   jupiter_y_0+=     0.00011988875 * cos( 5.29687602089 +      533.62311835770*t);

+   jupiter_y_0+=     0.00008443107 * cos( 1.91435801697 +      639.89728631400*t);

+   jupiter_y_0+=     0.00008163163 * cos( 4.00303742375 +     1478.86657406440*t);

+   jupiter_y_0+=     0.00008732789 * cos( 5.09607066097 +     1692.16566950240*t);

+   jupiter_y_0+=     0.00007414115 * cos( 4.41141990461 +      956.28915597060*t);

+   jupiter_y_0+=     0.00007619486 * cos( 5.59554151997 +     1265.56747862640*t);

+   jupiter_y_0+=     0.00007779184 * cos( 4.83346300662 +     1581.95934828300*t);

+   jupiter_y_0+=     0.00005322882 * cos( 5.81740472645 +      526.50957135690*t);

+   jupiter_y_0+=     0.00005217025 * cos( 1.66178643542 +      532.87235883230*t);

+   jupiter_y_0+=     0.00005772132 * cos( 3.46915716927 +       14.22709400160*t);

+   jupiter_y_0+=     0.00004528355 * cos( 2.18377558038 +     1375.77379984580*t);

+   jupiter_y_0+=     0.00003939875 * cos( 2.73830531054 +     1596.18644228460*t);

+   jupiter_y_0+=     0.00004567181 * cos( 3.71300776935 +       95.97922721780*t);

+   jupiter_y_0+=     0.00003235419 * cos( 4.76600347062 +      625.67019231240*t);

+   jupiter_y_0+=     0.00003140740 * cos( 5.59566796922 +      309.27832265580*t);

+   jupiter_y_0+=     0.00002855423 * cos( 4.44478286006 +      117.31986822020*t);

+   jupiter_y_0+=     0.00002445625 * cos( 2.67036952230 +      433.71173787680*t);

+   jupiter_y_0+=     0.00002253545 * cos( 4.28462825722 +      838.96928775040*t);

+   jupiter_y_0+=     0.00002672262 * cos( 1.61857897069 +     1169.58825140860*t);

+   jupiter_y_0+=     0.00002423639 * cos( 2.32942339839 +      220.41264243880*t);

+   jupiter_y_0+=     0.00002362662 * cos( 4.60417580207 +     1155.36115740700*t);

+   jupiter_y_0+=     0.00002409581 * cos( 4.33196301609 +     1045.15483618760*t);

+   jupiter_y_0+=     0.00001458169 * cos( 4.18761881277 +      853.19638175200*t);

+   jupiter_y_0+=     0.00001432195 * cos( 3.24824554500 +      942.06206196900*t);

+   jupiter_y_0+=     0.00001646568 * cos( 3.91965876562 +       74.78159856730*t);

+   jupiter_y_0+=     0.00001050270 * cos( 4.83706014327 +     1795.25844372100*t);

+   jupiter_y_0+=     0.00001002355 * cos( 1.50931939870 +     1272.68102562720*t);

+   jupiter_y_0+=     0.00001087727 * cos( 5.84673086939 +      527.24328453980*t);

+   jupiter_y_0+=     0.00001079512 * cos( 1.63448507346 +      532.13864564940*t);

+

+   double jupiter_y_1=0.0;

+   jupiter_y_1+=     0.01694798253 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_y_1+=     0.00634859798 * cos( 4.81903199650 +     1059.38193018920*t);

+   jupiter_y_1+=     0.00601160431 * cos( 0.85811249940 +      522.57741809380*t);

+   jupiter_y_1+=     0.00588928504 * cos( 0.34491576890 +      536.80451209540*t);

+   jupiter_y_1+=     0.00081187145 * cos( 1.90914316532 +        7.11354700080*t);

+   jupiter_y_1+=     0.00046888090 * cos( 1.91294535618 +      529.69096509460*t);

+   jupiter_y_1+=     0.00046194129 * cos( 5.16955994561 +     1589.07289528380*t);

+   jupiter_y_1+=     0.00032503453 * cos( 0.17640743623 +     1052.26838318840*t);

+   jupiter_y_1+=     0.00031231694 * cos( 0.77623645597 +     1066.49547719000*t);

+   jupiter_y_1+=     0.00019462096 * cos( 3.00957119470 +      110.20632121940*t);

+   jupiter_y_1+=     0.00017738615 * cos( 2.46531787101 +      426.59819087600*t);

+   jupiter_y_1+=     0.00013701692 * cos( 5.02070197804 +      632.78373931320*t);

+   jupiter_y_1+=     0.00013034616 * cos( 0.98979834442 +      515.46387109300*t);

+   jupiter_y_1+=     0.00009122660 * cos( 0.21022587969 +      543.91805909620*t);

+   jupiter_y_1+=     0.00008109050 * cos( 4.58123811601 +      949.17560896980*t);

+   jupiter_y_1+=     0.00007145229 * cos( 1.60381236094 +      323.50541665740*t);

+   jupiter_y_1+=     0.00003957592 * cos( 6.18550697817 +      206.18554843720*t);

+   jupiter_y_1+=     0.00004347346 * cos( 5.85522835488 +      735.87651353180*t);

+   jupiter_y_1+=     0.00003401735 * cos( 1.33033225252 +      526.50957135690*t);

+   jupiter_y_1+=     0.00003331887 * cos( 6.14951835712 +      532.87235883230*t);

+   jupiter_y_1+=     0.00003866147 * cos( 1.76877582038 +       14.22709400160*t);

+   jupiter_y_1+=     0.00003094257 * cos( 1.00670454701 +      419.48464387520*t);

+   jupiter_y_1+=     0.00003044205 * cos( 0.08329779827 +      525.75881183150*t);

+   jupiter_y_1+=     0.00003001484 * cos( 1.11280606283 +      533.62311835770*t);

+   jupiter_y_1+=     0.00002977284 * cos( 3.35507028507 +      103.09277421860*t);

+   jupiter_y_1+=     0.00002347100 * cos( 2.06781775390 +      316.39186965660*t);

+   jupiter_y_1+=     0.00002990192 * cos( 5.51944830506 +     2118.76386037840*t);

+   jupiter_y_1+=     0.00001875464 * cos( 5.32657356489 +      742.99006053260*t);

+   jupiter_y_1+=     0.00001854067 * cos( 1.19908734197 +     1596.18644228460*t);

+   jupiter_y_1+=     0.00001968401 * cos( 3.51896739844 +      956.28915597060*t);

+   jupiter_y_1+=     0.00001808627 * cos( 5.40287543026 +       95.97922721780*t);

+   jupiter_y_1+=     0.00001530472 * cos( 2.75094722237 +      117.31986822020*t);

+   jupiter_y_1+=     0.00001885393 * cos( 0.29905973710 +     1581.95934828300*t);

+   jupiter_y_1+=     0.00001516541 * cos( 6.21684203571 +      639.89728631400*t);

+   jupiter_y_1+=     0.00001636913 * cos( 6.09270756447 +     1045.15483618760*t);

+   jupiter_y_1+=     0.00001260123 * cos( 0.07143173954 +      625.67019231240*t);

+   jupiter_y_1+=     0.00001028165 * cos( 1.00301485824 +      433.71173787680*t);

+   jupiter_y_1+=     0.00001035933 * cos( 0.98273794152 +     1265.56747862640*t);

+   jupiter_y_1=jupiter_y_1 * t;

+

+   double jupiter_y_2=0.0;

+   jupiter_y_2+=     0.00124032509 * cos( 2.56495576833 +      522.57741809380*t);

+   jupiter_y_2+=     0.00121455991 * cos( 4.92398766380 +      536.80451209540*t);

+   jupiter_y_2+=     0.00076523263 * cos( 3.75913371793 +      529.69096509460*t);

+   jupiter_y_2+=     0.00076943042 * cos( 3.14159265359 +        0.00000000000*t);

+   jupiter_y_2+=     0.00041357600 * cos( 3.55228440457 +     1059.38193018920*t);

+   jupiter_y_2+=     0.00011277667 * cos( 0.18559902389 +        7.11354700080*t);

+   jupiter_y_2+=     0.00007051103 * cos( 5.45404368570 +     1066.49547719000*t);

+   jupiter_y_2+=     0.00005719440 * cos( 2.05970000230 +     1052.26838318840*t);

+   jupiter_y_2+=     0.00005286157 * cos( 2.69490465064 +      515.46387109300*t);

+   jupiter_y_2+=     0.00004039038 * cos( 4.01341034637 +     1589.07289528380*t);

+   jupiter_y_2+=     0.00003704528 * cos( 4.79029292271 +      543.91805909620*t);

+   jupiter_y_2+=     0.00001280283 * cos( 1.47574006861 +      110.20632121940*t);

+   jupiter_y_2+=     0.00001059783 * cos( 0.89610748176 +      426.59819087600*t);

+   jupiter_y_2+=     0.00001320627 * cos( 0.05786048417 +       14.22709400160*t);

+   jupiter_y_2=jupiter_y_2 * t * t;

+

+   double jupiter_y_3=0.0;

+   jupiter_y_3+=     0.00017085516 * cos( 4.29096904063 +      522.57741809380*t);

+   jupiter_y_3+=     0.00016701353 * cos( 3.20365737109 +      536.80451209540*t);

+   jupiter_y_3+=     0.00004006038 * cos( 0.00000000000 +        0.00000000000*t);

+   jupiter_y_3+=     0.00001782451 * cos( 1.99283071153 +     1059.38193018920*t);

+   jupiter_y_3+=     0.00001443816 * cos( 4.40866555269 +      515.46387109300*t);

+   jupiter_y_3+=     0.00001079405 * cos( 3.85450799252 +     1066.49547719000*t);

+   jupiter_y_3+=     0.00001013157 * cos( 3.07729621279 +      543.91805909620*t);

+   jupiter_y_3+=     0.00001055565 * cos( 4.70184773789 +        7.11354700080*t);

+   jupiter_y_3=jupiter_y_3 * t * t * t;

+

+   double jupiter_y_4=0.0;

+   jupiter_y_4+=     0.00001762645 * cos( 6.04159386554 +      522.57741809380*t);

+   jupiter_y_4+=     0.00001716045 * cos( 1.46206285710 +      536.80451209540*t);

+   jupiter_y_4=jupiter_y_4 * t * t * t * t;

+

+   return jupiter_y_0+jupiter_y_1+jupiter_y_2+jupiter_y_3+jupiter_y_4;

+}

+

+double vsop87a_milli_jupiter_z(double t){

+   double jupiter_z_0=0.0;

+   jupiter_z_0+=     0.11823100489 * cos( 3.55844646343 +      529.69096509460*t);

+   jupiter_z_0+=     0.00859031952 * cos( 0.00000000000 +        0.00000000000*t);

+   jupiter_z_0+=     0.00286562094 * cos( 3.90812238338 +     1059.38193018920*t);

+   jupiter_z_0+=     0.00042388592 * cos( 3.60144191032 +      522.57741809380*t);

+   jupiter_z_0+=     0.00033295491 * cos( 0.30297050585 +      536.80451209540*t);

+   jupiter_z_0+=     0.00010416160 * cos( 4.25764593061 +     1589.07289528380*t);

+   jupiter_z_0+=     0.00007449294 * cos( 5.24213104150 +      103.09277421860*t);

+   jupiter_z_0+=     0.00006910102 * cos( 1.75032945752 +        7.11354700080*t);

+   jupiter_z_0+=     0.00005292012 * cos( 1.68231447192 +      426.59819087600*t);

+   jupiter_z_0+=     0.00004313598 * cos( 3.70673689841 +      213.29909543800*t);

+   jupiter_z_0+=     0.00003784265 * cos( 2.71522544491 +      110.20632121940*t);

+   jupiter_z_0+=     0.00003798016 * cos( 2.16715743175 +      632.78373931320*t);

+   jupiter_z_0+=     0.00002455385 * cos( 2.96904135659 +     1052.26838318840*t);

+   jupiter_z_0+=     0.00002461547 * cos( 2.99889460411 +     1162.47470440780*t);

+   jupiter_z_0+=     0.00002001451 * cos( 2.68535838309 +      419.48464387520*t);

+   jupiter_z_0+=     0.00002163471 * cos( 6.26718259854 +      846.08283475120*t);

+   jupiter_z_0+=     0.00001633653 * cos( 0.64194743493 +     1066.49547719000*t);

+   jupiter_z_0+=     0.00001450672 * cos( 1.17108416193 +      949.17560896980*t);

+

+   double jupiter_z_1=0.0;

+   jupiter_z_1+=     0.00407072175 * cos( 1.52699353482 +      529.69096509460*t);

+   jupiter_z_1+=     0.00020307341 * cos( 2.59878269248 +     1059.38193018920*t);

+   jupiter_z_1+=     0.00014424953 * cos( 4.85400155025 +      536.80451209540*t);

+   jupiter_z_1+=     0.00015474611 * cos( 0.00000000000 +        0.00000000000*t);

+   jupiter_z_1+=     0.00012730364 * cos( 5.45536715732 +      522.57741809380*t);

+   jupiter_z_1+=     0.00002100882 * cos( 0.09538864287 +        7.11354700080*t);

+   jupiter_z_1+=     0.00001230425 * cos( 3.14222500244 +     1589.07289528380*t);

+   jupiter_z_1=jupiter_z_1 * t;

+

+   double jupiter_z_2=0.0;

+   jupiter_z_2+=     0.00028635326 * cos( 3.01374166973 +      529.69096509460*t);

+   jupiter_z_2+=     0.00003114752 * cos( 3.13228646176 +      536.80451209540*t);

+   jupiter_z_2+=     0.00002379765 * cos( 0.95574345340 +      522.57741809380*t);

+   jupiter_z_2+=     0.00001310111 * cos( 2.05263704913 +     1059.38193018920*t);

+   jupiter_z_2=jupiter_z_2 * t * t;

+

+   return jupiter_z_0+jupiter_z_1+jupiter_z_2;

+}

+

+double vsop87a_milli_mars_x(double t){

+   double mars_x_0=0.0;

+   mars_x_0+=     1.51769936383 * cos( 6.20403346548 +     3340.61242669980*t);

+   mars_x_0+=     0.19502945246 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_x_0+=     0.07070919655 * cos( 0.25870338558 +     6681.22485339960*t);

+   mars_x_0+=     0.00494196914 * cos( 0.59669127768 +    10021.83728009940*t);

+   mars_x_0+=     0.00040938237 * cos( 0.93473307419 +    13362.44970679920*t);

+   mars_x_0+=     0.00021067199 * cos( 1.80435656154 +     3337.08930835080*t);

+   mars_x_0+=     0.00021041626 * cos( 1.17895619474 +     3344.13554504880*t);

+   mars_x_0+=     0.00011370375 * cos( 4.83265211109 +     1059.38193018920*t);

+   mars_x_0+=     0.00013527976 * cos( 0.63010765169 +      529.69096509460*t);

+   mars_x_0+=     0.00006774107 * cos( 3.61785048282 +     3340.59517304760*t);

+   mars_x_0+=     0.00006774060 * cos( 5.64862211431 +     3340.62968035200*t);

+   mars_x_0+=     0.00008226069 * cos( 1.86843519535 +     2281.23049651060*t);

+   mars_x_0+=     0.00005469046 * cos( 1.13324429003 +     2942.46342329160*t);

+   mars_x_0+=     0.00004817134 * cos( 1.85091045536 +     3738.76143010800*t);

+   mars_x_0+=     0.00004937579 * cos( 4.43241440654 +     5621.84292321040*t);

+   mars_x_0+=     0.00005276260 * cos( 2.33148083116 +     6151.53388830500*t);

+   mars_x_0+=     0.00003636667 * cos( 6.11397592106 +      796.29800681640*t);

+   mars_x_0+=     0.00003725823 * cos( 1.27280182943 +    16703.06213349900*t);

+   mars_x_0+=     0.00003729746 * cos( 1.21398323637 +      398.14900340820*t);

+   mars_x_0+=     0.00002368513 * cos( 2.96841895360 +     2544.31441988340*t);

+   mars_x_0+=     0.00002397865 * cos( 0.63553674054 +     3149.16416058820*t);

+   mars_x_0+=     0.00002274646 * cos( 2.35708328853 +     3532.06069281140*t);

+   mars_x_0+=     0.00001977579 * cos( 2.14087826110 +     6677.70173505060*t);

+   mars_x_0+=     0.00002229176 * cos( 1.69588962513 +     3340.54511639700*t);

+   mars_x_0+=     0.00002229117 * cos( 1.28739323821 +     3340.67973700260*t);

+   mars_x_0+=     0.00002182206 * cos( 1.69655112969 +     6283.07584999140*t);

+   mars_x_0+=     0.00002241010 * cos( 4.82218655311 +     8962.45534991020*t);

+   mars_x_0+=     0.00001677693 * cos( 3.14442612046 +     5884.92684658320*t);

+   mars_x_0+=     0.00001630482 * cos( 0.24117974845 +     4136.91043351620*t);

+   mars_x_0+=     0.00001958162 * cos( 1.51914544555 +     6684.74797174860*t);

+   mars_x_0+=     0.00001378470 * cos( 2.18011900021 +     1751.53953141600*t);

+   mars_x_0+=     0.00001289804 * cos( 4.70970778621 +     1194.44701022460*t);

+   mars_x_0+=     0.00001468124 * cos( 1.87869730543 +     3870.30339179440*t);

+   mars_x_0+=     0.00001290170 * cos( 0.43596325296 +     2810.92146160520*t);

+   mars_x_0+=     0.00001572540 * cos( 4.84809921789 +     1589.07289528380*t);

+

+   double mars_x_1=0.0;

+   mars_x_1+=     0.00861441374 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_x_1+=     0.00552437949 * cos( 5.09565872891 +     6681.22485339960*t);

+   mars_x_1+=     0.00077184977 * cos( 5.43315636209 +    10021.83728009940*t);

+   mars_x_1+=     0.00020467294 * cos( 5.57051812369 +     3340.61242669980*t);

+   mars_x_1+=     0.00009589581 * cos( 5.77107234791 +    13362.44970679920*t);

+   mars_x_1+=     0.00002620610 * cos( 6.22441295122 +     3344.13554504880*t);

+   mars_x_1+=     0.00002620537 * cos( 3.04172154436 +     3337.08930835080*t);

+   mars_x_1+=     0.00001163612 * cos( 6.10909257097 +    16703.06213349900*t);

+   mars_x_1=mars_x_1 * t;

+

+   double mars_x_2=0.0;

+   mars_x_2+=     0.00056323939 * cos( 0.00000000000 +        0.00000000000*t);

+   mars_x_2+=     0.00022122528 * cos( 3.54372113272 +     6681.22485339960*t);

+   mars_x_2+=     0.00006091409 * cos( 3.93272649649 +    10021.83728009940*t);

+   mars_x_2+=     0.00001451998 * cos( 3.64655666460 +     3340.61242669980*t);

+   mars_x_2+=     0.00001130613 * cos( 4.28827023222 +    13362.44970679920*t);

+   mars_x_2=mars_x_2 * t * t;

+

+   return mars_x_0+mars_x_1+mars_x_2;

+}

+

+double vsop87a_milli_mars_y(double t){

+   double mars_y_0=0.0;

+   mars_y_0+=     1.51558976277 * cos( 4.63212206588 +     3340.61242669980*t);

+   mars_y_0+=     0.07064550239 * cos( 4.97051892902 +     6681.22485339960*t);

+   mars_y_0+=     0.08655481102 * cos( 0.00000000000 +        0.00000000000*t);

+   mars_y_0+=     0.00493872848 * cos( 5.30877806694 +    10021.83728009940*t);

+   mars_y_0+=     0.00040917422 * cos( 5.64698263703 +    13362.44970679920*t);

+   mars_y_0+=     0.00021036784 * cos( 0.23240270955 +     3337.08930835080*t);

+   mars_y_0+=     0.00021012921 * cos( 5.89022773653 +     3344.13554504880*t);

+   mars_y_0+=     0.00011370034 * cos( 3.26131408801 +     1059.38193018920*t);

+   mars_y_0+=     0.00013324177 * cos( 5.34259389724 +      529.69096509460*t);

+   mars_y_0+=     0.00006764653 * cos( 4.07671230062 +     3340.62968035200*t);

+   mars_y_0+=     0.00006764700 * cos( 2.04594066912 +     3340.59517304760*t);

+   mars_y_0+=     0.00008346220 * cos( 3.42464704002 +     2281.23049651060*t);

+   mars_y_0+=     0.00005400042 * cos( 5.81507793194 +     2942.46342329160*t);

+   mars_y_0+=     0.00004809528 * cos( 0.27875310553 +     3738.76143010800*t);

+   mars_y_0+=     0.00004849523 * cos( 2.85190987550 +     5621.84292321040*t);

+   mars_y_0+=     0.00005263268 * cos( 0.75811089992 +     6151.53388830500*t);

+   mars_y_0+=     0.00003609527 * cos( 4.53244488294 +      796.29800681640*t);

+   mars_y_0+=     0.00003724293 * cos( 5.98516013322 +    16703.06213349900*t);

+   mars_y_0+=     0.00003805073 * cos( 5.94234296399 +      398.14900340820*t);

+   mars_y_0+=     0.00002394490 * cos( 5.34678816191 +     3149.16416058820*t);

+   mars_y_0+=     0.00002251027 * cos( 0.76938193892 +     3532.06069281140*t);

+   mars_y_0+=     0.00001975769 * cos( 0.56949816579 +     6677.70173505060*t);

+   mars_y_0+=     0.00002226030 * cos( 5.99867316288 +     3340.67973700260*t);

+   mars_y_0+=     0.00002226089 * cos( 0.12398424247 +     3340.54511639700*t);

+   mars_y_0+=     0.00002177591 * cos( 0.12334436516 +     6283.07584999140*t);

+   mars_y_0+=     0.00001690439 * cos( 1.58331163985 +     5884.92684658320*t);

+   mars_y_0+=     0.00002234121 * cos( 3.24909113765 +     8962.45534991020*t);

+   mars_y_0+=     0.00001628395 * cos( 4.95250906888 +     4136.91043351620*t);

+   mars_y_0+=     0.00001956411 * cos( 6.23095843554 +     6684.74797174860*t);

+   mars_y_0+=     0.00001697214 * cos( 0.81869636263 +     2544.31441988340*t);

+   mars_y_0+=     0.00001385946 * cos( 3.73437191158 +     1751.53953141600*t);

+   mars_y_0+=     0.00001439619 * cos( 5.19505958438 +     2810.92146160520*t);

+   mars_y_0+=     0.00001281890 * cos( 3.13035275682 +     1194.44701022460*t);

+   mars_y_0+=     0.00001469783 * cos( 0.30415060688 +     3870.30339179440*t);

+   mars_y_0+=     0.00001571880 * cos( 3.27679498650 +     1589.07289528380*t);

+   mars_y_0+=     0.00001575854 * cos( 2.78266835243 +     5092.15195811580*t);

+

+   double mars_y_1=0.0;

+   mars_y_1+=     0.01427324210 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_y_1+=     0.00551063753 * cos( 3.52128320402 +     6681.22485339960*t);

+   mars_y_1+=     0.00077091913 * cos( 3.86082685753 +    10021.83728009940*t);

+   mars_y_1+=     0.00037310491 * cos( 1.16016958445 +     3340.61242669980*t);

+   mars_y_1+=     0.00009582122 * cos( 4.19942354479 +    13362.44970679920*t);

+   mars_y_1+=     0.00002617695 * cos( 1.47284555520 +     3337.08930835080*t);

+   mars_y_1+=     0.00002611572 * cos( 4.65030772498 +     3344.13554504880*t);

+   mars_y_1+=     0.00001162955 * cos( 4.53778503576 +    16703.06213349900*t);

+   mars_y_1=mars_y_1 * t;

+

+   double mars_y_2=0.0;

+   mars_y_2+=     0.00035396765 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_y_2+=     0.00021950759 * cos( 1.96291594946 +     6681.22485339960*t);

+   mars_y_2+=     0.00006075990 * cos( 2.35864321001 +    10021.83728009940*t);

+   mars_y_2+=     0.00002571425 * cos( 5.64795745327 +     3340.61242669980*t);

+   mars_y_2+=     0.00001129099 * cos( 2.71576248963 +    13362.44970679920*t);

+   mars_y_2=mars_y_2 * t * t;

+

+   double mars_y_3=0.0;

+   mars_y_3+=     0.00001448778 * cos( 0.00000000000 +        0.00000000000*t);

+   mars_y_3=mars_y_3 * t * t * t;

+

+   return mars_y_0+mars_y_1+mars_y_2+mars_y_3;

+}

+

+double vsop87a_milli_mars_z(double t){

+   double mars_z_0=0.0;

+   mars_z_0+=     0.04901207220 * cos( 3.76712324286 +     3340.61242669980*t);

+   mars_z_0+=     0.00660669541 * cos( 0.00000000000 +        0.00000000000*t);

+   mars_z_0+=     0.00228333904 * cos( 4.10544022266 +     6681.22485339960*t);

+   mars_z_0+=     0.00015958402 * cos( 4.44367058261 +    10021.83728009940*t);

+   mars_z_0+=     0.00001321976 * cos( 4.78186604114 +    13362.44970679920*t);

+

+   double mars_z_1=0.0;

+   mars_z_1+=     0.00331842958 * cos( 6.05027773492 +     3340.61242669980*t);

+   mars_z_1+=     0.00047930411 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_z_1+=     0.00009896501 * cos( 1.61155844715 +     6681.22485339960*t);

+   mars_z_1+=     0.00001700147 * cos( 2.63703242065 +    10021.83728009940*t);

+   mars_z_1=mars_z_1 * t;

+

+   double mars_z_2=0.0;

+   mars_z_2+=     0.00013705360 * cos( 1.04212852598 +     3340.61242669980*t);

+   mars_z_2+=     0.00005931596 * cos( 3.14159265359 +        0.00000000000*t);

+   mars_z_2=mars_z_2 * t * t;

+

+   return mars_z_0+mars_z_1+mars_z_2;

+}

+

+double vsop87a_milli_mercury_x(double t){

+   double mercury_x_0=0.0;

+   mercury_x_0+=     0.37546291728 * cos( 4.39651506942 +    26087.90314157420*t);

+   mercury_x_0+=     0.03825746672 * cos( 1.16485604339 +    52175.80628314840*t);

+   mercury_x_0+=     0.02625615963 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_x_0+=     0.00584261333 * cos( 4.21599394757 +    78263.70942472259*t);

+   mercury_x_0+=     0.00105716695 * cos( 0.98379033182 +   104351.61256629678*t);

+   mercury_x_0+=     0.00021011730 * cos( 4.03469353923 +   130439.51570787099*t);

+   mercury_x_0+=     0.00004433373 * cos( 0.80236674527 +   156527.41884944518*t);

+

+   double mercury_x_1=0.0;

+   mercury_x_1+=     0.00318848034 * cos( 0.00000000000 +        0.00000000000*t);

+   mercury_x_1+=     0.00105289019 * cos( 5.91600475006 +    52175.80628314840*t);

+   mercury_x_1+=     0.00032316001 * cos( 2.68247273347 +    78263.70942472259*t);

+   mercury_x_1+=     0.00011992889 * cos( 5.81575112963 +    26087.90314157420*t);

+   mercury_x_1+=     0.00008783200 * cos( 5.73285747425 +   104351.61256629678*t);

+   mercury_x_1+=     0.00002329042 * cos( 2.50023793407 +   130439.51570787099*t);

+   mercury_x_1=mercury_x_1 * t;

+

+   double mercury_x_2=0.0;

+   mercury_x_2+=     0.00001484185 * cos( 4.35401210269 +    52175.80628314840*t);

+   mercury_x_2+=     0.00001214995 * cos( 0.00000000000 +        0.00000000000*t);

+   mercury_x_2=mercury_x_2 * t * t;

+

+   return mercury_x_0+mercury_x_1+mercury_x_2;

+}

+

+double vsop87a_milli_mercury_y(double t){

+   double mercury_y_0=0.0;

+   mercury_y_0+=     0.37953642888 * cos( 2.83780617820 +    26087.90314157420*t);

+   mercury_y_0+=     0.11626131831 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_y_0+=     0.03854668215 * cos( 5.88780608966 +    52175.80628314840*t);

+   mercury_y_0+=     0.00587711268 * cos( 2.65498896201 +    78263.70942472259*t);

+   mercury_y_0+=     0.00106235493 * cos( 5.70550616735 +   104351.61256629678*t);

+   mercury_y_0+=     0.00021100828 * cos( 2.47291315849 +   130439.51570787099*t);

+   mercury_y_0+=     0.00004450056 * cos( 5.52354907071 +   156527.41884944518*t);

+

+   double mercury_y_1=0.0;

+   mercury_y_1+=     0.00107803852 * cos( 4.34964793883 +    52175.80628314840*t);

+   mercury_y_1+=     0.00080651544 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_y_1+=     0.00032715354 * cos( 1.11763734425 +    78263.70942472259*t);

+   mercury_y_1+=     0.00008858158 * cos( 4.16852401867 +   104351.61256629678*t);

+   mercury_y_1+=     0.00011914709 * cos( 1.22139986340 +    26087.90314157420*t);

+   mercury_y_1+=     0.00002344469 * cos( 0.93615372641 +   130439.51570787099*t);

+   mercury_y_1=mercury_y_1 * t;

+

+   double mercury_y_2=0.0;

+   mercury_y_2+=     0.00004612157 * cos( 0.00000000000 +        0.00000000000*t);

+   mercury_y_2+=     0.00001575670 * cos( 2.81172733349 +    52175.80628314840*t);

+   mercury_y_2=mercury_y_2 * t * t;

+

+   return mercury_y_0+mercury_y_1+mercury_y_2;

+}

+

+double vsop87a_milli_mercury_z(double t){

+   double mercury_z_0=0.0;

+   mercury_z_0+=     0.04607665326 * cos( 1.99295081967 +    26087.90314157420*t);

+   mercury_z_0+=     0.00708734365 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_z_0+=     0.00469171617 * cos( 5.04215742764 +    52175.80628314840*t);

+   mercury_z_0+=     0.00071626395 * cos( 1.80894256071 +    78263.70942472259*t);

+   mercury_z_0+=     0.00012957446 * cos( 4.85922032010 +   104351.61256629678*t);

+   mercury_z_0+=     0.00002575002 * cos( 1.62646731545 +   130439.51570787099*t);

+

+   double mercury_z_1=0.0;

+   mercury_z_1+=     0.00108722177 * cos( 3.91134750825 +    26087.90314157420*t);

+   mercury_z_1+=     0.00057826621 * cos( 3.14159265359 +        0.00000000000*t);

+   mercury_z_1+=     0.00004297352 * cos( 2.56373047177 +    52175.80628314840*t);

+   mercury_z_1+=     0.00002435833 * cos( 0.05112640506 +    78263.70942472259*t);

+   mercury_z_1=mercury_z_1 * t;

+

+   double mercury_z_2=0.0;

+   mercury_z_2+=     0.00001053118 * cos( 5.37979214357 +    26087.90314157420*t);

+   mercury_z_2+=     0.00001185024 * cos( 0.00000000000 +        0.00000000000*t);

+   mercury_z_2=mercury_z_2 * t * t;

+

+   return mercury_z_0+mercury_z_1+mercury_z_2;

+}

+

+double vsop87a_milli_neptune_x(double t){

+   double neptune_x_0=0.0;

+   neptune_x_0+=    30.05890004476 * cos( 5.31211340029 +       38.13303563780*t);

+   neptune_x_0+=     0.27080164222 * cos( 3.14159265359 +        0.00000000000*t);

+   neptune_x_0+=     0.13505661755 * cos( 3.50078975634 +       76.26607127560*t);

+   neptune_x_0+=     0.15726094556 * cos( 0.11319072675 +       36.64856292950*t);

+   neptune_x_0+=     0.14935120126 * cos( 1.08499403018 +       39.61750834610*t);

+   neptune_x_0+=     0.02597313814 * cos( 1.99590301412 +        1.48447270830*t);

+   neptune_x_0+=     0.01074040708 * cos( 5.38502938672 +       74.78159856730*t);

+   neptune_x_0+=     0.00823793287 * cos( 1.43221581862 +       35.16409022120*t);

+   neptune_x_0+=     0.00817588813 * cos( 0.78180174031 +        2.96894541660*t);

+   neptune_x_0+=     0.00565534918 * cos( 5.98964907613 +       41.10198105440*t);

+   neptune_x_0+=     0.00495719107 * cos( 0.59948143567 +      529.69096509460*t);

+   neptune_x_0+=     0.00307525907 * cos( 0.40023311011 +       73.29712585900*t);

+   neptune_x_0+=     0.00272253551 * cos( 0.87443494387 +      213.29909543800*t);

+   neptune_x_0+=     0.00135887219 * cos( 5.54676577816 +       77.75054398390*t);

+   neptune_x_0+=     0.00090965704 * cos( 1.68910246115 +      114.39910691340*t);

+   neptune_x_0+=     0.00069040539 * cos( 5.83469123520 +        4.45341812490*t);

+   neptune_x_0+=     0.00060813556 * cos( 2.62589958380 +       33.67961751290*t);

+   neptune_x_0+=     0.00054690827 * cos( 1.55799996661 +       71.81265315070*t);

+   neptune_x_0+=     0.00028889260 * cos( 4.78966826027 +       42.58645376270*t);

+   neptune_x_0+=     0.00012614732 * cos( 3.57002516434 +      112.91463420510*t);

+   neptune_x_0+=     0.00012749153 * cos( 2.73719269645 +      111.43016149680*t);

+   neptune_x_0+=     0.00012013994 * cos( 0.94912933496 +     1059.38193018920*t);

+   neptune_x_0+=     0.00007540650 * cos( 2.77783477855 +       70.32818044240*t);

+   neptune_x_0+=     0.00007573383 * cos( 0.10011329853 +      426.59819087600*t);

+   neptune_x_0+=     0.00008004318 * cos( 1.63965626260 +      108.46121608020*t);

+   neptune_x_0+=     0.00006464842 * cos( 4.62580066013 +        5.93789083320*t);

+   neptune_x_0+=     0.00005565860 * cos( 3.82502185953 +       32.19514480460*t);

+   neptune_x_0+=     0.00004654361 * cos( 0.10385887980 +       37.61177077600*t);

+   neptune_x_0+=     0.00004732434 * cos( 4.09723977191 +       79.23501669220*t);

+   neptune_x_0+=     0.00004557247 * cos( 1.09712669317 +       38.65430049960*t);

+   neptune_x_0+=     0.00004322550 * cos( 2.37744780188 +       38.08485152800*t);

+   neptune_x_0+=     0.00004315539 * cos( 5.10473142056 +       38.18121974760*t);

+   neptune_x_0+=     0.00004089036 * cos( 1.99429048244 +       37.16982779130*t);

+   neptune_x_0+=     0.00004249674 * cos( 5.63324475823 +       28.57180808220*t);

+   neptune_x_0+=     0.00003920412 * cos( 5.49263784865 +       39.09624348430*t);

+   neptune_x_0+=     0.00003951848 * cos( 2.29996934110 +       98.89998852460*t);

+   neptune_x_0+=     0.00003322735 * cos( 4.68798591938 +        4.19278569400*t);

+   neptune_x_0+=     0.00003108292 * cos( 1.84434543409 +       47.69426319340*t);

+   neptune_x_0+=     0.00003260095 * cos( 1.81839652878 +      145.10977900970*t);

+   neptune_x_0+=     0.00002723442 * cos( 3.82296285941 +      109.94568878850*t);

+   neptune_x_0+=     0.00002522938 * cos( 4.66296126912 +      312.19908396260*t);

+   neptune_x_0+=     0.00001887430 * cos( 3.20485417792 +       35.68535508300*t);

+   neptune_x_0+=     0.00001648985 * cos( 4.06990666591 +       30.05628079050*t);

+   neptune_x_0+=     0.00001826700 * cos( 3.58024318649 +       44.07092647100*t);

+   neptune_x_0+=     0.00001945462 * cos( 4.15326825288 +      206.18554843720*t);

+   neptune_x_0+=     0.00001681255 * cos( 4.27560304282 +       40.58071619260*t);

+   neptune_x_0+=     0.00001533383 * cos( 1.17732211665 +       38.02116105320*t);

+   neptune_x_0+=     0.00001891892 * cos( 0.74998855536 +      220.41264243880*t);

+   neptune_x_0+=     0.00001527526 * cos( 0.02173640246 +       38.24491022240*t);

+   neptune_x_0+=     0.00002084477 * cos( 1.56821671369 +      149.56319713460*t);

+   neptune_x_0+=     0.00002083682 * cos( 2.83676961811 +      137.03302416240*t);

+   neptune_x_0+=     0.00001615063 * cos( 2.91063835010 +      106.97674337190*t);

+   neptune_x_0+=     0.00001265797 * cos( 3.42037275447 +       46.20979048510*t);

+   neptune_x_0+=     0.00001560429 * cos( 0.55865739143 +       37.87240320690*t);

+   neptune_x_0+=     0.00001545705 * cos( 0.64028780672 +       38.39366806870*t);

+   neptune_x_0+=     0.00001434798 * cos( 0.72658718863 +      522.57741809380*t);

+   neptune_x_0+=     0.00001271543 * cos( 2.74412981229 +       33.94024994380*t);

+   neptune_x_0+=     0.00001407422 * cos( 3.61743288666 +      536.80451209540*t);

+   neptune_x_0+=     0.00001387922 * cos( 3.71814330952 +      115.88357962170*t);

+   neptune_x_0+=     0.00001228939 * cos( 2.78878211792 +       72.07328558160*t);

+   neptune_x_0+=     0.00001448439 * cos( 1.98814317259 +      181.75834193920*t);

+   neptune_x_0+=     0.00001170078 * cos( 3.98594689041 +        8.07675484730*t);

+   neptune_x_0+=     0.00001080795 * cos( 4.75485636019 +       42.32582133180*t);

+   neptune_x_0+=     0.00001220341 * cos( 2.64791449584 +      148.07872442630*t);

+

+   double neptune_x_1=0.0;

+   neptune_x_1+=     0.00255840261 * cos( 2.01935686795 +       36.64856292950*t);

+   neptune_x_1+=     0.00243125299 * cos( 5.46214902873 +       39.61750834610*t);

+   neptune_x_1+=     0.00118398168 * cos( 2.88251845061 +       76.26607127560*t);

+   neptune_x_1+=     0.00037965449 * cos( 3.14159265359 +        0.00000000000*t);

+   neptune_x_1+=     0.00021924705 * cos( 3.20156164152 +       35.16409022120*t);

+   neptune_x_1+=     0.00017459808 * cos( 4.26349398817 +       41.10198105440*t);

+   neptune_x_1+=     0.00013130617 * cos( 5.36424961848 +        2.96894541660*t);

+   neptune_x_1+=     0.00005086527 * cos( 1.92377354729 +       38.13303563780*t);

+   neptune_x_1+=     0.00004899718 * cos( 2.09349497813 +       73.29712585900*t);

+   neptune_x_1+=     0.00002745267 * cos( 4.06252818667 +       77.75054398390*t);

+   neptune_x_1+=     0.00002204414 * cos( 4.38855639521 +       33.67961751290*t);

+   neptune_x_1+=     0.00002168719 * cos( 4.11768012563 +        4.45341812490*t);

+   neptune_x_1+=     0.00001572202 * cos( 1.07606611589 +      114.39910691340*t);

+   neptune_x_1+=     0.00001344022 * cos( 3.03802059051 +       42.58645376270*t);

+   neptune_x_1+=     0.00001285542 * cos( 6.02367554997 +       74.78159856730*t);

+   neptune_x_1=neptune_x_1 * t;

+

+   double neptune_x_2=0.0;

+   neptune_x_2+=     0.00005371138 * cos( 0.00000000000 +        0.00000000000*t);

+   neptune_x_2+=     0.00004536283 * cos( 5.02700751836 +       36.64856292950*t);

+   neptune_x_2+=     0.00004350766 * cos( 2.45420254304 +       39.61750834610*t);

+   neptune_x_2+=     0.00003092965 * cos( 0.62250463031 +       38.13303563780*t);

+   neptune_x_2+=     0.00002163703 * cos( 1.79218168368 +       76.26607127560*t);

+   neptune_x_2=neptune_x_2 * t * t;

+

+   return neptune_x_0+neptune_x_1+neptune_x_2;

+}

+

+double vsop87a_milli_neptune_y(double t){

+   double neptune_y_0=0.0;

+   neptune_y_0+=    30.06056351665 * cos( 3.74086294714 +       38.13303563780*t);

+   neptune_y_0+=     0.30205857683 * cos( 3.14159265359 +        0.00000000000*t);

+   neptune_y_0+=     0.13506391797 * cos( 1.92953034883 +       76.26607127560*t);

+   neptune_y_0+=     0.15706589373 * cos( 4.82539970129 +       36.64856292950*t);

+   neptune_y_0+=     0.14936165806 * cos( 5.79694900665 +       39.61750834610*t);

+   neptune_y_0+=     0.02584250749 * cos( 0.42549700754 +        1.48447270830*t);

+   neptune_y_0+=     0.01073739772 * cos( 3.81371728533 +       74.78159856730*t);

+   neptune_y_0+=     0.00815187583 * cos( 5.49429775826 +        2.96894541660*t);

+   neptune_y_0+=     0.00582199295 * cos( 6.19633718936 +       35.16409022120*t);

+   neptune_y_0+=     0.00565576412 * cos( 4.41843009015 +       41.10198105440*t);

+   neptune_y_0+=     0.00495581047 * cos( 5.31205825784 +      529.69096509460*t);

+   neptune_y_0+=     0.00304525203 * cos( 5.11048113661 +       73.29712585900*t);

+   neptune_y_0+=     0.00272640298 * cos( 5.58603690785 +      213.29909543800*t);

+   neptune_y_0+=     0.00135897385 * cos( 3.97553750964 +       77.75054398390*t);

+   neptune_y_0+=     0.00090970871 * cos( 0.11783619888 +      114.39910691340*t);

+   neptune_y_0+=     0.00068790261 * cos( 4.26391997151 +        4.45341812490*t);

+   neptune_y_0+=     0.00028893355 * cos( 3.21848975032 +       42.58645376270*t);

+   neptune_y_0+=     0.00020081559 * cos( 1.19787916085 +       33.67961751290*t);

+   neptune_y_0+=     0.00012613583 * cos( 1.99777332934 +      112.91463420510*t);

+   neptune_y_0+=     0.00012828708 * cos( 1.16740053443 +      111.43016149680*t);

+   neptune_y_0+=     0.00012012961 * cos( 5.66157563804 +     1059.38193018920*t);

+   neptune_y_0+=     0.00008768580 * cos( 3.23487156950 +      108.46121608020*t);

+   neptune_y_0+=     0.00007581788 * cos( 4.81169168396 +      426.59819087600*t);

+   neptune_y_0+=     0.00006439265 * cos( 3.05453259951 +        5.93789083320*t);

+   neptune_y_0+=     0.00005297978 * cos( 0.79002313990 +       71.81265315070*t);

+   neptune_y_0+=     0.00004650708 * cos( 4.81540983294 +       37.61177077600*t);

+   neptune_y_0+=     0.00004733483 * cos( 2.52620194642 +       79.23501669220*t);

+   neptune_y_0+=     0.00004557247 * cos( 5.80951552318 +       38.65430049960*t);

+   neptune_y_0+=     0.00004322550 * cos( 0.80665145881 +       38.08485152800*t);

+   neptune_y_0+=     0.00004315539 * cos( 3.53393506841 +       38.18121974760*t);

+   neptune_y_0+=     0.00004089036 * cos( 0.42349446479 +       37.16982779130*t);

+   neptune_y_0+=     0.00004247643 * cos( 4.06355336504 +       28.57180808220*t);

+   neptune_y_0+=     0.00003932515 * cos( 3.91607592815 +       39.09624348430*t);

+   neptune_y_0+=     0.00003930135 * cos( 3.86614178174 +       98.89998852460*t);

+   neptune_y_0+=     0.00003323991 * cos( 3.11674274385 +        4.19278569400*t);

+   neptune_y_0+=     0.00003112636 * cos( 0.27319642944 +       47.69426319340*t);

+   neptune_y_0+=     0.00003373281 * cos( 3.39616255650 +      145.10977900970*t);

+   neptune_y_0+=     0.00002670944 * cos( 2.31235275416 +      109.94568878850*t);

+   neptune_y_0+=     0.00002523042 * cos( 6.23400745185 +      312.19908396260*t);

+   neptune_y_0+=     0.00001888827 * cos( 1.63364331324 +       35.68535508300*t);

+   neptune_y_0+=     0.00001647474 * cos( 2.50010254963 +       30.05628079050*t);

+   neptune_y_0+=     0.00001826390 * cos( 2.00938305966 +       44.07092647100*t);

+   neptune_y_0+=     0.00001967147 * cos( 2.56634772532 +      206.18554843720*t);

+   neptune_y_0+=     0.00001681258 * cos( 2.70480318579 +       40.58071619260*t);

+   neptune_y_0+=     0.00001533383 * cos( 5.88971113590 +       38.02116105320*t);

+   neptune_y_0+=     0.00001894261 * cos( 5.46274825258 +      220.41264243880*t);

+   neptune_y_0+=     0.00001527526 * cos( 4.73412534395 +       38.24491022240*t);

+   neptune_y_0+=     0.00002086907 * cos( 6.28313624461 +      149.56319713460*t);

+   neptune_y_0+=     0.00002057794 * cos( 4.38552505781 +      137.03302416240*t);

+   neptune_y_0+=     0.00001720954 * cos( 4.49400805134 +      106.97674337190*t);

+   neptune_y_0+=     0.00001314116 * cos( 1.80386443362 +       46.20979048510*t);

+   neptune_y_0+=     0.00001732739 * cos( 4.14518500834 +       70.32818044240*t);

+   neptune_y_0+=     0.00001559193 * cos( 5.27114846878 +       37.87240320690*t);

+   neptune_y_0+=     0.00001545705 * cos( 5.35267669439 +       38.39366806870*t);

+   neptune_y_0+=     0.00001435274 * cos( 5.44292013172 +      522.57741809380*t);

+   neptune_y_0+=     0.00001404991 * cos( 2.04611088339 +      536.80451209540*t);

+   neptune_y_0+=     0.00001242929 * cos( 1.10242173566 +       33.94024994380*t);

+   neptune_y_0+=     0.00001388024 * cos( 2.14792830412 +      115.88357962170*t);

+   neptune_y_0+=     0.00001467042 * cos( 3.56226463770 +      181.75834193920*t);

+   neptune_y_0+=     0.00001227926 * cos( 1.21334651843 +       72.07328558160*t);

+   neptune_y_0+=     0.00001080807 * cos( 3.18401661435 +       42.32582133180*t);

+   neptune_y_0+=     0.00001111708 * cos( 5.51669920239 +        8.07675484730*t);

+   neptune_y_0+=     0.00001237027 * cos( 1.08622199668 +      148.07872442630*t);

+

+   double neptune_y_1=0.0;

+   neptune_y_1+=     0.00352947493 * cos( 3.14159265359 +        0.00000000000*t);

+   neptune_y_1+=     0.00256125493 * cos( 0.44757496817 +       36.64856292950*t);

+   neptune_y_1+=     0.00243147725 * cos( 3.89099798696 +       39.61750834610*t);

+   neptune_y_1+=     0.00118427205 * cos( 1.31128027037 +       76.26607127560*t);

+   neptune_y_1+=     0.00021936702 * cos( 1.63124087591 +       35.16409022120*t);

+   neptune_y_1+=     0.00017462332 * cos( 2.69229902966 +       41.10198105440*t);

+   neptune_y_1+=     0.00012992380 * cos( 3.79578633002 +        2.96894541660*t);

+   neptune_y_1+=     0.00004945117 * cos( 0.51727080684 +       73.29712585900*t);

+   neptune_y_1+=     0.00002745921 * cos( 2.49178311082 +       77.75054398390*t);

+   neptune_y_1+=     0.00002145481 * cos( 2.54768447291 +        4.45341812490*t);

+   neptune_y_1+=     0.00001572289 * cos( 5.78853350711 +      114.39910691340*t);

+   neptune_y_1+=     0.00001565725 * cos( 2.89846266272 +       33.67961751290*t);

+   neptune_y_1+=     0.00001458269 * cos( 1.61835542699 +       38.13303563780*t);

+   neptune_y_1+=     0.00001293459 * cos( 4.45868061082 +       74.78159856730*t);

+   neptune_y_1+=     0.00001343731 * cos( 1.46712622109 +       42.58645376270*t);

+   neptune_y_1=neptune_y_1 * t;

+

+   double neptune_y_2=0.0;

+   neptune_y_2+=     0.00004539421 * cos( 3.45613207922 +       36.64856292950*t);

+   neptune_y_2+=     0.00004347956 * cos( 0.88317230351 +       39.61750834610*t);

+   neptune_y_2+=     0.00003595394 * cos( 3.14159265359 +        0.00000000000*t);

+   neptune_y_2+=     0.00003058647 * cos( 5.31956613665 +       38.13303563780*t);

+   neptune_y_2+=     0.00002163809 * cos( 0.22086532214 +       76.26607127560*t);

+   neptune_y_2=neptune_y_2 * t * t;

+

+   return neptune_y_0+neptune_y_1+neptune_y_2;

+}

+

+double vsop87a_milli_neptune_z(double t){

+   double neptune_z_0=0.0;

+   neptune_z_0+=     0.92866054405 * cos( 1.44103930278 +       38.13303563780*t);

+   neptune_z_0+=     0.01245978462 * cos( 0.00000000000 +        0.00000000000*t);

+   neptune_z_0+=     0.00474333567 * cos( 2.52218774238 +       36.64856292950*t);

+   neptune_z_0+=     0.00451987936 * cos( 3.50949720541 +       39.61750834610*t);

+   neptune_z_0+=     0.00417558068 * cos( 5.91310695421 +       76.26607127560*t);

+   neptune_z_0+=     0.00084104329 * cos( 4.38928900096 +        1.48447270830*t);

+   neptune_z_0+=     0.00032704958 * cos( 1.52048692001 +       74.78159856730*t);

+   neptune_z_0+=     0.00030873335 * cos( 3.29017611456 +       35.16409022120*t);

+   neptune_z_0+=     0.00025812584 * cos( 3.19303128782 +        2.96894541660*t);

+   neptune_z_0+=     0.00016865319 * cos( 2.13251104425 +       41.10198105440*t);

+   neptune_z_0+=     0.00011789909 * cos( 3.60001877675 +      213.29909543800*t);

+   neptune_z_0+=     0.00009770125 * cos( 2.80133971586 +       73.29712585900*t);

+   neptune_z_0+=     0.00011279680 * cos( 3.55816676334 +      529.69096509460*t);

+   neptune_z_0+=     0.00004119873 * cos( 1.67934316836 +       77.75054398390*t);

+   neptune_z_0+=     0.00002818034 * cos( 4.10661077794 +      114.39910691340*t);

+   neptune_z_0+=     0.00002868677 * cos( 4.27011526203 +       33.67961751290*t);

+   neptune_z_0+=     0.00002213464 * cos( 1.96045135168 +        4.45341812490*t);

+   neptune_z_0+=     0.00001865650 * cos( 5.05540709577 +       71.81265315070*t);

+

+   double neptune_z_1=0.0;

+   neptune_z_1+=     0.00154885971 * cos( 2.14239039664 +       38.13303563780*t);

+   neptune_z_1+=     0.00007783708 * cos( 4.40146905905 +       36.64856292950*t);

+   neptune_z_1+=     0.00006862414 * cos( 1.65930160610 +       39.61750834610*t);

+   neptune_z_1+=     0.00009464276 * cos( 0.00000000000 +        0.00000000000*t);

+   neptune_z_1+=     0.00003891873 * cos( 5.46761139427 +       76.26607127560*t);

+   neptune_z_1=neptune_z_1 * t;

+

+   double neptune_z_2=0.0;

+   neptune_z_2+=     0.00001264840 * cos( 1.91401498992 +       38.13303563780*t);

+   neptune_z_2=neptune_z_2 * t * t;

+

+   return neptune_z_0+neptune_z_1+neptune_z_2;

+}

+

+double vsop87a_milli_saturn_x(double t){

+   double saturn_x_0=0.0;

+   saturn_x_0+=     9.51638335797 * cos( 0.87441380794 +      213.29909543800*t);

+   saturn_x_0+=     0.26412374238 * cos( 0.12390892620 +      426.59819087600*t);

+   saturn_x_0+=     0.06760430339 * cos( 4.16767145778 +      206.18554843720*t);

+   saturn_x_0+=     0.06624260115 * cos( 0.75094737780 +      220.41264243880*t);

+   saturn_x_0+=     0.04244797817 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_x_0+=     0.02336340488 * cos( 2.02227784673 +        7.11354700080*t);

+   saturn_x_0+=     0.01255372247 * cos( 2.17338917731 +      110.20632121940*t);

+   saturn_x_0+=     0.01115684467 * cos( 3.15686878377 +      419.48464387520*t);

+   saturn_x_0+=     0.01097683232 * cos( 5.65753337256 +      639.89728631400*t);

+   saturn_x_0+=     0.00716328481 * cos( 2.71149993708 +      316.39186965660*t);

+   saturn_x_0+=     0.00509313365 * cos( 4.95865624780 +      103.09277421860*t);

+   saturn_x_0+=     0.00433994439 * cos( 0.72012820974 +      529.69096509460*t);

+   saturn_x_0+=     0.00372894461 * cos( 0.00137195497 +      433.71173787680*t);

+   saturn_x_0+=     0.00097843523 * cos( 1.01485750417 +      323.50541665740*t);

+   saturn_x_0+=     0.00080600536 * cos( 5.62103979796 +       11.04570026390*t);

+   saturn_x_0+=     0.00083782316 * cos( 0.62038893702 +      227.52618943960*t);

+   saturn_x_0+=     0.00074150224 * cos( 2.38206066655 +      632.78373931320*t);

+   saturn_x_0+=     0.00070219382 * cos( 0.88789752415 +      209.36694217490*t);

+   saturn_x_0+=     0.00068855792 * cos( 4.01788097627 +      217.23124870110*t);

+   saturn_x_0+=     0.00065620467 * cos( 2.69728593339 +      202.25339517410*t);

+   saturn_x_0+=     0.00058297911 * cos( 2.16155251399 +      224.34479570190*t);

+   saturn_x_0+=     0.00054022837 * cos( 4.90928184374 +      853.19638175200*t);

+   saturn_x_0+=     0.00045550446 * cos( 1.88235037830 +       14.22709400160*t);

+   saturn_x_0+=     0.00038345667 * cos( 4.39815501478 +      199.07200143640*t);

+   saturn_x_0+=     0.00044551703 * cos( 5.60763553535 +       63.73589830340*t);

+   saturn_x_0+=     0.00025165185 * cos( 0.37800582257 +      216.48048917570*t);

+   saturn_x_0+=     0.00024554499 * cos( 4.53150598095 +      210.11770170030*t);

+   saturn_x_0+=     0.00024673219 * cos( 5.90891573850 +      522.57741809380*t);

+   saturn_x_0+=     0.00024677050 * cos( 5.60389382420 +      415.55249061210*t);

+   saturn_x_0+=     0.00025491374 * cos( 1.63922423181 +      117.31986822020*t);

+   saturn_x_0+=     0.00031253049 * cos( 4.62976601833 +      735.87651353180*t);

+   saturn_x_0+=     0.00023372467 * cos( 5.53491987276 +      647.01083331480*t);

+   saturn_x_0+=     0.00023355468 * cos( 0.18791490124 +      149.56319713460*t);

+   saturn_x_0+=     0.00024805815 * cos( 5.50327676733 +       74.78159856730*t);

+   saturn_x_0+=     0.00014731703 * cos( 4.67981909838 +      277.03499374140*t);

+   saturn_x_0+=     0.00012427525 * cos( 1.02995545746 +     1059.38193018920*t);

+   saturn_x_0+=     0.00009943329 * cos( 0.84628387596 +        3.93215326310*t);

+   saturn_x_0+=     0.00012393514 * cos( 4.19747622821 +      490.33408917940*t);

+   saturn_x_0+=     0.00012026472 * cos( 5.66372282839 +      351.81659230870*t);

+   saturn_x_0+=     0.00008222014 * cos( 2.47875301104 +      742.99006053260*t);

+   saturn_x_0+=     0.00009087093 * cos( 4.33505326762 +     1052.26838318840*t);

+   saturn_x_0+=     0.00006717741 * cos( 5.51897460997 +      838.96928775040*t);

+   saturn_x_0+=     0.00006232999 * cos( 2.45837758015 +      846.08283475120*t);

+   saturn_x_0+=     0.00007161671 * cos( 2.18152751738 +       95.97922721780*t);

+   saturn_x_0+=     0.00006321101 * cos( 0.83915408770 +      309.27832265580*t);

+   saturn_x_0+=     0.00006074958 * cos( 6.15905897331 +      440.82528487760*t);

+   saturn_x_0+=     0.00005343894 * cos( 3.60046273598 +      412.37109687440*t);

+   saturn_x_0+=     0.00004860582 * cos( 0.26461045175 +      536.80451209540*t);

+   saturn_x_0+=     0.00005775802 * cos( 5.30717695229 +       38.13303563780*t);

+   saturn_x_0+=     0.00005194178 * cos( 4.54584467686 +      210.85141488320*t);

+   saturn_x_0+=     0.00005152474 * cos( 0.34669517150 +      215.74677599280*t);

+   saturn_x_0+=     0.00003792540 * cos( 5.99766568983 +      422.66603761290*t);

+   saturn_x_0+=     0.00003762834 * cos( 3.72112920226 +      212.33588759150*t);

+   saturn_x_0+=     0.00003747433 * cos( 1.16965137714 +      214.26230328450*t);

+   saturn_x_0+=     0.00003114576 * cos( 0.84631897292 +      213.25091132820*t);

+   saturn_x_0+=     0.00003113641 * cos( 4.04410367190 +      213.34727954780*t);

+   saturn_x_0+=     0.00002990421 * cos( 0.04148806852 +      625.67019231240*t);

+   saturn_x_0+=     0.00004111695 * cos( 5.96153153046 +      137.03302416240*t);

+   saturn_x_0+=     0.00002966450 * cos( 5.39568820046 +      138.51749687070*t);

+   saturn_x_0+=     0.00002827527 * cos( 0.73252555642 +      330.61896365820*t);

+   saturn_x_0+=     0.00003363323 * cos( 1.42089586686 +      437.64389113990*t);

+   saturn_x_0+=     0.00002886599 * cos( 1.14057922619 +       85.82729883120*t);

+   saturn_x_0+=     0.00002634075 * cos( 5.40645201521 +      288.08069400530*t);

+   saturn_x_0+=     0.00002713354 * cos( 0.96812639712 +      203.73786788240*t);

+   saturn_x_0+=     0.00003169390 * cos( 5.76640408988 +       76.26607127560*t);

+   saturn_x_0+=     0.00002618634 * cos( 5.49334837098 +      127.47179660680*t);

+   saturn_x_0+=     0.00002527746 * cos( 5.09752068381 +      628.85158605010*t);

+   saturn_x_0+=     0.00002989778 * cos( 4.15673836604 +     1066.49547719000*t);

+   saturn_x_0+=     0.00002507415 * cos( 1.49447138038 +        9.56122755560*t);

+   saturn_x_0+=     0.00002470181 * cos( 5.27435870056 +     1155.36115740700*t);

+   saturn_x_0+=     0.00002427626 * cos( 3.97311214231 +      222.86032299360*t);

+   saturn_x_0+=     0.00003128325 * cos( 4.05483976553 +     1368.66025284500*t);

+   saturn_x_0+=     0.00002309076 * cos( 3.67821438247 +      430.53034413910*t);

+   saturn_x_0+=     0.00002162629 * cos( 3.26951119901 +      340.77089204480*t);

+   saturn_x_0+=     0.00002912676 * cos( 1.76893577106 +        3.18139373770*t);

+   saturn_x_0+=     0.00002095366 * cos( 3.55759089756 +      423.41679713830*t);

+   saturn_x_0+=     0.00002335270 * cos( 5.86791072516 +      388.46515523820*t);

+   saturn_x_0+=     0.00001634262 * cos( 4.54357767539 +       12.53017297220*t);

+   saturn_x_0+=     0.00001635975 * cos( 2.19968869780 +      212.77783057620*t);

+   saturn_x_0+=     0.00001632759 * cos( 2.69164822165 +      213.82036029980*t);

+   saturn_x_0+=     0.00001498689 * cos( 3.60168057129 +       52.69019803950*t);

+   saturn_x_0+=     0.00001461217 * cos( 5.92456743836 +      429.77958461370*t);

+   saturn_x_0+=     0.00001963947 * cos( 2.05086487180 +        1.48447270830*t);

+   saturn_x_0+=     0.00001538425 * cos( 4.78544077085 +      860.30992875280*t);

+   saturn_x_0+=     0.00001485856 * cos( 5.65501463408 +      949.17560896980*t);

+   saturn_x_0+=     0.00001418116 * cos( 5.41419993599 +      350.33211960040*t);

+   saturn_x_0+=     0.00001147607 * cos( 0.19147238521 +      942.06206196900*t);

+   saturn_x_0+=     0.00001111703 * cos( 0.47907488492 +      234.63973644040*t);

+   saturn_x_0+=     0.00001019566 * cos( 5.00707811029 +     1471.75302706360*t);

+   saturn_x_0+=     0.00001009190 * cos( 1.34289487761 +      265.98929347750*t);

+   saturn_x_0+=     0.00001089450 * cos( 5.82690672710 +      362.86229257260*t);

+   saturn_x_0+=     0.00001092244 * cos( 1.13561107749 +      173.94221952280*t);

+   saturn_x_0+=     0.00001173456 * cos( 3.79591687208 +     1685.05212250160*t);

+   saturn_x_0+=     0.00001118369 * cos( 3.46624149583 +      703.63318461740*t);

+   saturn_x_0+=     0.00001150595 * cos( 3.74707160019 +      200.76892246580*t);

+   saturn_x_0+=     0.00001007761 * cos( 1.08964371328 +      225.82926841020*t);

+

+   double saturn_x_1=0.0;

+   saturn_x_1+=     0.07575103962 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_x_1+=     0.03085041716 * cos( 4.27565749128 +      426.59819087600*t);

+   saturn_x_1+=     0.02714918399 * cos( 5.85229412397 +      206.18554843720*t);

+   saturn_x_1+=     0.02643100909 * cos( 5.33291950584 +      220.41264243880*t);

+   saturn_x_1+=     0.00627104520 * cos( 0.32898307969 +        7.11354700080*t);

+   saturn_x_1+=     0.00256560953 * cos( 3.52478934343 +      639.89728631400*t);

+   saturn_x_1+=     0.00312356512 * cos( 4.83001724941 +      419.48464387520*t);

+   saturn_x_1+=     0.00189196274 * cos( 4.48642453552 +      433.71173787680*t);

+   saturn_x_1+=     0.00203646570 * cos( 1.10998681782 +      213.29909543800*t);

+   saturn_x_1+=     0.00119531145 * cos( 1.14735096078 +      110.20632121940*t);

+   saturn_x_1+=     0.00066764238 * cos( 3.72346596928 +      316.39186965660*t);

+   saturn_x_1+=     0.00066901225 * cos( 5.20257500380 +      227.52618943960*t);

+   saturn_x_1+=     0.00031000840 * cos( 6.06067919437 +      199.07200143640*t);

+   saturn_x_1+=     0.00030418100 * cos( 0.18746903351 +       14.22709400160*t);

+   saturn_x_1+=     0.00022275210 * cos( 6.19530878014 +      103.09277421860*t);

+   saturn_x_1+=     0.00018939377 * cos( 2.77618306725 +      853.19638175200*t);

+   saturn_x_1+=     0.00018093009 * cos( 5.09162723865 +      209.36694217490*t);

+   saturn_x_1+=     0.00017777854 * cos( 6.10381593351 +      217.23124870110*t);

+   saturn_x_1+=     0.00016296201 * cos( 4.86945681437 +      216.48048917570*t);

+   saturn_x_1+=     0.00017120250 * cos( 4.59611664188 +      632.78373931320*t);

+   saturn_x_1+=     0.00015894491 * cos( 0.03653502304 +      210.11770170030*t);

+   saturn_x_1+=     0.00016192653 * cos( 5.60798014450 +      323.50541665740*t);

+   saturn_x_1+=     0.00014466010 * cos( 3.67449380090 +      647.01083331480*t);

+   saturn_x_1+=     0.00011061528 * cos( 0.03163071461 +      117.31986822020*t);

+   saturn_x_1+=     0.00009873183 * cos( 5.20065307357 +      202.25339517410*t);

+   saturn_x_1+=     0.00008707608 * cos( 6.03511731637 +      224.34479570190*t);

+   saturn_x_1+=     0.00005499109 * cos( 4.40350603415 +      440.82528487760*t);

+   saturn_x_1+=     0.00005512222 * cos( 2.60556642348 +       11.04570026390*t);

+   saturn_x_1+=     0.00004008257 * cos( 1.48942966807 +      522.57741809380*t);

+   saturn_x_1+=     0.00003571196 * cos( 5.10821908379 +      412.37109687440*t);

+   saturn_x_1+=     0.00002731381 * cos( 4.10892223660 +      149.56319713460*t);

+   saturn_x_1+=     0.00002763786 * cos( 3.96253590209 +       95.97922721780*t);

+   saturn_x_1+=     0.00001875862 * cos( 2.52384080586 +        3.93215326310*t);

+   saturn_x_1+=     0.00001765816 * cos( 0.75684544353 +      277.03499374140*t);

+   saturn_x_1+=     0.00001688957 * cos( 3.98270950731 +      422.66603761290*t);

+   saturn_x_1+=     0.00001544787 * cos( 5.30283923836 +      330.61896365820*t);

+   saturn_x_1+=     0.00001449143 * cos( 6.26507179861 +      529.69096509460*t);

+   saturn_x_1+=     0.00001395551 * cos( 2.03533642541 +     1066.49547719000*t);

+   saturn_x_1+=     0.00001330413 * cos( 5.06312203212 +      234.63973644040*t);

+   saturn_x_1+=     0.00001511648 * cos( 6.23274598777 +        3.18139373770*t);

+   saturn_x_1+=     0.00001271050 * cos( 2.40338468675 +      415.55249061210*t);

+   saturn_x_1+=     0.00001171680 * cos( 4.59341412127 +      536.80451209540*t);

+   saturn_x_1+=     0.00001129056 * cos( 5.45794529295 +      423.41679713830*t);

+   saturn_x_1+=     0.00001126400 * cos( 2.88173213734 +      860.30992875280*t);

+   saturn_x_1+=     0.00001101245 * cos( 4.07698108824 +      429.77958461370*t);

+   saturn_x_1+=     0.00001273315 * cos( 0.09572429396 +      742.99006053260*t);

+   saturn_x_1+=     0.00001342277 * cos( 2.98929557875 +      210.85141488320*t);

+   saturn_x_1+=     0.00001331045 * cos( 1.90899526877 +      215.74677599280*t);

+   saturn_x_1=saturn_x_1 * t;

+

+   double saturn_x_2=0.0;

+   saturn_x_2+=     0.00560746334 * cos( 1.26401632282 +      206.18554843720*t);

+   saturn_x_2+=     0.00545834518 * cos( 3.62343709657 +      220.41264243880*t);

+   saturn_x_2+=     0.00443342186 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_x_2+=     0.00336109713 * cos( 2.42547432460 +      213.29909543800*t);

+   saturn_x_2+=     0.00224302269 * cos( 2.49151203519 +      426.59819087600*t);

+   saturn_x_2+=     0.00087170924 * cos( 4.89048951691 +        7.11354700080*t);

+   saturn_x_2+=     0.00050028094 * cos( 2.70119046081 +      433.71173787680*t);

+   saturn_x_2+=     0.00045122590 * cos( 0.36735068943 +      419.48464387520*t);

+   saturn_x_2+=     0.00032847824 * cos( 1.59210153669 +      639.89728631400*t);

+   saturn_x_2+=     0.00027153555 * cos( 3.49804002218 +      227.52618943960*t);

+   saturn_x_2+=     0.00012676167 * cos( 1.45465729530 +      199.07200143640*t);

+   saturn_x_2+=     0.00010330738 * cos( 4.76949531290 +       14.22709400160*t);

+   saturn_x_2+=     0.00007249149 * cos( 5.70264553247 +      110.20632121940*t);

+   saturn_x_2+=     0.00004653214 * cos( 1.83710048213 +      647.01083331480*t);

+   saturn_x_2+=     0.00004923585 * cos( 3.08463039042 +      216.48048917570*t);

+   saturn_x_2+=     0.00004777358 * cos( 1.81695155349 +      210.11770170030*t);

+   saturn_x_2+=     0.00004166633 * cos( 5.32887874226 +      316.39186965660*t);

+   saturn_x_2+=     0.00003508385 * cos( 0.78251653369 +      853.19638175200*t);

+   saturn_x_2+=     0.00002660470 * cos( 3.16731393212 +      209.36694217490*t);

+   saturn_x_2+=     0.00002538027 * cos( 2.65097612407 +      440.82528487760*t);

+   saturn_x_2+=     0.00002568114 * cos( 1.74024228572 +      217.23124870110*t);

+   saturn_x_2+=     0.00002503277 * cos( 4.69450368911 +      117.31986822020*t);

+   saturn_x_2+=     0.00002506986 * cos( 1.74781817701 +      103.09277421860*t);

+   saturn_x_2+=     0.00002129256 * cos( 0.28453141367 +      632.78373931320*t);

+   saturn_x_2+=     0.00001841989 * cos( 3.99269872894 +      323.50541665740*t);

+   saturn_x_2+=     0.00001228511 * cos( 0.42906039519 +      412.37109687440*t);

+   saturn_x_2=saturn_x_2 * t * t;

+

+   double saturn_x_3=0.0;

+   saturn_x_3+=     0.00077115952 * cos( 2.97714385362 +      206.18554843720*t);

+   saturn_x_3+=     0.00075340436 * cos( 1.89208005248 +      220.41264243880*t);

+   saturn_x_3+=     0.00018450895 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_x_3+=     0.00010527244 * cos( 0.66368256891 +      426.59819087600*t);

+   saturn_x_3+=     0.00008994946 * cos( 0.91696559755 +      433.71173787680*t);

+   saturn_x_3+=     0.00007403594 * cos( 1.78627385870 +      227.52618943960*t);

+   saturn_x_3+=     0.00008045160 * cos( 3.12864412887 +        7.11354700080*t);

+   saturn_x_3+=     0.00004505149 * cos( 2.24531319187 +      419.48464387520*t);

+   saturn_x_3+=     0.00003468010 * cos( 3.14590544446 +      199.07200143640*t);

+   saturn_x_3+=     0.00002974601 * cos( 6.00030641555 +      639.89728631400*t);

+   saturn_x_3+=     0.00002342089 * cos( 3.06091771643 +       14.22709400160*t);

+   saturn_x_3+=     0.00001230715 * cos( 4.38196130069 +      213.29909543800*t);

+   saturn_x_3+=     0.00001023888 * cos( 0.01138655869 +      647.01083331480*t);

+   saturn_x_3=saturn_x_3 * t * t * t;

+

+   double saturn_x_4=0.0;

+   saturn_x_4+=     0.00007959921 * cos( 4.70523623364 +      206.18554843720*t);

+   saturn_x_4+=     0.00007836652 * cos( 0.13981693631 +      220.41264243880*t);

+   saturn_x_4+=     0.00001511196 * cos( 0.06561560462 +      227.52618943960*t);

+   saturn_x_4+=     0.00001223066 * cos( 5.41618485361 +      433.71173787680*t);

+   saturn_x_4=saturn_x_4 * t * t * t * t;

+

+   return saturn_x_0+saturn_x_1+saturn_x_2+saturn_x_3+saturn_x_4;

+}

+

+double vsop87a_milli_saturn_y(double t){

+   double saturn_y_0=0.0;

+   saturn_y_0+=     9.52986882699 * cos( 5.58600556665 +      213.29909543800*t);

+   saturn_y_0+=     0.79387988806 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_y_0+=     0.26441781302 * cos( 4.83528061849 +      426.59819087600*t);

+   saturn_y_0+=     0.06916653915 * cos( 2.55279408706 +      206.18554843720*t);

+   saturn_y_0+=     0.06633570703 * cos( 5.46258848288 +      220.41264243880*t);

+   saturn_y_0+=     0.02345609742 * cos( 0.44652132519 +        7.11354700080*t);

+   saturn_y_0+=     0.01183874652 * cos( 1.34638298371 +      419.48464387520*t);

+   saturn_y_0+=     0.01245790434 * cos( 0.60367177975 +      110.20632121940*t);

+   saturn_y_0+=     0.01098751131 * cos( 4.08608782813 +      639.89728631400*t);

+   saturn_y_0+=     0.00700849336 * cos( 1.13611298025 +      316.39186965660*t);

+   saturn_y_0+=     0.00434466176 * cos( 5.42474696262 +      529.69096509460*t);

+   saturn_y_0+=     0.00373327342 * cos( 4.71308726958 +      433.71173787680*t);

+   saturn_y_0+=     0.00335162363 * cos( 0.66422253983 +      103.09277421860*t);

+   saturn_y_0+=     0.00097837745 * cos( 5.72844290173 +      323.50541665740*t);

+   saturn_y_0+=     0.00080571808 * cos( 4.05295449910 +       11.04570026390*t);

+   saturn_y_0+=     0.00083899691 * cos( 5.33204070267 +      227.52618943960*t);

+   saturn_y_0+=     0.00070158491 * cos( 5.59777963629 +      209.36694217490*t);

+   saturn_y_0+=     0.00065937657 * cos( 1.25969608208 +      202.25339517410*t);

+   saturn_y_0+=     0.00070957225 * cos( 0.88888207567 +      632.78373931320*t);

+   saturn_y_0+=     0.00068985859 * cos( 2.44460312617 +      217.23124870110*t);

+   saturn_y_0+=     0.00058382264 * cos( 0.58978766922 +      224.34479570190*t);

+   saturn_y_0+=     0.00054049836 * cos( 3.33757904879 +      853.19638175200*t);

+   saturn_y_0+=     0.00045790930 * cos( 0.30331527632 +       14.22709400160*t);

+   saturn_y_0+=     0.00041976402 * cos( 2.62591355948 +      199.07200143640*t);

+   saturn_y_0+=     0.00044697175 * cos( 0.90661238256 +       63.73589830340*t);

+   saturn_y_0+=     0.00025199575 * cos( 5.08963506006 +      216.48048917570*t);

+   saturn_y_0+=     0.00024640836 * cos( 2.95445247282 +      210.11770170030*t);

+   saturn_y_0+=     0.00024835151 * cos( 4.02630190571 +      415.55249061210*t);

+   saturn_y_0+=     0.00025545907 * cos( 0.06626229252 +      117.31986822020*t);

+   saturn_y_0+=     0.00029666833 * cos( 6.09910638345 +      735.87651353180*t);

+   saturn_y_0+=     0.00023396742 * cos( 3.96337393635 +      647.01083331480*t);

+   saturn_y_0+=     0.00023380691 * cos( 4.90051072276 +      149.56319713460*t);

+   saturn_y_0+=     0.00020272215 * cos( 2.34319548198 +      309.27832265580*t);

+   saturn_y_0+=     0.00020099552 * cos( 0.98365186365 +      522.57741809380*t);

+   saturn_y_0+=     0.00024827950 * cos( 3.92681428900 +       74.78159856730*t);

+   saturn_y_0+=     0.00015383927 * cos( 3.10227822627 +      277.03499374140*t);

+   saturn_y_0+=     0.00011629210 * cos( 5.74108283772 +     1059.38193018920*t);

+   saturn_y_0+=     0.00012422966 * cos( 2.62557865743 +      490.33408917940*t);

+   saturn_y_0+=     0.00012048048 * cos( 4.09265980116 +      351.81659230870*t);

+   saturn_y_0+=     0.00009551796 * cos( 3.48788042094 +       95.97922721780*t);

+   saturn_y_0+=     0.00007670379 * cos( 1.16594276164 +      742.99006053260*t);

+   saturn_y_0+=     0.00006919946 * cos( 1.17090063883 +      412.37109687440*t);

+   saturn_y_0+=     0.00009034877 * cos( 5.86816144198 +     1052.26838318840*t);

+   saturn_y_0+=     0.00006536751 * cos( 0.84246459392 +      838.96928775040*t);

+   saturn_y_0+=     0.00006082097 * cos( 4.58758280729 +      440.82528487760*t);

+   saturn_y_0+=     0.00005027211 * cos( 0.93213690546 +      846.08283475120*t);

+   saturn_y_0+=     0.00004838146 * cos( 4.98563812475 +      536.80451209540*t);

+   saturn_y_0+=     0.00005768897 * cos( 3.73776690402 +       38.13303563780*t);

+   saturn_y_0+=     0.00005201849 * cos( 2.97482802430 +      210.85141488320*t);

+   saturn_y_0+=     0.00005156578 * cos( 5.05796998564 +      215.74677599280*t);

+   saturn_y_0+=     0.00003792348 * cos( 4.41806046981 +      422.66603761290*t);

+   saturn_y_0+=     0.00003881104 * cos( 3.38026646963 +        3.93215326310*t);

+   saturn_y_0+=     0.00003768751 * cos( 2.14954247360 +      212.33588759150*t);

+   saturn_y_0+=     0.00003752010 * cos( 5.88125434018 +      214.26230328450*t);

+   saturn_y_0+=     0.00003118938 * cos( 5.55799397159 +      213.25091132820*t);

+   saturn_y_0+=     0.00003118056 * cos( 2.47259780102 +      213.34727954780*t);

+   saturn_y_0+=     0.00003815691 * cos( 2.44166851155 +      625.67019231240*t);

+   saturn_y_0+=     0.00004042463 * cos( 1.24471211016 +      137.03302416240*t);

+   saturn_y_0+=     0.00002829944 * cos( 5.44434225998 +      330.61896365820*t);

+   saturn_y_0+=     0.00003367270 * cos( 6.13298847057 +      437.64389113990*t);

+   saturn_y_0+=     0.00002891352 * cos( 5.85313497106 +       85.82729883120*t);

+   saturn_y_0+=     0.00002774595 * cos( 5.61594351302 +      203.73786788240*t);

+   saturn_y_0+=     0.00002638715 * cos( 3.83678156812 +      288.08069400530*t);

+   saturn_y_0+=     0.00003171680 * cos( 4.19553075395 +       76.26607127560*t);

+   saturn_y_0+=     0.00002532374 * cos( 3.52629372341 +      628.85158605010*t);

+   saturn_y_0+=     0.00002533632 * cos( 3.89788590926 +      138.51749687070*t);

+   saturn_y_0+=     0.00002982174 * cos( 2.58535107213 +     1066.49547719000*t);

+   saturn_y_0+=     0.00002620642 * cos( 0.69751279148 +      127.47179660680*t);

+   saturn_y_0+=     0.00002501775 * cos( 6.19929274396 +        9.56122755560*t);

+   saturn_y_0+=     0.00002448467 * cos( 0.54179432209 +     1155.36115740700*t);

+   saturn_y_0+=     0.00002431496 * cos( 2.40122451395 +      222.86032299360*t);

+   saturn_y_0+=     0.00003138628 * cos( 5.63058455924 +     1368.66025284500*t);

+   saturn_y_0+=     0.00002269226 * cos( 2.12401905105 +      430.53034413910*t);

+   saturn_y_0+=     0.00002078049 * cos( 1.95682348964 +      423.41679713830*t);

+   saturn_y_0+=     0.00002670750 * cos( 0.18165311734 +        3.18139373770*t);

+   saturn_y_0+=     0.00002339764 * cos( 4.29619053852 +      388.46515523820*t);

+   saturn_y_0+=     0.00001636580 * cos( 2.97440139727 +       12.53017297220*t);

+   saturn_y_0+=     0.00001639181 * cos( 0.62823227849 +      212.77783057620*t);

+   saturn_y_0+=     0.00001634235 * cos( 1.12043073218 +      213.82036029980*t);

+   saturn_y_0+=     0.00001499665 * cos( 5.16865990579 +       52.69019803950*t);

+   saturn_y_0+=     0.00001462908 * cos( 4.35285690993 +      429.77958461370*t);

+   saturn_y_0+=     0.00001678952 * cos( 2.07211719214 +      949.17560896980*t);

+   saturn_y_0+=     0.00001989253 * cos( 0.42496478369 +        1.48447270830*t);

+   saturn_y_0+=     0.00001540242 * cos( 3.21449770483 +      860.30992875280*t);

+   saturn_y_0+=     0.00001437063 * cos( 3.84293543293 +      350.33211960040*t);

+   saturn_y_0+=     0.00001276377 * cos( 2.98728987770 +      340.77089204480*t);

+   saturn_y_0+=     0.00001152164 * cos( 1.78736848302 +      942.06206196900*t);

+   saturn_y_0+=     0.00001112617 * cos( 5.19114183145 +      234.63973644040*t);

+   saturn_y_0+=     0.00001011023 * cos( 0.27242160432 +     1471.75302706360*t);

+   saturn_y_0+=     0.00001162807 * cos( 2.35040840317 +      200.76892246580*t);

+   saturn_y_0+=     0.00001091025 * cos( 4.25638370205 +      362.86229257260*t);

+   saturn_y_0+=     0.00001090678 * cos( 5.85086226218 +      173.94221952280*t);

+   saturn_y_0+=     0.00001186647 * cos( 5.38323620554 +     1685.05212250160*t);

+   saturn_y_0+=     0.00001120819 * cos( 1.89478696683 +      703.63318461740*t);

+   saturn_y_0+=     0.00001008898 * cos( 5.80110302450 +      225.82926841020*t);

+

+   double saturn_y_1=0.0;

+   saturn_y_1+=     0.05373889135 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_y_1+=     0.03090575152 * cos( 2.70346890906 +      426.59819087600*t);

+   saturn_y_1+=     0.02741594312 * cos( 4.26667636015 +      206.18554843720*t);

+   saturn_y_1+=     0.02647489677 * cos( 3.76132298889 +      220.41264243880*t);

+   saturn_y_1+=     0.00631520527 * cos( 5.03245505280 +        7.11354700080*t);

+   saturn_y_1+=     0.00256799701 * cos( 1.95351819758 +      639.89728631400*t);

+   saturn_y_1+=     0.00312271930 * cos( 3.25850205023 +      419.48464387520*t);

+   saturn_y_1+=     0.00189433319 * cos( 2.91501840819 +      433.71173787680*t);

+   saturn_y_1+=     0.00164133553 * cos( 5.29239290066 +      213.29909543800*t);

+   saturn_y_1+=     0.00116791227 * cos( 5.89146675760 +      110.20632121940*t);

+   saturn_y_1+=     0.00067210919 * cos( 2.17042636344 +      316.39186965660*t);

+   saturn_y_1+=     0.00067003292 * cos( 3.63101075514 +      227.52618943960*t);

+   saturn_y_1+=     0.00033002406 * cos( 4.35527405801 +      199.07200143640*t);

+   saturn_y_1+=     0.00030628998 * cos( 4.88861760772 +       14.22709400160*t);

+   saturn_y_1+=     0.00022234714 * cos( 4.62212779231 +      103.09277421860*t);

+   saturn_y_1+=     0.00018945004 * cos( 1.20412493845 +      853.19638175200*t);

+   saturn_y_1+=     0.00018079959 * cos( 3.51566153251 +      209.36694217490*t);

+   saturn_y_1+=     0.00017791543 * cos( 4.53214140649 +      217.23124870110*t);

+   saturn_y_1+=     0.00016320701 * cos( 3.29784030970 +      216.48048917570*t);

+   saturn_y_1+=     0.00015944258 * cos( 4.74503265169 +      210.11770170030*t);

+   saturn_y_1+=     0.00016717122 * cos( 3.00270792752 +      632.78373931320*t);

+   saturn_y_1+=     0.00016149947 * cos( 4.04186432517 +      323.50541665740*t);

+   saturn_y_1+=     0.00014481431 * cos( 2.10298298650 +      647.01083331480*t);

+   saturn_y_1+=     0.00011084040 * cos( 4.74073871754 +      117.31986822020*t);

+   saturn_y_1+=     0.00009905491 * cos( 3.60258599375 +      202.25339517410*t);

+   saturn_y_1+=     0.00008726051 * cos( 4.46341342877 +      224.34479570190*t);

+   saturn_y_1+=     0.00006585597 * cos( 4.07326320487 +      309.27832265580*t);

+   saturn_y_1+=     0.00005505978 * cos( 2.83207390240 +      440.82528487760*t);

+   saturn_y_1+=     0.00005424041 * cos( 1.03197684410 +       11.04570026390*t);

+   saturn_y_1+=     0.00004178266 * cos( 3.01038512076 +      412.37109687440*t);

+   saturn_y_1+=     0.00004049905 * cos( 5.17488767645 +       95.97922721780*t);

+   saturn_y_1+=     0.00002735256 * cos( 2.53975850409 +      149.56319713460*t);

+   saturn_y_1+=     0.00002369024 * cos( 2.40497927917 +      522.57741809380*t);

+   saturn_y_1+=     0.00001745258 * cos( 5.50576015456 +      277.03499374140*t);

+   saturn_y_1+=     0.00001692790 * cos( 2.39926502529 +      422.66603761290*t);

+   saturn_y_1+=     0.00001546006 * cos( 3.73156925599 +      330.61896365820*t);

+   saturn_y_1+=     0.00001389354 * cos( 0.46207025895 +     1066.49547719000*t);

+   saturn_y_1+=     0.00001332553 * cos( 3.49199812296 +      234.63973644040*t);

+   saturn_y_1+=     0.00001300934 * cos( 0.83727681906 +      415.55249061210*t);

+   saturn_y_1+=     0.00001393622 * cos( 4.62214277175 +        3.18139373770*t);

+   saturn_y_1+=     0.00001174319 * cos( 2.72609984335 +      846.08283475120*t);

+   saturn_y_1+=     0.00001148010 * cos( 3.04374738882 +      536.80451209540*t);

+   saturn_y_1+=     0.00001314125 * cos( 4.38891656600 +      625.67019231240*t);

+   saturn_y_1+=     0.00001127952 * cos( 3.87309692307 +      423.41679713830*t);

+   saturn_y_1+=     0.00001127646 * cos( 1.31088906213 +      860.30992875280*t);

+   saturn_y_1+=     0.00001519732 * cos( 6.12880664637 +        3.93215326310*t);

+   saturn_y_1+=     0.00001102361 * cos( 2.50535306014 +      429.77958461370*t);

+   saturn_y_1+=     0.00001344891 * cos( 1.41793593685 +      210.85141488320*t);

+   saturn_y_1+=     0.00001331786 * cos( 0.33834520814 +      215.74677599280*t);

+   saturn_y_1=saturn_y_1 * t;

+

+   double saturn_y_2=0.0;

+   saturn_y_2+=     0.00563706537 * cos( 5.97115878242 +      206.18554843720*t);

+   saturn_y_2+=     0.00547012116 * cos( 2.05154973426 +      220.41264243880*t);

+   saturn_y_2+=     0.00458518613 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_y_2+=     0.00362294249 * cos( 0.89540100509 +      213.29909543800*t);

+   saturn_y_2+=     0.00225521642 * cos( 0.91699821445 +      426.59819087600*t);

+   saturn_y_2+=     0.00088390611 * cos( 3.30289449917 +        7.11354700080*t);

+   saturn_y_2+=     0.00050101314 * cos( 1.12976163835 +      433.71173787680*t);

+   saturn_y_2+=     0.00045516403 * cos( 5.07669466539 +      419.48464387520*t);

+   saturn_y_2+=     0.00032896745 * cos( 0.02089057938 +      639.89728631400*t);

+   saturn_y_2+=     0.00027199743 * cos( 1.92638417640 +      227.52618943960*t);

+   saturn_y_2+=     0.00013251505 * cos( 6.07693099404 +      199.07200143640*t);

+   saturn_y_2+=     0.00010425984 * cos( 3.18246869028 +       14.22709400160*t);

+   saturn_y_2+=     0.00006673556 * cos( 4.24747633887 +      110.20632121940*t);

+   saturn_y_2+=     0.00004658591 * cos( 0.26557833758 +      647.01083331480*t);

+   saturn_y_2+=     0.00004934094 * cos( 1.51301179516 +      216.48048917570*t);

+   saturn_y_2+=     0.00004789554 * cos( 0.24337901916 +      210.11770170030*t);

+   saturn_y_2+=     0.00004167268 * cos( 3.73203671391 +      316.39186965660*t);

+   saturn_y_2+=     0.00003509537 * cos( 5.49281440568 +      853.19638175200*t);

+   saturn_y_2+=     0.00002743470 * cos( 6.21939083886 +      103.09277421860*t);

+   saturn_y_2+=     0.00002661172 * cos( 1.58795412736 +      209.36694217490*t);

+   saturn_y_2+=     0.00002541191 * cos( 1.07964653574 +      440.82528487760*t);

+   saturn_y_2+=     0.00002568018 * cos( 0.16811216098 +      217.23124870110*t);

+   saturn_y_2+=     0.00002507738 * cos( 3.11882746290 +      117.31986822020*t);

+   saturn_y_2+=     0.00002159089 * cos( 4.99912567024 +      632.78373931320*t);

+   saturn_y_2+=     0.00001828412 * cos( 2.43368650590 +      323.50541665740*t);

+   saturn_y_2+=     0.00001351629 * cos( 4.81673889364 +      412.37109687440*t);

+   saturn_y_2+=     0.00001177305 * cos( 5.84484412189 +      309.27832265580*t);

+   saturn_y_2=saturn_y_2 * t * t;

+

+   double saturn_y_3=0.0;

+   saturn_y_3+=     0.00077376615 * cos( 1.40391048961 +      206.18554843720*t);

+   saturn_y_3+=     0.00075564351 * cos( 0.31962896379 +      220.41264243880*t);

+   saturn_y_3+=     0.00022843837 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_y_3+=     0.00010672263 * cos( 5.36495663820 +      426.59819087600*t);

+   saturn_y_3+=     0.00009010175 * cos( 5.62865146645 +      433.71173787680*t);

+   saturn_y_3+=     0.00007418018 * cos( 0.21442310101 +      227.52618943960*t);

+   saturn_y_3+=     0.00008298723 * cos( 1.52262563519 +        7.11354700080*t);

+   saturn_y_3+=     0.00004507061 * cos( 0.67248969480 +      419.48464387520*t);

+   saturn_y_3+=     0.00003581682 * cos( 1.51466786030 +      199.07200143640*t);

+   saturn_y_3+=     0.00002981969 * cos( 4.42868951627 +      639.89728631400*t);

+   saturn_y_3+=     0.00002376221 * cos( 1.46232779180 +       14.22709400160*t);

+   saturn_y_3+=     0.00001024263 * cos( 4.72337917196 +      647.01083331480*t);

+   saturn_y_3=saturn_y_3 * t * t * t;

+

+   double saturn_y_4=0.0;

+   saturn_y_4+=     0.00007978886 * cos( 3.13229268011 +      206.18554843720*t);

+   saturn_y_4+=     0.00007868379 * cos( 4.84940260021 +      220.41264243880*t);

+   saturn_y_4+=     0.00001514835 * cos( 4.77675733867 +      227.52618943960*t);

+   saturn_y_4+=     0.00001225569 * cos( 3.84500138574 +      433.71173787680*t);

+   saturn_y_4=saturn_y_4 * t * t * t * t;

+

+   return saturn_y_0+saturn_y_1+saturn_y_2+saturn_y_3+saturn_y_4;

+}

+

+double vsop87a_milli_saturn_z(double t){

+   double saturn_z_0=0.0;

+   saturn_z_0+=     0.41356950940 * cos( 3.60234142982 +      213.29909543800*t);

+   saturn_z_0+=     0.01148283576 * cos( 2.85128367469 +      426.59819087600*t);

+   saturn_z_0+=     0.01214249867 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_z_0+=     0.00329280791 * cos( 0.57121407104 +      206.18554843720*t);

+   saturn_z_0+=     0.00286934048 * cos( 3.48073526693 +      220.41264243880*t);

+   saturn_z_0+=     0.00099076584 * cos( 4.73369511264 +        7.11354700080*t);

+   saturn_z_0+=     0.00057361820 * cos( 4.92611225093 +      110.20632121940*t);

+   saturn_z_0+=     0.00047738127 * cos( 2.10039779728 +      639.89728631400*t);

+   saturn_z_0+=     0.00043458803 * cos( 5.84904978051 +      419.48464387520*t);

+   saturn_z_0+=     0.00034565673 * cos( 5.42614229590 +      316.39186965660*t);

+   saturn_z_0+=     0.00016185391 * cos( 2.72987173675 +      433.71173787680*t);

+   saturn_z_0+=     0.00009001270 * cos( 1.38140102737 +      103.09277421860*t);

+   saturn_z_0+=     0.00011433574 * cos( 3.71662021072 +      529.69096509460*t);

+   saturn_z_0+=     0.00005398708 * cos( 5.13204892363 +      202.25339517410*t);

+   saturn_z_0+=     0.00003902467 * cos( 3.71499738796 +      323.50541665740*t);

+   saturn_z_0+=     0.00003709212 * cos( 5.05549348785 +      632.78373931320*t);

+   saturn_z_0+=     0.00003614100 * cos( 3.35210451276 +      227.52618943960*t);

+   saturn_z_0+=     0.00003379953 * cos( 2.13868919206 +       11.04570026390*t);

+   saturn_z_0+=     0.00003089874 * cos( 3.62572857085 +      209.36694217490*t);

+   saturn_z_0+=     0.00002683064 * cos( 4.87689555581 +      224.34479570190*t);

+   saturn_z_0+=     0.00002963493 * cos( 0.46490184985 +      217.23124870110*t);

+   saturn_z_0+=     0.00002343367 * cos( 1.34558278340 +      853.19638175200*t);

+   saturn_z_0+=     0.00002423663 * cos( 2.92907094760 +       63.73589830340*t);

+   saturn_z_0+=     0.00001701916 * cos( 1.89892525654 +      735.87651353180*t);

+   saturn_z_0+=     0.00001941205 * cos( 4.59421314662 +       14.22709400160*t);

+   saturn_z_0+=     0.00001990145 * cos( 0.73166053611 +      199.07200143640*t);

+   saturn_z_0+=     0.00001460265 * cos( 3.12851339724 +      522.57741809380*t);

+   saturn_z_0+=     0.00001148341 * cos( 4.41139213915 +      117.31986822020*t);

+   saturn_z_0+=     0.00001092809 * cos( 3.10679381209 +      216.48048917570*t);

+   saturn_z_0+=     0.00001015179 * cos( 1.97897195994 +      647.01083331480*t);

+   saturn_z_0+=     0.00001098254 * cos( 0.96097709156 +      210.11770170030*t);

+   saturn_z_0+=     0.00001028743 * cos( 2.11933059243 +      415.55249061210*t);

+

+   double saturn_z_1=0.0;

+   saturn_z_1+=     0.01906503283 * cos( 4.94544746116 +      213.29909543800*t);

+   saturn_z_1+=     0.00528301265 * cos( 3.14159265359 +        0.00000000000*t);

+   saturn_z_1+=     0.00130262284 * cos( 2.26140980879 +      206.18554843720*t);

+   saturn_z_1+=     0.00101466332 * cos( 1.79095829545 +      220.41264243880*t);

+   saturn_z_1+=     0.00085947578 * cos( 0.51612788497 +      426.59819087600*t);

+   saturn_z_1+=     0.00022257446 * cos( 3.07684015656 +        7.11354700080*t);

+   saturn_z_1+=     0.00016179946 * cos( 1.19987517506 +      419.48464387520*t);

+   saturn_z_1+=     0.00009117402 * cos( 6.17205626814 +      639.89728631400*t);

+   saturn_z_1+=     0.00007470703 * cos( 0.93135621171 +      433.71173787680*t);

+   saturn_z_1+=     0.00004966668 * cos( 0.19044864213 +      316.39186965660*t);

+   saturn_z_1+=     0.00003816564 * cos( 4.38284565245 +      110.20632121940*t);

+   saturn_z_1+=     0.00002724120 * cos( 1.65580138665 +      227.52618943960*t);

+   saturn_z_1+=     0.00001734540 * cos( 3.51628075636 +      103.09277421860*t);

+   saturn_z_1+=     0.00001541995 * cos( 2.42323572812 +      199.07200143640*t);

+   saturn_z_1+=     0.00001209302 * cos( 2.91140089093 +       14.22709400160*t);

+   saturn_z_1=saturn_z_1 * t;

+

+   double saturn_z_2=0.0;

+   saturn_z_2+=     0.00131275155 * cos( 0.08868998101 +      213.29909543800*t);

+   saturn_z_2+=     0.00030147649 * cos( 3.91396203887 +      206.18554843720*t);

+   saturn_z_2+=     0.00019322173 * cos( 0.09228748624 +      220.41264243880*t);

+   saturn_z_2+=     0.00006868926 * cos( 5.48420255395 +      426.59819087600*t);

+   saturn_z_2+=     0.00002826107 * cos( 1.36583318555 +        7.11354700080*t);

+   saturn_z_2+=     0.00002646332 * cos( 2.94607395955 +      419.48464387520*t);

+   saturn_z_2+=     0.00003138233 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_z_2+=     0.00001844798 * cos( 5.43612062856 +      433.71173787680*t);

+   saturn_z_2+=     0.00001055383 * cos( 6.23890785179 +      227.52618943960*t);

+   saturn_z_2+=     0.00001036435 * cos( 4.33916308552 +      639.89728631400*t);

+   saturn_z_2=saturn_z_2 * t * t;

+

+   double saturn_z_3=0.0;

+   saturn_z_3+=     0.00004559419 * cos( 1.70646871501 +      213.29909543800*t);

+   saturn_z_3+=     0.00004779074 * cos( 5.57723756330 +      206.18554843720*t);

+   saturn_z_3+=     0.00003965402 * cos( 0.00000000000 +        0.00000000000*t);

+   saturn_z_3+=     0.00002508242 * cos( 4.64959056313 +      220.41264243880*t);

+   saturn_z_3=saturn_z_3 * t * t * t;

+

+   return saturn_z_0+saturn_z_1+saturn_z_2+saturn_z_3;

+}

+

+double vsop87a_milli_uranus_x(double t){

+   double uranus_x_0=0.0;

+   uranus_x_0+=    19.17370730359 * cos( 5.48133416489 +       74.78159856730*t);

+   uranus_x_0+=     1.32272523872 * cos( 0.00000000000 +        0.00000000000*t);

+   uranus_x_0+=     0.44402496796 * cos( 1.65967519586 +      149.56319713460*t);

+   uranus_x_0+=     0.14668209481 * cos( 3.42395862804 +       73.29712585900*t);

+   uranus_x_0+=     0.14130269479 * cos( 4.39572927934 +       76.26607127560*t);

+   uranus_x_0+=     0.06201106178 * cos( 5.14043574125 +        1.48447270830*t);

+   uranus_x_0+=     0.01542951343 * cos( 4.12121838072 +      224.34479570190*t);

+   uranus_x_0+=     0.01444216660 * cos( 2.65117115201 +      148.07872442630*t);

+   uranus_x_0+=     0.00944995563 * cos( 1.65869338757 +       11.04570026390*t);

+   uranus_x_0+=     0.00657524815 * cos( 0.57595170636 +      151.04766984290*t);

+   uranus_x_0+=     0.00621624676 * cos( 3.05882246638 +       77.75054398390*t);

+   uranus_x_0+=     0.00585182542 * cos( 4.79934779678 +       71.81265315070*t);

+   uranus_x_0+=     0.00634000270 * cos( 4.09556589724 +       63.73589830340*t);

+   uranus_x_0+=     0.00547699056 * cos( 3.63127725056 +       85.82729883120*t);

+   uranus_x_0+=     0.00458219984 * cos( 3.90788284112 +        2.96894541660*t);

+   uranus_x_0+=     0.00496087649 * cos( 0.59947400861 +      529.69096509460*t);

+   uranus_x_0+=     0.00383625535 * cos( 6.18762010576 +      138.51749687070*t);

+   uranus_x_0+=     0.00267938156 * cos( 0.96885660137 +      213.29909543800*t);

+   uranus_x_0+=     0.00215368005 * cos( 5.30877641428 +       38.13303563780*t);

+   uranus_x_0+=     0.00145505389 * cos( 2.31759757085 +       70.84944530420*t);

+   uranus_x_0+=     0.00135340032 * cos( 5.51062460816 +       78.71375183040*t);

+   uranus_x_0+=     0.00119593859 * cos( 4.10138544267 +       39.61750834610*t);

+   uranus_x_0+=     0.00125105686 * cos( 2.51455273063 +      111.43016149680*t);

+   uranus_x_0+=     0.00111260244 * cos( 5.12252784325 +      222.86032299360*t);

+   uranus_x_0+=     0.00104619827 * cos( 3.90538916334 +      146.59425171800*t);

+   uranus_x_0+=     0.00110125387 * cos( 4.45473528724 +       35.16409022120*t);

+   uranus_x_0+=     0.00063584588 * cos( 0.29966233158 +      299.12639426920*t);

+   uranus_x_0+=     0.00053904041 * cos( 3.92590422507 +        3.93215326310*t);

+   uranus_x_0+=     0.00065066905 * cos( 3.73008452906 +      109.94568878850*t);

+   uranus_x_0+=     0.00039181662 * cos( 2.68841280769 +        4.45341812490*t);

+   uranus_x_0+=     0.00034341683 * cos( 3.03781661928 +      225.82926841020*t);

+   uranus_x_0+=     0.00033134636 * cos( 2.54201591218 +       65.22037101170*t);

+   uranus_x_0+=     0.00034555652 * cos( 1.84699329257 +       79.23501669220*t);

+   uranus_x_0+=     0.00033867050 * cos( 5.98418436103 +       70.32818044240*t);

+   uranus_x_0+=     0.00028371614 * cos( 2.58026657123 +      127.47179660680*t);

+   uranus_x_0+=     0.00035943348 * cos( 4.08754543016 +      202.25339517410*t);

+   uranus_x_0+=     0.00025208833 * cos( 5.30272144657 +        9.56122755560*t);

+   uranus_x_0+=     0.00023467802 * cos( 4.09729860322 +      145.63104387150*t);

+   uranus_x_0+=     0.00022963939 * cos( 5.51475073655 +       84.34282612290*t);

+   uranus_x_0+=     0.00031823951 * cos( 5.53948583244 +      152.53214255120*t);

+   uranus_x_0+=     0.00028384953 * cos( 6.01785430306 +      184.72728735580*t);

+   uranus_x_0+=     0.00026657176 * cos( 6.11027939727 +      160.60889739850*t);

+   uranus_x_0+=     0.00019676762 * cos( 5.53431398332 +       74.66972398270*t);

+   uranus_x_0+=     0.00019653873 * cos( 2.28660913421 +       74.89347315190*t);

+   uranus_x_0+=     0.00019954280 * cos( 0.57450958037 +       12.53017297220*t);

+   uranus_x_0+=     0.00018565067 * cos( 0.62225019017 +       52.69019803950*t);

+   uranus_x_0+=     0.00020084756 * cos( 4.47297488471 +       22.09140052780*t);

+   uranus_x_0+=     0.00019926329 * cos( 1.39878194708 +      112.91463420510*t);

+   uranus_x_0+=     0.00018575632 * cos( 5.70217475790 +       33.67961751290*t);

+   uranus_x_0+=     0.00016587870 * cos( 4.86920309163 +      108.46121608020*t);

+   uranus_x_0+=     0.00015171194 * cos( 2.88415453399 +       41.10198105440*t);

+   uranus_x_0+=     0.00011245800 * cos( 6.11597016146 +       71.60020482960*t);

+   uranus_x_0+=     0.00013948521 * cos( 6.27545694160 +      221.37585028530*t);

+   uranus_x_0+=     0.00010798350 * cos( 1.70031857078 +       77.96299230500*t);

+   uranus_x_0+=     0.00013593955 * cos( 2.55407820633 +       87.31177153950*t);

+   uranus_x_0+=     0.00011997848 * cos( 0.94875212305 +     1059.38193018920*t);

+   uranus_x_0+=     0.00012884351 * cos( 5.08737999470 +      145.10977900970*t);

+   uranus_x_0+=     0.00012394786 * cos( 6.21892878850 +       72.33391801250*t);

+   uranus_x_0+=     0.00012253318 * cos( 0.19452856525 +       36.64856292950*t);

+   uranus_x_0+=     0.00011538642 * cos( 1.77241794539 +       77.22927912210*t);

+   uranus_x_0+=     0.00008738409 * cos( 4.96956808452 +      186.21176006410*t);

+   uranus_x_0+=     0.00007095608 * cos( 1.30384750044 +      297.64192156090*t);

+   uranus_x_0+=     0.00006262602 * cos( 1.71385983783 +      153.49535039770*t);

+   uranus_x_0+=     0.00007487302 * cos( 0.11408470667 +      426.59819087600*t);

+   uranus_x_0+=     0.00007798974 * cos( 5.82410372587 +      340.77089204480*t);

+   uranus_x_0+=     0.00006669249 * cos( 5.08626589612 +       62.25142559510*t);

+   uranus_x_0+=     0.00005505358 * cos( 3.31282108025 +      140.00196957900*t);

+   uranus_x_0+=     0.00005372927 * cos( 4.12498282863 +       75.30286342910*t);

+   uranus_x_0+=     0.00005354242 * cos( 3.69263973447 +       74.26033370550*t);

+   uranus_x_0+=     0.00004478123 * cos( 1.11838191479 +       66.70484372000*t);

+   uranus_x_0+=     0.00004233075 * cos( 3.94913608184 +      265.98929347750*t);

+   uranus_x_0+=     0.00005038353 * cos( 4.68664376918 +       18.15924726470*t);

+   uranus_x_0+=     0.00004570470 * cos( 0.97536665751 +      183.24281464750*t);

+   uranus_x_0+=     0.00004751325 * cos( 4.95762395337 +       73.81839072080*t);

+   uranus_x_0+=     0.00004448651 * cos( 0.29436142982 +      114.39910691340*t);

+   uranus_x_0+=     0.00003312340 * cos( 0.52418923788 +       82.85835341460*t);

+   uranus_x_0+=     0.00004515952 * cos( 2.88576303120 +       75.74480641380*t);

+   uranus_x_0+=     0.00003559276 * cos( 1.47627607503 +        5.93789083320*t);

+   uranus_x_0+=     0.00003268117 * cos( 0.51827231333 +      220.41264243880*t);

+   uranus_x_0+=     0.00003578235 * cos( 1.11528903208 +      137.03302416240*t);

+   uranus_x_0+=     0.00003004737 * cos( 5.12122132051 +        7.11354700080*t);

+   uranus_x_0+=     0.00002882392 * cos( 2.76136583899 +      373.90799283650*t);

+   uranus_x_0+=     0.00002579454 * cos( 3.84784330333 +      277.03499374140*t);

+   uranus_x_0+=     0.00002597765 * cos( 0.22409539936 +       96.87299909510*t);

+   uranus_x_0+=     0.00002560744 * cos( 4.44236223450 +       80.19822453870*t);

+   uranus_x_0+=     0.00002722745 * cos( 6.09456175016 +      106.97674337190*t);

+   uranus_x_0+=     0.00002528025 * cos( 0.89508396542 +       68.84370773410*t);

+   uranus_x_0+=     0.00002631138 * cos( 0.04831552531 +      305.34616939270*t);

+   uranus_x_0+=     0.00002541716 * cos( 0.64495056482 +       32.19514480460*t);

+   uranus_x_0+=     0.00002241129 * cos( 5.22377697501 +        3.18139373770*t);

+   uranus_x_0+=     0.00001965145 * cos( 0.09207526632 +       20.60692781950*t);

+   uranus_x_0+=     0.00002232022 * cos( 0.63571664756 +       80.71948940050*t);

+   uranus_x_0+=     0.00001933814 * cos( 5.75490033864 +       74.73341445750*t);

+   uranus_x_0+=     0.00001933817 * cos( 2.06557585395 +       74.82978267710*t);

+   uranus_x_0+=     0.00002138391 * cos( 4.20897429922 +       74.52096613640*t);

+   uranus_x_0+=     0.00002126427 * cos( 3.61171465436 +       75.04223099820*t);

+   uranus_x_0+=     0.00002215516 * cos( 2.18613112875 +      259.50888592310*t);

+   uranus_x_0+=     0.00001891213 * cos( 5.49941424248 +      300.61086697750*t);

+   uranus_x_0+=     0.00001927679 * cos( 1.29228021932 +      159.12442469020*t);

+   uranus_x_0+=     0.00001796558 * cos( 5.73271543335 +       74.62153987290*t);

+   uranus_x_0+=     0.00001792522 * cos( 2.08789166984 +       74.94165726170*t);

+   uranus_x_0+=     0.00001873542 * cos( 4.23391867169 +      206.18554843720*t);

+   uranus_x_0+=     0.00002182901 * cos( 1.23755478345 +      479.28838891550*t);

+   uranus_x_0+=     0.00001860591 * cos( 1.67536711716 +       42.58645376270*t);

+   uranus_x_0+=     0.00002075591 * cos( 3.15586933464 +      131.40394986990*t);

+   uranus_x_0+=     0.00001912582 * cos( 5.83091918696 +       14.97785352700*t);

+   uranus_x_0+=     0.00001529180 * cos( 2.05204104820 +      191.20769491020*t);

+   uranus_x_0+=     0.00002064173 * cos( 3.60208606410 +      835.03713448730*t);

+   uranus_x_0+=     0.00001768763 * cos( 1.19254481620 +      219.89137757700*t);

+   uranus_x_0+=     0.00001892359 * cos( 4.32128621847 +      154.01661525950*t);

+   uranus_x_0+=     0.00001797047 * cos( 1.73417465594 +      227.31374111850*t);

+   uranus_x_0+=     0.00001558489 * cos( 6.16891070489 +       59.80374504030*t);

+   uranus_x_0+=     0.00001672893 * cos( 0.01232646186 +      143.62530630140*t);

+   uranus_x_0+=     0.00001467268 * cos( 2.10975578758 +        2.44768055480*t);

+   uranus_x_0+=     0.00001677659 * cos( 0.42525121334 +        8.07675484730*t);

+   uranus_x_0+=     0.00001347303 * cos( 5.46763140224 +      288.08069400530*t);

+   uranus_x_0+=     0.00001744555 * cos( 0.82022450313 +       56.62235130260*t);

+   uranus_x_0+=     0.00001427180 * cos( 0.38786175669 +       92.94084583200*t);

+   uranus_x_0+=     0.00001263032 * cos( 5.63689596853 +      404.50679034820*t);

+   uranus_x_0+=     0.00001221506 * cos( 5.20012455894 +       54.17467074780*t);

+   uranus_x_0+=     0.00001574905 * cos( 5.72297800263 +       39.35687591520*t);

+   uranus_x_0+=     0.00001269686 * cos( 2.66330104031 +      142.44965013380*t);

+   uranus_x_0+=     0.00001438869 * cos( 0.72633739717 +      522.57741809380*t);

+   uranus_x_0+=     0.00001408997 * cos( 3.61751904356 +      536.80451209540*t);

+   uranus_x_0+=     0.00001418300 * cos( 2.29718712012 +      235.39049596580*t);

+   uranus_x_0+=     0.00001040948 * cos( 2.74644165501 +        5.41662597140*t);

+   uranus_x_0+=     0.00001256867 * cos( 5.61684736425 +       67.66805156650*t);

+   uranus_x_0+=     0.00001164218 * cos( 2.08302637541 +       81.89514556810*t);

+   uranus_x_0+=     0.00001009252 * cos( 2.02320517037 +       74.03083904190*t);

+   uranus_x_0+=     0.00001077810 * cos( 1.05685900920 +      128.95626931510*t);

+   uranus_x_0+=     0.00001212025 * cos( 3.41577832660 +      211.81462272970*t);

+   uranus_x_0+=     0.00001223648 * cos( 3.84373514640 +      187.69623277240*t);

+   uranus_x_0+=     0.00001334371 * cos( 2.17621743689 +      380.12776796000*t);

+   uranus_x_0+=     0.00001144565 * cos( 2.42148845239 +      296.15744885260*t);

+   uranus_x_0+=     0.00001241589 * cos( 1.81282962357 +      134.58534360760*t);

+   uranus_x_0+=     0.00001192274 * cos( 5.58661990233 +       50.40257617910*t);

+   uranus_x_0+=     0.00001093678 * cos( 3.94451812233 +      230.56457082540*t);

+   uranus_x_0+=     0.00001077916 * cos( 5.01417740021 +      181.75834193920*t);

+   uranus_x_0+=     0.00001166898 * cos( 2.02955848543 +      110.20632121940*t);

+   uranus_x_0+=     0.00001056848 * cos( 5.53440854164 +       14.01464568050*t);

+

+   double uranus_x_1=0.0;

+   uranus_x_1+=     0.00739730021 * cos( 6.01067825116 +      149.56319713460*t);

+   uranus_x_1+=     0.00526878306 * cos( 3.14159265359 +        0.00000000000*t);

+   uranus_x_1+=     0.00239840801 * cos( 5.33657762707 +       73.29712585900*t);

+   uranus_x_1+=     0.00229676787 * cos( 2.48204455775 +       76.26607127560*t);

+   uranus_x_1+=     0.00111045158 * cos( 5.57157235960 +       11.04570026390*t);

+   uranus_x_1+=     0.00096352822 * cos( 0.35070389084 +       63.73589830340*t);

+   uranus_x_1+=     0.00081511870 * cos( 1.21058618039 +       85.82729883120*t);

+   uranus_x_1+=     0.00045687564 * cos( 2.29216583843 +      138.51749687070*t);

+   uranus_x_1+=     0.00051382501 * cos( 2.18935125260 +      224.34479570190*t);

+   uranus_x_1+=     0.00038844330 * cos( 0.30724575951 +       70.84944530420*t);

+   uranus_x_1+=     0.00036158493 * cos( 1.23634798757 +       78.71375183040*t);

+   uranus_x_1+=     0.00032333094 * cos( 5.06666556704 +       74.78159856730*t);

+   uranus_x_1+=     0.00021685656 * cos( 4.93710968392 +      151.04766984290*t);

+   uranus_x_1+=     0.00019441970 * cos( 1.30617490304 +       77.75054398390*t);

+   uranus_x_1+=     0.00017376241 * cos( 0.24607221230 +       71.81265315070*t);

+   uranus_x_1+=     0.00015211071 * cos( 5.53141633140 +        3.93215326310*t);

+   uranus_x_1+=     0.00007735984 * cos( 1.61349552789 +       71.60020482960*t);

+   uranus_x_1+=     0.00007425078 * cos( 6.20357977116 +       77.96299230500*t);

+   uranus_x_1+=     0.00006995857 * cos( 2.40633283814 +      145.63104387150*t);

+   uranus_x_1+=     0.00007291691 * cos( 2.23597571444 +        2.96894541660*t);

+   uranus_x_1+=     0.00007585264 * cos( 2.76074218330 +      148.07872442630*t);

+   uranus_x_1+=     0.00004378335 * cos( 3.74296322240 +      160.60889739850*t);

+   uranus_x_1+=     0.00004127713 * cos( 1.48475181305 +       22.09140052780*t);

+   uranus_x_1+=     0.00003933541 * cos( 4.73864204208 +       65.22037101170*t);

+   uranus_x_1+=     0.00002910312 * cos( 5.91941333050 +      127.47179660680*t);

+   uranus_x_1+=     0.00002788434 * cos( 4.90117297196 +      213.29909543800*t);

+   uranus_x_1+=     0.00002802392 * cos( 3.76505436434 +       52.69019803950*t);

+   uranus_x_1+=     0.00002545264 * cos( 3.36768337628 +        9.56122755560*t);

+   uranus_x_1+=     0.00002647073 * cos( 4.53813176345 +       12.53017297220*t);

+   uranus_x_1+=     0.00003177614 * cos( 4.65226634926 +      299.12639426920*t);

+   uranus_x_1+=     0.00002228396 * cos( 0.18087986338 +       87.31177153950*t);

+   uranus_x_1+=     0.00002824668 * cos( 3.40143685673 +       84.34282612290*t);

+   uranus_x_1+=     0.00002525203 * cos( 2.83821144961 +       18.15924726470*t);

+   uranus_x_1+=     0.00002216987 * cos( 4.78338909951 +       72.33391801250*t);

+   uranus_x_1+=     0.00001624493 * cos( 3.75817281127 +      153.49535039770*t);

+   uranus_x_1+=     0.00001928881 * cos( 2.39940180311 +       39.61750834610*t);

+   uranus_x_1+=     0.00001555444 * cos( 4.13741667297 +       73.81839072080*t);

+   uranus_x_1+=     0.00001600865 * cos( 0.08376247543 +       79.23501669220*t);

+   uranus_x_1+=     0.00001476317 * cos( 3.67283851029 +       75.74480641380*t);

+   uranus_x_1+=     0.00001427088 * cos( 1.45690759014 +       70.32818044240*t);

+   uranus_x_1+=     0.00001533469 * cos( 3.71776498048 +      152.53214255120*t);

+   uranus_x_1+=     0.00001747266 * cos( 3.24870046809 +       77.22927912210*t);

+   uranus_x_1+=     0.00001716831 * cos( 3.39415662657 +      222.86032299360*t);

+   uranus_x_1+=     0.00001707504 * cos( 1.11296012106 +      225.82926841020*t);

+   uranus_x_1+=     0.00001734228 * cos( 5.39619902298 +      146.59425171800*t);

+   uranus_x_1+=     0.00001476617 * cos( 3.53047075439 +        3.18139373770*t);

+   uranus_x_1+=     0.00001179645 * cos( 5.13953276367 +      220.41264243880*t);

+   uranus_x_1+=     0.00001239315 * cos( 0.98221206501 +        4.45341812490*t);

+   uranus_x_1+=     0.00001099691 * cos( 1.35138854505 +       62.25142559510*t);

+   uranus_x_1+=     0.00001061312 * cos( 5.00125105380 +      131.40394986990*t);

+   uranus_x_1+=     0.00001029261 * cos( 5.42434597865 +      109.94568878850*t);

+   uranus_x_1=uranus_x_1 * t;

+

+   double uranus_x_2=0.0;

+   uranus_x_2+=     0.00016015732 * cos( 3.83700026619 +       74.78159856730*t);

+   uranus_x_2+=     0.00010915299 * cos( 3.02987776270 +      149.56319713460*t);

+   uranus_x_2+=     0.00007497619 * cos( 3.83429136661 +       11.04570026390*t);

+   uranus_x_2+=     0.00008053623 * cos( 2.54646146122 +       63.73589830340*t);

+   uranus_x_2+=     0.00005408033 * cos( 4.78033642303 +       70.84944530420*t);

+   uranus_x_2+=     0.00005021971 * cos( 3.04632772928 +       78.71375183040*t);

+   uranus_x_2+=     0.00006717313 * cos( 5.31264214501 +       85.82729883120*t);

+   uranus_x_2+=     0.00005284684 * cos( 2.11901942097 +       73.29712585900*t);

+   uranus_x_2+=     0.00004874936 * cos( 5.68616132176 +       76.26607127560*t);

+   uranus_x_2+=     0.00003002124 * cos( 4.07944398452 +      138.51749687070*t);

+   uranus_x_2+=     0.00002521797 * cos( 3.36028253173 +       71.60020482960*t);

+   uranus_x_2+=     0.00002413832 * cos( 4.45865225690 +       77.96299230500*t);

+   uranus_x_2+=     0.00002221373 * cos( 0.87427485235 +        3.93215326310*t);

+   uranus_x_2+=     0.00002291767 * cos( 0.00000000000 +        0.00000000000*t);

+   uranus_x_2+=     0.00001040250 * cos( 0.73133408837 +      145.63104387150*t);

+   uranus_x_2+=     0.00001046100 * cos( 5.85311910228 +      224.34479570190*t);

+   uranus_x_2=uranus_x_2 * t * t;

+

+   double uranus_x_3=0.0;

+   uranus_x_3+=     0.00001307049 * cos( 0.00000000000 +        0.00000000000*t);

+   uranus_x_3=uranus_x_3 * t * t * t;

+

+   return uranus_x_0+uranus_x_1+uranus_x_2+uranus_x_3;

+}

+

+double vsop87a_milli_uranus_y(double t){

+   double uranus_y_0=0.0;

+   uranus_y_0+=    19.16518231584 * cos( 3.91045677002 +       74.78159856730*t);

+   uranus_y_0+=     0.44390465203 * cos( 0.08884111329 +      149.56319713460*t);

+   uranus_y_0+=     0.16256125476 * cos( 3.14159265359 +        0.00000000000*t);

+   uranus_y_0+=     0.14755940186 * cos( 1.85423280679 +       73.29712585900*t);

+   uranus_y_0+=     0.14123958128 * cos( 2.82486076549 +       76.26607127560*t);

+   uranus_y_0+=     0.06250078231 * cos( 3.56960243857 +        1.48447270830*t);

+   uranus_y_0+=     0.01542668264 * cos( 2.55040539213 +      224.34479570190*t);

+   uranus_y_0+=     0.01442356575 * cos( 1.08004542712 +      148.07872442630*t);

+   uranus_y_0+=     0.00938975501 * cos( 0.09275714761 +       11.04570026390*t);

+   uranus_y_0+=     0.00650331846 * cos( 2.76142680222 +       63.73589830340*t);

+   uranus_y_0+=     0.00657343120 * cos( 5.28830704469 +      151.04766984290*t);

+   uranus_y_0+=     0.00621326770 * cos( 1.48795811387 +       77.75054398390*t);

+   uranus_y_0+=     0.00541961958 * cos( 3.24476486661 +       71.81265315070*t);

+   uranus_y_0+=     0.00547472694 * cos( 2.06037924573 +       85.82729883120*t);

+   uranus_y_0+=     0.00459589120 * cos( 2.33745536070 +        2.96894541660*t);

+   uranus_y_0+=     0.00495936105 * cos( 5.31205753740 +      529.69096509460*t);

+   uranus_y_0+=     0.00387922853 * cos( 4.62026923885 +      138.51749687070*t);

+   uranus_y_0+=     0.00268363417 * cos( 5.68085299020 +      213.29909543800*t);

+   uranus_y_0+=     0.00216239629 * cos( 3.73800767580 +       38.13303563780*t);

+   uranus_y_0+=     0.00144032475 * cos( 0.75015700920 +       70.84944530420*t);

+   uranus_y_0+=     0.00135290820 * cos( 3.93970260616 +       78.71375183040*t);

+   uranus_y_0+=     0.00119670613 * cos( 2.53058783780 +       39.61750834610*t);

+   uranus_y_0+=     0.00124868545 * cos( 0.94315917319 +      111.43016149680*t);

+   uranus_y_0+=     0.00111204860 * cos( 3.55163219419 +      222.86032299360*t);

+   uranus_y_0+=     0.00104507929 * cos( 2.33345675603 +      146.59425171800*t);

+   uranus_y_0+=     0.00108584454 * cos( 6.02234848388 +       35.16409022120*t);

+   uranus_y_0+=     0.00063573747 * cos( 5.01204967920 +      299.12639426920*t);

+   uranus_y_0+=     0.00053289771 * cos( 2.38437587876 +        3.93215326310*t);

+   uranus_y_0+=     0.00063774261 * cos( 2.15607602904 +      109.94568878850*t);

+   uranus_y_0+=     0.00039218598 * cos( 1.11841109252 +        4.45341812490*t);

+   uranus_y_0+=     0.00034205426 * cos( 0.92405922576 +       65.22037101170*t);

+   uranus_y_0+=     0.00034334377 * cos( 1.46696169843 +      225.82926841020*t);

+   uranus_y_0+=     0.00034538316 * cos( 0.27613780697 +       79.23501669220*t);

+   uranus_y_0+=     0.00039256771 * cos( 5.75956853703 +      202.25339517410*t);

+   uranus_y_0+=     0.00026157754 * cos( 3.74097610798 +        9.56122755560*t);

+   uranus_y_0+=     0.00023427328 * cos( 2.52740125551 +      145.63104387150*t);

+   uranus_y_0+=     0.00022933138 * cos( 3.94455540350 +       84.34282612290*t);

+   uranus_y_0+=     0.00031816303 * cos( 3.96860170484 +      152.53214255120*t);

+   uranus_y_0+=     0.00025237176 * cos( 4.45141413666 +       70.32818044240*t);

+   uranus_y_0+=     0.00028372491 * cos( 4.44714627097 +      184.72728735580*t);

+   uranus_y_0+=     0.00026652859 * cos( 4.53944395347 +      160.60889739850*t);

+   uranus_y_0+=     0.00019666208 * cos( 3.96350065335 +       74.66972398270*t);

+   uranus_y_0+=     0.00019643845 * cos( 0.71577796385 +       74.89347315190*t);

+   uranus_y_0+=     0.00019838981 * cos( 5.29113397354 +       12.53017297220*t);

+   uranus_y_0+=     0.00021523908 * cos( 4.93565132068 +       36.64856292950*t);

+   uranus_y_0+=     0.00015537967 * cos( 1.87863275460 +       52.69019803950*t);

+   uranus_y_0+=     0.00020115100 * cos( 3.45473780762 +      127.47179660680*t);

+   uranus_y_0+=     0.00020051641 * cos( 2.90386352937 +       22.09140052780*t);

+   uranus_y_0+=     0.00019901477 * cos( 6.11075402434 +      112.91463420510*t);

+   uranus_y_0+=     0.00018126776 * cos( 0.98478853787 +       33.67961751290*t);

+   uranus_y_0+=     0.00015174962 * cos( 1.31314034959 +       41.10198105440*t);

+   uranus_y_0+=     0.00011239020 * cos( 4.54508334011 +       71.60020482960*t);

+   uranus_y_0+=     0.00013948849 * cos( 4.70474945682 +      221.37585028530*t);

+   uranus_y_0+=     0.00010819728 * cos( 0.12807029856 +       77.96299230500*t);

+   uranus_y_0+=     0.00013589665 * cos( 0.98313719930 +       87.31177153950*t);

+   uranus_y_0+=     0.00011996772 * cos( 5.66129275335 +     1059.38193018920*t);

+   uranus_y_0+=     0.00012407787 * cos( 4.64945783340 +       72.33391801250*t);

+   uranus_y_0+=     0.00011531140 * cos( 0.20190074645 +       77.22927912210*t);

+   uranus_y_0+=     0.00008736150 * cos( 3.39874828293 +      186.21176006410*t);

+   uranus_y_0+=     0.00007093587 * cos( 6.01613487245 +      297.64192156090*t);

+   uranus_y_0+=     0.00006408245 * cos( 3.93246367895 +       62.25142559510*t);

+   uranus_y_0+=     0.00006261153 * cos( 0.14258542752 +      153.49535039770*t);

+   uranus_y_0+=     0.00007494000 * cos( 4.82565771386 +      426.59819087600*t);

+   uranus_y_0+=     0.00007856014 * cos( 1.12354254831 +      340.77089204480*t);

+   uranus_y_0+=     0.00005516018 * cos( 1.73758326119 +      140.00196957900*t);

+   uranus_y_0+=     0.00005556643 * cos( 3.68095215063 +      145.10977900970*t);

+   uranus_y_0+=     0.00005368405 * cos( 2.55422957958 +       75.30286342910*t);

+   uranus_y_0+=     0.00005350948 * cos( 2.12171493922 +       74.26033370550*t);

+   uranus_y_0+=     0.00004508794 * cos( 5.82224064821 +       66.70484372000*t);

+   uranus_y_0+=     0.00004290374 * cos( 5.54490766551 +      265.98929347750*t);

+   uranus_y_0+=     0.00005013871 * cos( 3.11907749268 +       18.15924726470*t);

+   uranus_y_0+=     0.00004326138 * cos( 5.70135056853 +      183.24281464750*t);

+   uranus_y_0+=     0.00004750018 * cos( 3.38678300054 +       73.81839072080*t);

+   uranus_y_0+=     0.00004445347 * cos( 5.00638490308 +      114.39910691340*t);

+   uranus_y_0+=     0.00003314154 * cos( 5.23054574329 +       82.85835341460*t);

+   uranus_y_0+=     0.00004509054 * cos( 1.31254342829 +       75.74480641380*t);

+   uranus_y_0+=     0.00003553107 * cos( 6.18906516846 +        5.93789083320*t);

+   uranus_y_0+=     0.00003265634 * cos( 5.23063560176 +      220.41264243880*t);

+   uranus_y_0+=     0.00003575435 * cos( 5.83994849224 +      137.03302416240*t);

+   uranus_y_0+=     0.00002880734 * cos( 1.19038424330 +      373.90799283650*t);

+   uranus_y_0+=     0.00002885443 * cos( 3.50279993038 +        7.11354700080*t);

+   uranus_y_0+=     0.00002594155 * cos( 4.93691413537 +       96.87299909510*t);

+   uranus_y_0+=     0.00002559357 * cos( 2.87184237678 +       80.19822453870*t);

+   uranus_y_0+=     0.00002676616 * cos( 1.61805362044 +      305.34616939270*t);

+   uranus_y_0+=     0.00002246530 * cos( 5.80081898763 +      108.46121608020*t);

+   uranus_y_0+=     0.00002474483 * cos( 2.21173751117 +       32.19514480460*t);

+   uranus_y_0+=     0.00002060991 * cos( 6.24178596384 +       56.62235130260*t);

+   uranus_y_0+=     0.00001958711 * cos( 4.80807045815 +       20.60692781950*t);

+   uranus_y_0+=     0.00002227451 * cos( 5.34765264557 +       80.71948940050*t);

+   uranus_y_0+=     0.00001937874 * cos( 0.49529839431 +       74.82978267710*t);

+   uranus_y_0+=     0.00001937871 * cos( 4.18462288684 +       74.73341445750*t);

+   uranus_y_0+=     0.00002164382 * cos( 0.47581392325 +        3.18139373770*t);

+   uranus_y_0+=     0.00002138407 * cos( 2.63817804331 +       74.52096613640*t);

+   uranus_y_0+=     0.00002130909 * cos( 2.04143912495 +       75.04223099820*t);

+   uranus_y_0+=     0.00001787737 * cos( 0.32096699926 +        2.44768055480*t);

+   uranus_y_0+=     0.00002212861 * cos( 0.61491281306 +      259.50888592310*t);

+   uranus_y_0+=     0.00001889369 * cos( 3.92852240171 +      300.61086697750*t);

+   uranus_y_0+=     0.00002275258 * cos( 1.55666401505 +      131.40394986990*t);

+   uranus_y_0+=     0.00001925946 * cos( 6.00527473515 +      159.12442469020*t);

+   uranus_y_0+=     0.00001802494 * cos( 4.16218259902 +       74.62153987290*t);

+   uranus_y_0+=     0.00001796292 * cos( 0.51761494342 +       74.94165726170*t);

+   uranus_y_0+=     0.00002240648 * cos( 0.47739127862 +      181.75834193920*t);

+   uranus_y_0+=     0.00001924499 * cos( 2.64284880495 +      206.18554843720*t);

+   uranus_y_0+=     0.00001626134 * cos( 3.70023731184 +      191.20769491020*t);

+   uranus_y_0+=     0.00001860824 * cos( 0.10445996392 +       42.58645376270*t);

+   uranus_y_0+=     0.00002177437 * cos( 2.80437422101 +      479.28838891550*t);

+   uranus_y_0+=     0.00001896184 * cos( 4.26975898003 +       14.97785352700*t);

+   uranus_y_0+=     0.00002045249 * cos( 5.17400788104 +      835.03713448730*t);

+   uranus_y_0+=     0.00001887812 * cos( 2.75000237791 +      154.01661525950*t);

+   uranus_y_0+=     0.00001794754 * cos( 0.16290844853 +      227.31374111850*t);

+   uranus_y_0+=     0.00001347410 * cos( 3.89237011696 +      288.08069400530*t);

+   uranus_y_0+=     0.00001572826 * cos( 5.93367812903 +      219.89137757700*t);

+   uranus_y_0+=     0.00001424804 * cos( 5.10004758033 +       92.94084583200*t);

+   uranus_y_0+=     0.00001267766 * cos( 0.92771324396 +      404.50679034820*t);

+   uranus_y_0+=     0.00001588897 * cos( 4.15115668974 +       39.35687591520*t);

+   uranus_y_0+=     0.00001269786 * cos( 1.09685727529 +      142.44965013380*t);

+   uranus_y_0+=     0.00001291065 * cos( 5.67425699047 +       68.84370773410*t);

+   uranus_y_0+=     0.00001436850 * cos( 5.44312198350 +      522.57741809380*t);

+   uranus_y_0+=     0.00001405564 * cos( 2.04677392527 +      536.80451209540*t);

+   uranus_y_0+=     0.00001416917 * cos( 0.72597245494 +      235.39049596580*t);

+   uranus_y_0+=     0.00001165315 * cos( 0.51071041452 +       81.89514556810*t);

+   uranus_y_0+=     0.00001035262 * cos( 1.20639876458 +        5.41662597140*t);

+   uranus_y_0+=     0.00001009454 * cos( 0.45375065997 +       74.03083904190*t);

+   uranus_y_0+=     0.00001220696 * cos( 1.84988185963 +      211.81462272970*t);

+   uranus_y_0+=     0.00001222886 * cos( 2.27306099902 +      187.69623277240*t);

+   uranus_y_0+=     0.00001336792 * cos( 3.74888989756 +      380.12776796000*t);

+   uranus_y_0+=     0.00001151803 * cos( 0.46579056125 +      128.95626931510*t);

+   uranus_y_0+=     0.00001149114 * cos( 0.85101218281 +      296.15744885260*t);

+   uranus_y_0+=     0.00001163762 * cos( 5.51157783762 +      230.56457082540*t);

+   uranus_y_0+=     0.00001192292 * cos( 0.68084398426 +       99.16062095550*t);

+   uranus_y_0+=     0.00001151286 * cos( 4.01147735438 +       67.66805156650*t);

+   uranus_y_0+=     0.00001189801 * cos( 4.01778306134 +       50.40257617910*t);

+   uranus_y_0+=     0.00001015998 * cos( 1.00290501307 +       35.42472265210*t);

+   uranus_y_0+=     0.00001174953 * cos( 0.45683512473 +      110.20632121940*t);

+   uranus_y_0+=     0.00001051606 * cos( 3.96907647535 +       14.01464568050*t);

+

+   double uranus_y_1=0.0;

+   uranus_y_1+=     0.02157896385 * cos( 0.00000000000 +        0.00000000000*t);

+   uranus_y_1+=     0.00739227349 * cos( 4.43963890935 +      149.56319713460*t);

+   uranus_y_1+=     0.00238545685 * cos( 3.76882493145 +       73.29712585900*t);

+   uranus_y_1+=     0.00229396424 * cos( 0.91090183978 +       76.26607127560*t);

+   uranus_y_1+=     0.00110137111 * cos( 4.00844441616 +       11.04570026390*t);

+   uranus_y_1+=     0.00094979054 * cos( 5.07141537066 +       63.73589830340*t);

+   uranus_y_1+=     0.00081474163 * cos( 5.92275367106 +       85.82729883120*t);

+   uranus_y_1+=     0.00045457174 * cos( 0.73292241207 +      138.51749687070*t);

+   uranus_y_1+=     0.00051366974 * cos( 0.61844114994 +      224.34479570190*t);

+   uranus_y_1+=     0.00038296005 * cos( 5.01873578671 +       70.84944530420*t);

+   uranus_y_1+=     0.00036146116 * cos( 5.94859452787 +       78.71375183040*t);

+   uranus_y_1+=     0.00032420558 * cos( 4.32617271732 +       74.78159856730*t);

+   uranus_y_1+=     0.00021673269 * cos( 3.36607263522 +      151.04766984290*t);

+   uranus_y_1+=     0.00019425087 * cos( 6.01842187783 +       77.75054398390*t);

+   uranus_y_1+=     0.00017393206 * cos( 4.96098895488 +       71.81265315070*t);

+   uranus_y_1+=     0.00014991169 * cos( 3.97176856758 +        3.93215326310*t);

+   uranus_y_1+=     0.00007732367 * cos( 0.04256630122 +       71.60020482960*t);

+   uranus_y_1+=     0.00007438492 * cos( 4.63165436478 +       77.96299230500*t);

+   uranus_y_1+=     0.00006979238 * cos( 0.83723520791 +      145.63104387150*t);

+   uranus_y_1+=     0.00007321559 * cos( 0.66348425538 +        2.96894541660*t);

+   uranus_y_1+=     0.00007595636 * cos( 1.19807643487 +      148.07872442630*t);

+   uranus_y_1+=     0.00004376824 * cos( 2.17182724016 +      160.60889739850*t);

+   uranus_y_1+=     0.00003962568 * cos( 3.18042711824 +       65.22037101170*t);

+   uranus_y_1+=     0.00004117202 * cos( 6.19931612790 +       22.09140052780*t);

+   uranus_y_1+=     0.00002830313 * cos( 3.34365222278 +      213.29909543800*t);

+   uranus_y_1+=     0.00002690065 * cos( 1.78946471198 +        9.56122755560*t);

+   uranus_y_1+=     0.00002628159 * cos( 2.97459067399 +       12.53017297220*t);

+   uranus_y_1+=     0.00003174617 * cos( 3.08131638838 +      299.12639426920*t);

+   uranus_y_1+=     0.00002227510 * cos( 4.89407437055 +       87.31177153950*t);

+   uranus_y_1+=     0.00002821206 * cos( 1.83130010947 +       84.34282612290*t);

+   uranus_y_1+=     0.00002510693 * cos( 1.27166561854 +       18.15924726470*t);

+   uranus_y_1+=     0.00002224655 * cos( 3.21541108798 +       72.33391801250*t);

+   uranus_y_1+=     0.00001929662 * cos( 4.68383962079 +       52.69019803950*t);

+   uranus_y_1+=     0.00001707606 * cos( 5.60415260609 +      127.47179660680*t);

+   uranus_y_1+=     0.00001620819 * cos( 2.18676505386 +      153.49535039770*t);

+   uranus_y_1+=     0.00001926926 * cos( 0.82821252139 +       39.61750834610*t);

+   uranus_y_1+=     0.00001555611 * cos( 2.56681954823 +       73.81839072080*t);

+   uranus_y_1+=     0.00001595703 * cos( 4.79558057860 +       79.23501669220*t);

+   uranus_y_1+=     0.00001476550 * cos( 2.10111459539 +       75.74480641380*t);

+   uranus_y_1+=     0.00001531355 * cos( 2.14701519407 +      152.53214255120*t);

+   uranus_y_1+=     0.00001744564 * cos( 1.67897185084 +       77.22927912210*t);

+   uranus_y_1+=     0.00001713945 * cos( 1.82334975258 +      222.86032299360*t);

+   uranus_y_1+=     0.00001705184 * cos( 5.82532917611 +      225.82926841020*t);

+   uranus_y_1+=     0.00001739019 * cos( 3.82452086292 +      146.59425171800*t);

+   uranus_y_1+=     0.00001291753 * cos( 6.19666243545 +       70.32818044240*t);

+   uranus_y_1+=     0.00001458526 * cos( 5.10147126404 +        3.18139373770*t);

+   uranus_y_1+=     0.00001179966 * cos( 3.56807126055 +      220.41264243880*t);

+   uranus_y_1+=     0.00001234914 * cos( 5.69239889831 +        4.45341812490*t);

+   uranus_y_1+=     0.00001075108 * cos( 1.76286452034 +       56.62235130260*t);

+   uranus_y_1+=     0.00001035661 * cos( 6.12642568708 +       62.25142559510*t);

+   uranus_y_1+=     0.00001114523 * cos( 3.41304662369 +      131.40394986990*t);

+   uranus_y_1+=     0.00001050191 * cos( 3.84176879347 +      109.94568878850*t);

+   uranus_y_1=uranus_y_1 * t;

+

+   double uranus_y_2=0.0;

+   uranus_y_2+=     0.00034812647 * cos( 3.14159265359 +        0.00000000000*t);

+   uranus_y_2+=     0.00016589194 * cos( 2.29556740620 +       74.78159856730*t);

+   uranus_y_2+=     0.00010905147 * cos( 1.45737963668 +      149.56319713460*t);

+   uranus_y_2+=     0.00007484633 * cos( 2.27968076918 +       11.04570026390*t);

+   uranus_y_2+=     0.00007964298 * cos( 0.97230247087 +       63.73589830340*t);

+   uranus_y_2+=     0.00005307100 * cos( 3.20519221878 +       70.84944530420*t);

+   uranus_y_2+=     0.00005018595 * cos( 1.47518527303 +       78.71375183040*t);

+   uranus_y_2+=     0.00006713255 * cos( 3.74148881189 +       85.82729883120*t);

+   uranus_y_2+=     0.00005265170 * cos( 0.54901216905 +       73.29712585900*t);

+   uranus_y_2+=     0.00004864822 * cos( 4.11367426823 +       76.26607127560*t);

+   uranus_y_2+=     0.00002995853 * cos( 2.49432193549 +      138.51749687070*t);

+   uranus_y_2+=     0.00002519021 * cos( 1.78896824345 +       71.60020482960*t);

+   uranus_y_2+=     0.00002418371 * cos( 2.88675006488 +       77.96299230500*t);

+   uranus_y_2+=     0.00002185856 * cos( 5.58862614977 +        3.93215326310*t);

+   uranus_y_2+=     0.00001035578 * cos( 5.44752448275 +      145.63104387150*t);

+   uranus_y_2+=     0.00001044459 * cos( 4.27972239360 +      224.34479570190*t);

+   uranus_y_2=uranus_y_2 * t * t;

+

+   double uranus_y_3=0.0;

+   uranus_y_3+=     0.00001211380 * cos( 0.00000000000 +        0.00000000000*t);

+   uranus_y_3=uranus_y_3 * t * t * t;

+

+   return uranus_y_0+uranus_y_1+uranus_y_2+uranus_y_3;

+}

+

+double vsop87a_milli_uranus_z(double t){

+   double uranus_z_0=0.0;

+   uranus_z_0+=     0.25878127698 * cos( 2.61861272578 +       74.78159856730*t);

+   uranus_z_0+=     0.01774318778 * cos( 3.14159265359 +        0.00000000000*t);

+   uranus_z_0+=     0.00599316131 * cos( 5.08119500585 +      149.56319713460*t);

+   uranus_z_0+=     0.00190281890 * cos( 1.61643841193 +       76.26607127560*t);

+   uranus_z_0+=     0.00190881685 * cos( 0.57869575952 +       73.29712585900*t);

+   uranus_z_0+=     0.00084626761 * cos( 2.26030150166 +        1.48447270830*t);

+   uranus_z_0+=     0.00030734257 * cos( 0.23571721555 +       63.73589830340*t);

+   uranus_z_0+=     0.00020842052 * cos( 1.26054208091 +      224.34479570190*t);

+   uranus_z_0+=     0.00019734273 * cos( 6.04314677688 +      148.07872442630*t);

+   uranus_z_0+=     0.00012537530 * cos( 5.17169051466 +       11.04570026390*t);

+   uranus_z_0+=     0.00014582864 * cos( 6.14852037212 +       71.81265315070*t);

+   uranus_z_0+=     0.00010407529 * cos( 3.65320417038 +      213.29909543800*t);

+   uranus_z_0+=     0.00011261541 * cos( 3.55973769686 +      529.69096509460*t);

+   uranus_z_0+=     0.00008855669 * cos( 4.03774505739 +      151.04766984290*t);

+   uranus_z_0+=     0.00008239460 * cos( 0.34225652715 +       77.75054398390*t);

+   uranus_z_0+=     0.00007950169 * cos( 0.72564903051 +       85.82729883120*t);

+   uranus_z_0+=     0.00006867469 * cos( 0.81417174224 +        2.96894541660*t);

+   uranus_z_0+=     0.00005648720 * cos( 3.45324719543 +      138.51749687070*t);

+   uranus_z_0+=     0.00004581938 * cos( 1.69668682344 +       38.13303563780*t);

+   uranus_z_0+=     0.00002578399 * cos( 5.19696447390 +      111.43016149680*t);

+   uranus_z_0+=     0.00002964070 * cos( 6.14338802239 +       35.16409022120*t);

+   uranus_z_0+=     0.00001884104 * cos( 2.61192472648 +       78.71375183040*t);

+   uranus_z_0+=     0.00002330304 * cos( 5.72640226150 +       70.84944530420*t);

+   uranus_z_0+=     0.00001985215 * cos( 0.76408839812 +       39.61750834610*t);

+   uranus_z_0+=     0.00001743154 * cos( 1.20586281789 +      146.59425171800*t);

+   uranus_z_0+=     0.00002037011 * cos( 0.95353587037 +       70.32818044240*t);

+   uranus_z_0+=     0.00001508924 * cos( 2.26195448553 +      222.86032299360*t);

+   uranus_z_0+=     0.00001082736 * cos( 2.62872874057 +      108.46121608020*t);

+   uranus_z_0+=     0.00001051968 * cos( 0.75560753840 +      109.94568878850*t);

+

+   double uranus_z_1=0.0;

+   uranus_z_1+=     0.00655916626 * cos( 0.01271947660 +       74.78159856730*t);

+   uranus_z_1+=     0.00049648951 * cos( 0.00000000000 +        0.00000000000*t);

+   uranus_z_1+=     0.00023874178 * cos( 2.73870491220 +      149.56319713460*t);

+   uranus_z_1+=     0.00007552177 * cos( 5.49304207700 +       76.26607127560*t);

+   uranus_z_1+=     0.00005941304 * cos( 3.61254073304 +       73.29712585900*t);

+   uranus_z_1+=     0.00002868429 * cos( 4.17954157878 +       63.73589830340*t);

+   uranus_z_1+=     0.00002087455 * cos( 5.97858625817 +        1.48447270830*t);

+   uranus_z_1+=     0.00001827697 * cos( 2.71810813335 +       11.04570026390*t);

+   uranus_z_1+=     0.00001305063 * cos( 4.52337002195 +       85.82729883120*t);

+   uranus_z_1+=     0.00001158250 * cos( 5.31913504112 +      224.34479570190*t);

+   uranus_z_1=uranus_z_1 * t;

+

+   double uranus_z_2=0.0;

+   uranus_z_2+=     0.00014697858 * cos( 1.75149165003 +       74.78159856730*t);

+   uranus_z_2+=     0.00001600044 * cos( 3.14159265359 +        0.00000000000*t);

+   uranus_z_2=uranus_z_2 * t * t;

+

+   return uranus_z_0+uranus_z_1+uranus_z_2;

+}

+

+double vsop87a_milli_venus_x(double t){

+   double venus_x_0=0.0;

+   venus_x_0+=     0.72211281391 * cos( 3.17575836361 +    10213.28554621100*t);

+   venus_x_0+=     0.00486448018 * cos( 0.00000000000 +        0.00000000000*t);

+   venus_x_0+=     0.00244500474 * cos( 4.05566613861 +    20426.57109242200*t);

+   venus_x_0+=     0.00002800281 * cos( 0.33147492492 +     2352.86615377180*t);

+   venus_x_0+=     0.00001949669 * cos( 4.23196016801 +     1577.34354244780*t);

+   venus_x_0+=     0.00001241717 * cos( 4.93573787058 +    30639.85663863300*t);

+   venus_x_0+=     0.00001162258 * cos( 2.87958246189 +    18073.70493865020*t);

+   venus_x_0+=     0.00001046690 * cos( 1.75434920413 +     6283.07584999140*t);

+

+   double venus_x_1=0.0;

+   venus_x_1+=     0.00033862636 * cos( 3.14159265359 +        0.00000000000*t);

+   venus_x_1+=     0.00017234992 * cos( 0.92721124604 +    20426.57109242200*t);

+   venus_x_1+=     0.00006510416 * cos( 2.19289889733 +    10213.28554621100*t);

+   venus_x_1=venus_x_1 * t;

+

+   return venus_x_0+venus_x_1;

+}

+

+double vsop87a_milli_venus_y(double t){

+   double venus_y_0=0.0;

+   venus_y_0+=     0.72324820731 * cos( 1.60573808356 +    10213.28554621100*t);

+   venus_y_0+=     0.00549506273 * cos( 3.14159265359 +        0.00000000000*t);

+   venus_y_0+=     0.00244884790 * cos( 2.48564954004 +    20426.57109242200*t);

+   venus_y_0+=     0.00002789807 * cos( 5.04214523606 +     2352.86615377180*t);

+   venus_y_0+=     0.00001933868 * cos( 5.80597990261 +     1577.34354244780*t);

+   venus_y_0+=     0.00001243658 * cos( 3.36573697344 +    30639.85663863300*t);

+   venus_y_0+=     0.00001164480 * cos( 1.30970620277 +    18073.70493865020*t);

+   venus_y_0+=     0.00001041872 * cos( 0.18129136925 +     6283.07584999140*t);

+

+   double venus_y_1=0.0;

+   venus_y_1+=     0.00039231430 * cos( 0.00000000000 +        0.00000000000*t);

+   venus_y_1+=     0.00017282326 * cos( 5.63824735900 +    20426.57109242200*t);

+   venus_y_1+=     0.00005968075 * cos( 3.60854944086 +    10213.28554621100*t);

+   venus_y_1=venus_y_1 * t;

+

+   double venus_y_2=0.0;

+   venus_y_2+=     0.00002007155 * cos( 3.14159265359 +        0.00000000000*t);

+   venus_y_2=venus_y_2 * t * t;

+

+   return venus_y_0+venus_y_1+venus_y_2;

+}

+

+double vsop87a_milli_venus_z(double t){

+   double venus_z_0=0.0;

+   venus_z_0+=     0.04282990302 * cos( 0.26703856476 +    10213.28554621100*t);

+   venus_z_0+=     0.00035588343 * cos( 3.14159265359 +        0.00000000000*t);

+   venus_z_0+=     0.00014501879 * cos( 1.14696911390 +    20426.57109242200*t);

+

+   double venus_z_1=0.0;

+   venus_z_1+=     0.00208096402 * cos( 1.88967278742 +    10213.28554621100*t);

+   venus_z_1+=     0.00001264989 * cos( 3.71037501321 +    20426.57109242200*t);

+   venus_z_1+=     0.00001364144 * cos( 0.00000000000 +        0.00000000000*t);

+   venus_z_1=venus_z_1 * t;

+

+   double venus_z_2=0.0;

+   venus_z_2+=     0.00009148044 * cos( 3.34791005272 +    10213.28554621100*t);

+   venus_z_2=venus_z_2 * t * t;

+

+   return venus_z_0+venus_z_1+venus_z_2;

+}

+

diff --git a/movement/lib/vsop87/vsop87a_milli.h b/movement/lib/vsop87/vsop87a_milli.h
new file mode 100755
index 00000000..4c820e87
--- /dev/null
+++ b/movement/lib/vsop87/vsop87a_milli.h
@@ -0,0 +1,17 @@
+//VSOP87-Multilang http://www.astrogreg.com/vsop87-multilang/index.html

+//Greg Miller (gmiller@gregmiller.net) 2019.  Released as Public Domain

+

+#ifndef VSOP87A_MILLI

+#define VSOP87A_MILLI

+

+   void vsop87a_milli_getEarth(double t,double temp[]);

+   void vsop87a_milli_getEmb(double t,double temp[]);

+   void vsop87a_milli_getJupiter(double t,double temp[]);

+   void vsop87a_milli_getMars(double t,double temp[]);

+   void vsop87a_milli_getMercury(double t,double temp[]);

+   void vsop87a_milli_getNeptune(double t,double temp[]);

+   void vsop87a_milli_getSaturn(double t,double temp[]);

+   void vsop87a_milli_getUranus(double t,double temp[]);

+   void vsop87a_milli_getVenus(double t,double temp[]);

+   void vsop87a_milli_getMoon(double earth[], double emb[],double temp[]);

+#endif

diff --git a/movement/make/Makefile b/movement/make/Makefile
index 415bc152..2516cc44 100755
--- a/movement/make/Makefile
+++ b/movement/make/Makefile
@@ -18,6 +18,8 @@ INCLUDES += \
   -I../watch_faces/demo/ \
   -I../lib/TOTP-MCU/ \
   -I../lib/sunriset/ \
+  -I../lib/vsop87/ \
+  -I../lib/astrolib/ \
 
 # If you add any other source files you wish to compile, add them after ../app.c
 # Note that you will need to add a backslash at the end of any line you wish to continue, i.e.
@@ -29,6 +31,8 @@ SRCS += \
   ../lib/TOTP-MCU/sha1.c \
   ../lib/TOTP-MCU/TOTP.c \
   ../lib/sunriset/sunriset.c \
+  ../lib/vsop87/vsop87a_milli.c \
+  ../lib/astrolib/astrolib.c \
   ../movement.c \
   ../watch_faces/clock/simple_clock_face.c \
   ../watch_faces/clock/world_clock_face.c \
@@ -37,6 +41,7 @@ SRCS += \
   ../watch_faces/settings/set_time_face.c \
   ../watch_faces/sensor/thermistor_readout_face.c \
   ../watch_faces/sensor/thermistor_logging_face.c \
+  ../watch_faces/sensor/thermistor_testing_face.c \
   ../watch_faces/demo/character_set_face.c \
   ../watch_faces/demo/voltage_face.c \
   ../watch_faces/demo/lis2dh_logging_face.c \
@@ -51,6 +56,9 @@ SRCS += \
   ../watch_faces/complication/blinky_face.c \
   ../watch_faces/complication/moon_phase_face.c \
   ../watch_faces/clock/mars_time_face.c \
+  ../watch_faces/complication/orrery_face.c \
+  ../watch_faces/complication/astronomy_face.c \
+  ../watch_faces/complication/tomato_face.c \
 # New watch faces go above this line.
 
 # Leave this line at the bottom of the file; it has all the targets for making your project.
diff --git a/movement/movement_config.h b/movement/movement_config.h
index e68fcc9a..94456776 100644
--- a/movement/movement_config.h
+++ b/movement/movement_config.h
@@ -29,8 +29,10 @@
 
 const watch_face_t watch_faces[] = {
     simple_clock_face,
-    beats_face,
-    voltage_face,
+    world_clock_face,
+    sunrise_sunset_face,
+    moon_phase_face,
+    thermistor_readout_face,
     preferences_face,
     set_time_face,
 };
diff --git a/movement/movement_faces.h b/movement/movement_faces.h
index 15186286..d068a7f9 100644
--- a/movement/movement_faces.h
+++ b/movement/movement_faces.h
@@ -32,6 +32,7 @@
 #include "pulsometer_face.h"
 #include "thermistor_readout_face.h"
 #include "thermistor_logging_face.h"
+#include "thermistor_testing_face.h"
 #include "character_set_face.h"
 #include "beats_face.h"
 #include "day_one_face.h"
@@ -46,6 +47,9 @@
 #include "blinky_face.h"
 #include "moon_phase_face.h"
 #include "mars_time_face.h"
+#include "orrery_face.h"
+#include "astronomy_face.h"
+#include "tomato_face.h"
 // New includes go above this line.
 
 #endif // MOVEMENT_FACES_H_
diff --git a/movement/watch_faces/clock/mars_time_face.c b/movement/watch_faces/clock/mars_time_face.c
index 264f714f..609d461b 100644
--- a/movement/watch_faces/clock/mars_time_face.c
+++ b/movement/watch_faces/clock/mars_time_face.c
@@ -108,6 +108,7 @@ static void _update(movement_settings_t *settings, mars_time_state_t *state) {
 
 void mars_time_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr) {
     (void) settings;
+    (void) watch_face_index;
     if (*context_ptr == NULL) {
         *context_ptr = malloc(sizeof(mars_time_state_t));
         memset(*context_ptr, 0, sizeof(mars_time_state_t));
diff --git a/movement/watch_faces/complication/astronomy_face.c b/movement/watch_faces/complication/astronomy_face.c
new file mode 100644
index 00000000..50e5221b
--- /dev/null
+++ b/movement/watch_faces/complication/astronomy_face.c
@@ -0,0 +1,280 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Joey Castillo
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include <math.h>
+#include "astronomy_face.h"
+#include "watch_utility.h"
+
+#if __EMSCRIPTEN__
+#include <emscripten.h>
+#endif
+
+#define NUM_AVAILABLE_BODIES 9
+
+static const char astronomy_available_celestial_bodies[NUM_AVAILABLE_BODIES] = {
+    ASTRO_BODY_SUN,
+    ASTRO_BODY_MERCURY,
+    ASTRO_BODY_VENUS,
+    ASTRO_BODY_MOON,
+    ASTRO_BODY_MARS,
+    ASTRO_BODY_JUPITER,
+    ASTRO_BODY_SATURN,
+    ASTRO_BODY_URANUS,
+    ASTRO_BODY_NEPTUNE
+};
+
+static const char astronomy_celestial_body_names[NUM_AVAILABLE_BODIES][3] = {
+    "SO",   // Sol
+    "ME",   // Mercury
+    "VE",   // Venus
+    "LU",   // Moon (Luna)
+    "MA",   // Mars
+    "JU",   // Jupiter
+    "SA",   // Saturn
+    "UR",   // Uranus
+    "NE"    // Neptune
+};
+
+static void _astronomy_face_recalculate(movement_settings_t *settings, astronomy_state_t *state) {
+#if __EMSCRIPTEN__
+    int16_t browser_lat = EM_ASM_INT({
+        return lat;
+    });
+    int16_t browser_lon = EM_ASM_INT({
+        return lon;
+    });
+    if ((watch_get_backup_data(1) == 0) && (browser_lat || browser_lon)) {
+        movement_location_t browser_loc;
+        browser_loc.bit.latitude = browser_lat;
+        browser_loc.bit.longitude = browser_lon;
+        watch_store_backup_data(browser_loc.reg, 1);
+        double lat = (double)browser_lat / 100.0;
+        double lon = (double)browser_lon / 100.0;
+        state->latitude_radians = astro_degrees_to_radians(lat);
+        state->longitude_radians = astro_degrees_to_radians(lon);
+    }
+#endif
+
+    watch_date_time date_time = watch_rtc_get_date_time();
+    uint32_t timestamp = watch_utility_date_time_to_unix_time(date_time, movement_timezone_offsets[settings->bit.time_zone] * 60);
+    date_time = watch_utility_date_time_from_unix_time(timestamp, 0);
+    double jd = astro_convert_date_to_julian_date(date_time.unit.year + WATCH_RTC_REFERENCE_YEAR, date_time.unit.month, date_time.unit.day, date_time.unit.hour, date_time.unit.minute, date_time.unit.second);
+
+    astro_equatorial_coordinates_t radec_precession = astro_get_ra_dec(jd, astronomy_available_celestial_bodies[state->active_body_index], state->latitude_radians, state->longitude_radians, true);
+    printf("\nParams to convert: %f %f %f %f %f\n",
+            jd,
+            astro_radians_to_degrees(state->latitude_radians),
+            astro_radians_to_degrees(state->longitude_radians),
+            astro_radians_to_degrees(radec_precession.right_ascension),
+            astro_radians_to_degrees(radec_precession.declination));
+
+    astro_horizontal_coordinates_t horiz = astro_ra_dec_to_alt_az(jd, state->latitude_radians, state->longitude_radians, radec_precession.right_ascension, radec_precession.declination);
+    astro_equatorial_coordinates_t radec = astro_get_ra_dec(jd, astronomy_available_celestial_bodies[state->active_body_index], state->latitude_radians, state->longitude_radians, false);
+    state->altitude = astro_radians_to_degrees(horiz.altitude);
+    state->azimuth = astro_radians_to_degrees(horiz.azimuth);
+    state->right_ascension = astro_radians_to_hms(radec.right_ascension);
+    state->declination = astro_radians_to_dms(radec.declination);
+    state->distance = radec.distance;
+
+    printf("Calculated coordinates for %s on %f: \n\tRA  = %f / %2dh %2dm %2ds\n\tDec = %f / %3d° %3d' %3d\"\n\tAzi = %f\n\tAlt = %f\n\tDst = %f AU\n",
+            astronomy_celestial_body_names[state->active_body_index],
+            jd,
+            astro_radians_to_degrees(radec.right_ascension),
+            state->right_ascension.hours,
+            state->right_ascension.minutes,
+            state->right_ascension.seconds,
+            astro_radians_to_degrees(radec.declination),
+            state->declination.degrees,
+            state->declination.minutes,
+            state->declination.seconds,
+            state->altitude,
+            state->azimuth,
+            state->distance);
+}
+
+static void _astronomy_face_update(movement_event_t event, movement_settings_t *settings, astronomy_state_t *state) {
+    char buf[16];
+    switch (state->mode) {
+        case ASTRONOMY_MODE_SELECTING_BODY:
+            watch_clear_colon();
+            watch_display_string(" Astro", 4);
+            if (event.subsecond % 2) {
+                watch_display_string((char *)astronomy_celestial_body_names[state->active_body_index], 0);
+            } else {
+                watch_display_string("  ", 0);
+            }
+            if (event.subsecond == 0) {
+                watch_display_string("  ", 2);
+                switch (state->animation_state) {
+                    case 0:
+                        watch_set_pixel(0, 7);
+                        watch_set_pixel(2, 6);
+                        break;
+                    case 1:
+                        watch_set_pixel(1, 7);
+                        watch_set_pixel(2, 9);
+                        break;
+                    case 2:
+                        watch_set_pixel(2, 7);
+                        watch_set_pixel(0, 9);
+                        break;
+                }
+                state->animation_state = (state->animation_state + 1) % 3;
+            }
+            break;
+        case ASTRONOMY_MODE_CALCULATING:
+            watch_clear_display();
+             // this takes a moment and locks the UI, flash C for "Calculating"
+            watch_start_character_blink('C', 100);
+            _astronomy_face_recalculate(settings, state);
+            watch_stop_blink();
+            state->mode = ASTRONOMY_MODE_DISPLAYING_ALT;
+            // fall through
+        case ASTRONOMY_MODE_DISPLAYING_ALT:
+            sprintf(buf, "%saL%6d", astronomy_celestial_body_names[state->active_body_index], (int16_t)round(state->altitude * 100));
+            watch_display_string(buf, 0);
+            break;
+        case ASTRONOMY_MODE_DISPLAYING_AZI:
+            sprintf(buf, "%saZ%6d", astronomy_celestial_body_names[state->active_body_index], (int16_t)round(state->azimuth * 100));
+            watch_display_string(buf, 0);
+            break;
+        case ASTRONOMY_MODE_DISPLAYING_RA:
+            watch_set_colon();
+            sprintf(buf, "ra H%02d%02d%02d", state->right_ascension.hours, state->right_ascension.minutes, state->right_ascension.seconds);
+            watch_display_string(buf, 0);
+            break;
+        case ASTRONOMY_MODE_DISPLAYING_DEC:
+            watch_clear_colon();
+            sprintf(buf, "de %3d%2d%2d", state->declination.degrees, state->declination.minutes, state->declination.seconds);
+            watch_display_string(buf, 0);
+            break;
+        case ASTRONOMY_MODE_DISPLAYING_DIST:
+            if (state->distance >= 0.00668456) {
+                // if >= 1,000,000 kilometers (all planets), we display distance in AU.
+                sprintf(buf, "diAU%6d", (uint16_t)round(state->distance * 100));
+            } else {
+                // otherwise distance in kilometers fits in 6 digits. This mode will only happen for Luna.
+                sprintf(buf, "di K%6ld", (uint32_t)round(state->distance * 149597871.0));
+            }
+            watch_display_string(buf, 0);
+            break;
+        case ASTRONOMY_MODE_NUM_MODES:
+            // this case does not happen, but we need it to silence a warning.
+            break;
+    }
+}
+
+void astronomy_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr) {
+    (void) settings;
+    (void) watch_face_index;
+    if (*context_ptr == NULL) {
+        *context_ptr = malloc(sizeof(astronomy_state_t));
+        memset(*context_ptr, 0, sizeof(astronomy_state_t));
+    }
+}
+
+void astronomy_face_activate(movement_settings_t *settings, void *context) {
+    (void) settings;
+    astronomy_state_t *state = (astronomy_state_t *)context;
+    movement_location_t movement_location = (movement_location_t) watch_get_backup_data(1);
+    int16_t lat_centi = (int16_t)movement_location.bit.latitude;
+    int16_t lon_centi = (int16_t)movement_location.bit.longitude;
+    double lat = (double)lat_centi / 100.0;
+    double lon = (double)lon_centi / 100.0;
+    state->latitude_radians = astro_degrees_to_radians(lat);
+    state->longitude_radians = astro_degrees_to_radians(lon);
+
+    movement_request_tick_frequency(4);
+}
+
+bool astronomy_face_loop(movement_event_t event, movement_settings_t *settings, void *context) {
+    astronomy_state_t *state = (astronomy_state_t *)context;
+
+    switch (event.event_type) {
+        case EVENT_ACTIVATE:
+        case EVENT_TICK:
+            _astronomy_face_update(event, settings, state);
+            break;
+        case EVENT_MODE_BUTTON_UP:
+            // You shouldn't need to change this case; Mode almost always moves to the next watch face.
+            movement_move_to_next_face();
+            break;
+        case EVENT_LIGHT_BUTTON_UP:
+            // If you have other uses for the Light button, you can opt not to illuminate the LED for this event.
+            movement_illuminate_led();
+            break;
+        case EVENT_ALARM_BUTTON_UP:
+            switch (state->mode) {
+                case ASTRONOMY_MODE_SELECTING_BODY:
+                    // advance to next celestial body (move to calculations with a long press)
+                    state->active_body_index = (state->active_body_index + 1) % NUM_AVAILABLE_BODIES;
+                    break;
+                case ASTRONOMY_MODE_CALCULATING:
+                    // ignore button press during calculations
+                    break;
+                case ASTRONOMY_MODE_DISPLAYING_DIST:
+                    // at last mode, wrap around
+                    state->mode = ASTRONOMY_MODE_DISPLAYING_ALT;
+                    break;
+                default:
+                    // otherwise, advance to next mode
+                    state->mode++;
+                    break;
+            }
+            _astronomy_face_update(event, settings, state);
+            break;
+        case EVENT_ALARM_LONG_PRESS:
+            if (state->mode == ASTRONOMY_MODE_SELECTING_BODY) {
+                // celestial body selected! this triggers a calculation in the update method.
+                state->mode = ASTRONOMY_MODE_CALCULATING;
+                movement_request_tick_frequency(1);
+                _astronomy_face_update(event, settings, state);
+            } else if (state->mode != ASTRONOMY_MODE_CALCULATING) {
+                // in all modes except "doing a calculation", return to the selection screen.
+                state->mode = ASTRONOMY_MODE_SELECTING_BODY;
+                movement_request_tick_frequency(4);
+            _astronomy_face_update(event, settings, state);
+            }
+            break;
+        case EVENT_TIMEOUT:
+            movement_move_to_face(0);
+            break;
+        case EVENT_LOW_ENERGY_UPDATE:
+            // TODO?
+            break;
+        default:
+            break;
+    }
+
+    return true;
+}
+
+void astronomy_face_resign(movement_settings_t *settings, void *context) {
+    (void) settings;
+    astronomy_state_t *state = (astronomy_state_t *)context;
+    state->mode = ASTRONOMY_MODE_SELECTING_BODY;
+}
diff --git a/movement/watch_faces/complication/astronomy_face.h b/movement/watch_faces/complication/astronomy_face.h
new file mode 100644
index 00000000..f956955b
--- /dev/null
+++ b/movement/watch_faces/complication/astronomy_face.h
@@ -0,0 +1,68 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Joey Castillo
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#ifndef ASTRONOMY_FACE_H_
+#define ASTRONOMY_FACE_H_
+
+#include "movement.h"
+#include "astrolib.h"
+
+typedef enum {
+    ASTRONOMY_MODE_SELECTING_BODY = 0,
+    ASTRONOMY_MODE_CALCULATING,
+    ASTRONOMY_MODE_DISPLAYING_ALT,
+    ASTRONOMY_MODE_DISPLAYING_AZI,
+    ASTRONOMY_MODE_DISPLAYING_RA,
+    ASTRONOMY_MODE_DISPLAYING_DEC,
+    ASTRONOMY_MODE_DISPLAYING_DIST,
+    ASTRONOMY_MODE_NUM_MODES
+} astronomy_mode_t;
+
+typedef struct {
+    astronomy_mode_t mode;
+    uint8_t active_body_index;
+    uint8_t animation_state;
+    double latitude_radians;    // this is the user location
+    double longitude_radians;   // but in radians
+    astro_angle_hms_t right_ascension;
+    astro_angle_dms_t declination;
+    double altitude;    // in decimal degrees
+    double azimuth;     // in decimal degrees
+    double distance;    // in AU
+} astronomy_state_t;
+
+void astronomy_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr);
+void astronomy_face_activate(movement_settings_t *settings, void *context);
+bool astronomy_face_loop(movement_event_t event, movement_settings_t *settings, void *context);
+void astronomy_face_resign(movement_settings_t *settings, void *context);
+
+#define astronomy_face ((const watch_face_t){ \
+    astronomy_face_setup, \
+    astronomy_face_activate, \
+    astronomy_face_loop, \
+    astronomy_face_resign, \
+    NULL, \
+})
+
+#endif // ASTRONOMY_FACE_H_
diff --git a/movement/watch_faces/complication/countdown_face.c b/movement/watch_faces/complication/countdown_face.c
index a910e96c..81836f37 100644
--- a/movement/watch_faces/complication/countdown_face.c
+++ b/movement/watch_faces/complication/countdown_face.c
@@ -35,14 +35,6 @@
 #define DEFAULT_MINUTES 3
 
 
-static uint32_t offset_date_time(uint32_t now, int8_t hours, int8_t minutes, int8_t seconds) {
-    uint32_t new = now;
-    new += hours * 60 * 60;
-    new += minutes * 60;
-    new += seconds;
-    return new;
-}
-
 static inline int32_t get_tz_offset(movement_settings_t *settings) {
     return movement_timezone_offsets[settings->bit.time_zone] * 60;
 }
@@ -52,7 +44,7 @@ static void start(countdown_state_t *state, movement_settings_t *settings) {
 
     state->mode = cd_running;
     state->now_ts = watch_utility_date_time_to_unix_time(now, get_tz_offset(settings));
-    state->target_ts = offset_date_time(state->now_ts, 0, state->minutes, state->seconds);
+    state->target_ts = watch_utility_offset_timestamp(state->now_ts, 0, state->minutes, state->seconds);
     watch_date_time target_dt = watch_utility_date_time_from_unix_time(state->target_ts, get_tz_offset(settings));
     movement_schedule_background_task(target_dt);
     watch_set_indicator(WATCH_INDICATOR_BELL);
diff --git a/movement/watch_faces/complication/counter_face.c b/movement/watch_faces/complication/counter_face.c
new file mode 100644
index 00000000..ac0388ab
--- /dev/null
+++ b/movement/watch_faces/complication/counter_face.c
@@ -0,0 +1,90 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Shogo Okamoto
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include <stdlib.h>
+#include <string.h>
+#include "counter_face.h"
+#include "watch.h"
+
+void counter_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr) {
+    (void) settings;
+    (void) watch_face_index;
+    if (*context_ptr == NULL) {
+        *context_ptr = malloc(sizeof(counter_state_t));
+        memset(*context_ptr, 0, sizeof(counter_state_t));
+    }
+}
+
+void counter_face_activate(movement_settings_t *settings, void *context) {
+    (void) settings;
+    (void) context;
+}
+
+bool counter_face_loop(movement_event_t event, movement_settings_t *settings, void *context) {
+    (void) settings;
+
+    counter_state_t *state = (counter_state_t *)context;
+
+    switch (event.event_type) {
+        case EVENT_MODE_BUTTON_UP:
+            movement_move_to_next_face();
+            break;
+        case EVENT_LIGHT_BUTTON_DOWN:
+            movement_illuminate_led();
+            break;
+        case EVENT_ALARM_BUTTON_UP:
+            state->counter_idx++; // increment counter index
+            if (state->counter_idx>99) { //0-99
+                state->counter_idx=0;//reset counter index
+            }
+            print_counter(state);
+            break;
+        case EVENT_ALARM_LONG_PRESS:
+            state->counter_idx=0; // reset counter index
+            print_counter(state);
+            break;
+        case EVENT_ACTIVATE:
+            print_counter(state);
+            break;
+        case EVENT_TIMEOUT:
+            // ignore timeout
+            break;
+        default:
+            break;
+    }
+
+    return true;
+}
+
+// print counter index at the center of display.
+void print_counter(counter_state_t *state) {
+    char buf[14];
+    sprintf(buf, "CO    %02d", state->counter_idx); // center of LCD display
+    watch_display_string(buf, 0);
+}
+
+void counter_face_resign(movement_settings_t *settings, void *context) {
+    (void) settings;
+    (void) context;
+}
diff --git a/movement/watch_faces/complication/counter_face.h b/movement/watch_faces/complication/counter_face.h
new file mode 100644
index 00000000..2d389a15
--- /dev/null
+++ b/movement/watch_faces/complication/counter_face.h
@@ -0,0 +1,51 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Shogo Okamoto
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#ifndef COUNTER_FACE_H_
+#define COUNTER_FACE_H_
+
+#include "movement.h"
+
+// Counter face is designed to count the number of running laps during excercises.
+typedef struct {
+    uint8_t counter_idx;
+} counter_state_t;
+
+
+void counter_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr);
+void counter_face_activate(movement_settings_t *settings, void *context);
+bool counter_face_loop(movement_event_t event, movement_settings_t *settings, void *context);
+void counter_face_resign(movement_settings_t *settings, void *context);
+
+void print_counter(counter_state_t *state);
+
+#define counter_face ((const watch_face_t){ \
+    counter_face_setup, \
+    counter_face_activate, \
+    counter_face_loop, \
+    counter_face_resign, \
+    NULL, \
+})
+
+#endif // COUNTER_FACE_H_
diff --git a/movement/watch_faces/complication/orrery_face.c b/movement/watch_faces/complication/orrery_face.c
new file mode 100644
index 00000000..3afced98
--- /dev/null
+++ b/movement/watch_faces/complication/orrery_face.c
@@ -0,0 +1,232 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Joey Castillo
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ */
+
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#include "orrery_face.h"
+#include "watch.h"
+#include "watch_utility.h"
+#include "vsop87a_micro.h" // smaller size, less accurate
+#include "vsop87a_milli.h"
+#include "astrolib.h"
+
+#define NUM_AVAILABLE_BODIES 9
+
+static const char orrery_celestial_body_names[NUM_AVAILABLE_BODIES][3] = {
+    "ME",   // Mercury
+    "VE",   // Venus
+    "EA",   // Earth
+    "LU",   // Moon (Luna)
+    "MA",   // Mars
+    "JU",   // Jupiter
+    "SA",   // Saturn
+    "UR",   // Uranus
+    "NE"    // Neptune
+};
+
+static void _orrery_face_recalculate(movement_settings_t *settings, orrery_state_t *state) {
+    watch_date_time date_time = watch_rtc_get_date_time();
+    uint32_t timestamp = watch_utility_date_time_to_unix_time(date_time, movement_timezone_offsets[settings->bit.time_zone] * 60);
+    date_time = watch_utility_date_time_from_unix_time(timestamp, 0);
+    double jd = astro_convert_date_to_julian_date(date_time.unit.year + WATCH_RTC_REFERENCE_YEAR, date_time.unit.month, date_time.unit.day, date_time.unit.hour, date_time.unit.minute, date_time.unit.second);
+    double et = astro_convert_jd_to_julian_millenia_since_j2000(jd);
+    double r[3] = {0};
+
+    switch(state->active_body_index) {
+        case 0:
+            vsop87a_milli_getMercury(et, r);
+            break;
+        case 1:
+            vsop87a_milli_getVenus(et, r);
+            break;
+        case 2:
+            vsop87a_milli_getEarth(et, r);
+            break;
+        case 3:
+            {
+                 double earth[3];
+                 double emb[3];
+                 vsop87a_milli_getEarth(et, earth);
+                 vsop87a_milli_getEmb(et, emb);
+                 vsop87a_milli_getMoon(earth, emb, r);
+             }
+            break;
+        case 4:
+            vsop87a_milli_getMars(et, r);
+            break;
+        case 5:
+            vsop87a_milli_getJupiter(et, r);
+            break;
+        case 6:
+            vsop87a_milli_getSaturn(et, r);
+            break;
+        case 7:
+            vsop87a_milli_getUranus(et, r);
+            break;
+        case 8:
+            vsop87a_milli_getNeptune(et, r);
+            break;
+    }
+    state->coords[0] = r[0];
+    state->coords[1] = r[1];
+    state->coords[2] = r[2];
+}
+
+static void _orrery_face_update(movement_event_t event, movement_settings_t *settings, orrery_state_t *state) {
+    char buf[11];
+    switch (state->mode) {
+        case ORRERY_MODE_SELECTING_BODY:
+            watch_display_string("Orrery", 4);
+            if (event.subsecond % 2) {
+                watch_display_string((char *)orrery_celestial_body_names[state->active_body_index], 0);
+            } else {
+                watch_display_string("  ", 0);
+            }
+            if (event.subsecond == 0) {
+                watch_display_string("  ", 2);
+                switch (state->animation_state) {
+                    case 0:
+                        watch_set_pixel(0, 7);
+                        watch_set_pixel(2, 6);
+                        break;
+                    case 1:
+                        watch_set_pixel(1, 7);
+                        watch_set_pixel(2, 9);
+                        break;
+                    case 2:
+                        watch_set_pixel(2, 7);
+                        watch_set_pixel(0, 9);
+                        break;
+                }
+                state->animation_state = (state->animation_state + 1) % 3;
+            }
+            break;
+        case ORRERY_MODE_CALCULATING:
+            watch_clear_display();
+             // this takes a moment and locks the UI, flash C for "Calculating"
+            watch_start_character_blink('C', 100);
+            _orrery_face_recalculate(settings, state);
+            watch_stop_blink();
+            state->mode = ORRERY_MODE_DISPLAYING_X;
+            // fall through
+        case ORRERY_MODE_DISPLAYING_X:
+            sprintf(buf, "%s X%6d", orrery_celestial_body_names[state->active_body_index], (int16_t)round(state->coords[0] * 100));
+            watch_display_string(buf, 0);
+            break;
+        case ORRERY_MODE_DISPLAYING_Y:
+            sprintf(buf, "%s Y%6d", orrery_celestial_body_names[state->active_body_index], (int16_t)round(state->coords[1] * 100));
+            watch_display_string(buf, 0);
+            break;
+        case ORRERY_MODE_DISPLAYING_Z:
+            sprintf(buf, "%s Z%6d", orrery_celestial_body_names[state->active_body_index], (int16_t)round(state->coords[2] * 100));
+            watch_display_string(buf, 0);
+            break;
+        case ORRERY_MODE_NUM_MODES:
+            // this case does not happen, but we need it to silence a warning.
+            break;
+    }
+}
+
+void orrery_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr) {
+    (void) settings;
+    (void) watch_face_index;
+    if (*context_ptr == NULL) {
+        *context_ptr = malloc(sizeof(orrery_state_t));
+        memset(*context_ptr, 0, sizeof(orrery_state_t));
+    }
+}
+
+void orrery_face_activate(movement_settings_t *settings, void *context) {
+    (void) settings;
+    (void) context;
+    movement_request_tick_frequency(4);
+}
+
+bool orrery_face_loop(movement_event_t event, movement_settings_t *settings, void *context) {
+    (void) settings;
+    orrery_state_t *state = (orrery_state_t *)context;
+
+    switch (event.event_type) {
+        case EVENT_ACTIVATE:
+        case EVENT_TICK:
+            _orrery_face_update(event, settings, state);
+            break;
+        case EVENT_MODE_BUTTON_UP:
+            movement_move_to_next_face();
+            break;
+        case EVENT_LIGHT_BUTTON_DOWN:
+            movement_illuminate_led();
+            break;
+        case EVENT_LIGHT_BUTTON_UP:
+            break;
+        case EVENT_ALARM_BUTTON_UP:
+            switch (state->mode) {
+                case ORRERY_MODE_SELECTING_BODY:
+                    // advance to next celestial body (move to calculations with a long press)
+                    state->active_body_index = (state->active_body_index + 1) % NUM_AVAILABLE_BODIES;
+                    break;
+                case ORRERY_MODE_CALCULATING:
+                    // ignore button press during calculations
+                    break;
+                case ORRERY_MODE_DISPLAYING_Z:
+                    // at last mode, wrap around
+                    state->mode = ORRERY_MODE_DISPLAYING_X;
+                    break;
+                default:
+                    // otherwise, advance to next mode
+                    state->mode++;
+                    break;
+            }
+            _orrery_face_update(event, settings, state);
+            break;
+        case EVENT_ALARM_LONG_PRESS:
+            if (state->mode == ORRERY_MODE_SELECTING_BODY) {
+                // celestial body selected! this triggers a calculation in the update method.
+                state->mode = ORRERY_MODE_CALCULATING;
+                movement_request_tick_frequency(1);
+                _orrery_face_update(event, settings, state);
+            } else if (state->mode != ORRERY_MODE_CALCULATING) {
+                // in all modes except "doing a calculation", return to the selection screen.
+                state->mode = ORRERY_MODE_SELECTING_BODY;
+                movement_request_tick_frequency(4);
+                _orrery_face_update(event, settings, state);
+            }
+            break;
+        case EVENT_TIMEOUT:
+            movement_move_to_face(0);
+            break;
+        default:
+            break;
+    }
+
+    return true;
+}
+
+void orrery_face_resign(movement_settings_t *settings, void *context) {
+    (void) settings;
+    orrery_state_t *state = (orrery_state_t *)context;
+    state->mode = ORRERY_MODE_SELECTING_BODY;
+}
diff --git a/movement/watch_faces/complication/orrery_face.h b/movement/watch_faces/complication/orrery_face.h
new file mode 100644
index 00000000..98060d97
--- /dev/null
+++ b/movement/watch_faces/complication/orrery_face.h
@@ -0,0 +1,59 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Joey Castillo
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#ifndef ORRERY_FACE_H_
+#define ORRERY_FACE_H_
+
+#include "movement.h"
+
+typedef enum {
+    ORRERY_MODE_SELECTING_BODY = 0,
+    ORRERY_MODE_CALCULATING,
+    ORRERY_MODE_DISPLAYING_X,
+    ORRERY_MODE_DISPLAYING_Y,
+    ORRERY_MODE_DISPLAYING_Z,
+    ORRERY_MODE_NUM_MODES
+} orrery_mode_t;
+
+typedef struct {
+    orrery_mode_t mode;
+    uint8_t active_body_index;
+    double coords[3];
+    uint8_t animation_state;
+} orrery_state_t;
+
+void orrery_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr);
+void orrery_face_activate(movement_settings_t *settings, void *context);
+bool orrery_face_loop(movement_event_t event, movement_settings_t *settings, void *context);
+void orrery_face_resign(movement_settings_t *settings, void *context);
+
+#define orrery_face ((const watch_face_t){ \
+    orrery_face_setup, \
+    orrery_face_activate, \
+    orrery_face_loop, \
+    orrery_face_resign, \
+    NULL, \
+})
+
+#endif // ORRERY_FACE_H_
diff --git a/movement/watch_faces/complication/tomato_face.c b/movement/watch_faces/complication/tomato_face.c
new file mode 100644
index 00000000..37798daf
--- /dev/null
+++ b/movement/watch_faces/complication/tomato_face.c
@@ -0,0 +1,191 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Wesley Ellis
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFtomato_ringEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include <stdlib.h>
+#include <string.h>
+#include "tomato_face.h"
+#include "watch_utility.h"
+
+static uint8_t focus_min = 25;
+static uint8_t break_min = 5;
+
+static inline int32_t get_tz_offset(movement_settings_t *settings) {
+    return movement_timezone_offsets[settings->bit.time_zone] * 60;
+}
+
+static uint8_t get_length(tomato_state_t *state) {
+    uint8_t length;
+    if (state->kind == tomato_focus) {
+        length = focus_min;
+    } else {
+        length = break_min;
+    }
+
+    return length;
+}
+
+static void tomato_start(tomato_state_t *state, movement_settings_t *settings) {
+    watch_date_time now = watch_rtc_get_date_time();
+    int8_t length = (int8_t) get_length(state);
+
+    state->mode = tomato_run;
+    state->now_ts = watch_utility_date_time_to_unix_time(now, get_tz_offset(settings));
+    state->target_ts = watch_utility_offset_timestamp(state->now_ts, 0, length, 0);
+    watch_date_time target_dt = watch_utility_date_time_from_unix_time(state->target_ts, get_tz_offset(settings));
+    movement_schedule_background_task(target_dt);
+    watch_set_indicator(WATCH_INDICATOR_BELL);
+}
+
+static void tomato_draw(tomato_state_t *state) {
+    char buf[16];
+
+    uint32_t delta;
+    div_t result;
+    uint8_t min = 0;
+    uint8_t sec = 0;
+    char kind;
+
+    if (state->kind == tomato_break) {
+        kind = 'b';
+    } else {
+        kind = 'f';
+    }
+
+    switch (state->mode) {
+        case tomato_run:
+            delta = state->target_ts - state->now_ts;
+            result = div(delta, 60);
+            min = result.quot;
+            sec = result.rem;
+            break;
+        case tomato_ready:
+            min = get_length(state);
+            sec = 0;
+            break;
+    }
+    sprintf(buf, "TO %c%2d%02d%2d", kind, min, sec, state->done_count);
+    watch_display_string(buf, 0);
+}
+
+static void tomato_reset(tomato_state_t *state) {
+    state->mode = tomato_ready;
+    movement_cancel_background_task();
+    watch_clear_indicator(WATCH_INDICATOR_BELL);
+}
+
+static void tomato_ring(tomato_state_t *state) {
+    movement_play_signal();
+    tomato_reset(state);
+    if (state->kind == tomato_focus) {
+        state->kind = tomato_break;
+        state->done_count++;
+    } else {
+        state->kind = tomato_focus;
+    }
+}
+
+void tomato_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr) {
+    (void) settings;
+    (void) watch_face_index;
+
+    if (*context_ptr == NULL) {
+        *context_ptr = malloc(sizeof(tomato_state_t));
+        tomato_state_t *state = (tomato_state_t*)*context_ptr;
+        memset(*context_ptr, 0, sizeof(tomato_state_t));
+        state->mode=tomato_ready;
+        state->kind= tomato_focus;
+        state->done_count = 0;
+    }
+}
+
+void tomato_face_activate(movement_settings_t *settings, void *context) {
+    tomato_state_t *state = (tomato_state_t *)context;
+    if (state->mode == tomato_run) {
+        watch_date_time now = watch_rtc_get_date_time();
+        state->now_ts = watch_utility_date_time_to_unix_time(now, get_tz_offset(settings));
+    }
+    watch_set_colon();
+}
+
+bool tomato_face_loop(movement_event_t event, movement_settings_t *settings, void *context) {
+    tomato_state_t *state = (tomato_state_t *)context;
+
+    switch (event.event_type) {
+        case EVENT_ACTIVATE:
+            tomato_draw(state);
+            break;
+        case EVENT_TICK:
+            if (state->mode == tomato_run) {
+                state->now_ts++;
+            }
+            tomato_draw(state);
+            break;
+        case EVENT_MODE_BUTTON_UP:
+            movement_move_to_next_face();
+            break;
+        case EVENT_LIGHT_BUTTON_UP:
+            movement_illuminate_led();
+            if (state->mode == tomato_ready) {
+                if (state->kind == tomato_break) {
+                    state->kind = tomato_focus;
+                } else {
+                    state->kind = tomato_break;
+                }
+            }
+            tomato_draw(state);
+            break;
+        case EVENT_ALARM_BUTTON_UP:
+            switch(state->mode) {
+                case tomato_run:
+                    tomato_reset(state);
+                    break;
+                case tomato_ready:
+                    tomato_start(state, settings);
+                    break;
+            }
+            tomato_draw(state);
+
+            break;
+        case EVENT_ALARM_LONG_PRESS:
+            state->done_count = 0;
+            break;
+        case EVENT_BACKGROUND_TASK:
+            tomato_ring(state);
+            tomato_draw(state);
+            break;
+        case EVENT_TIMEOUT:
+            movement_move_to_face(0);
+            break;
+        default:
+            break;
+    }
+
+    return true;
+}
+
+void tomato_face_resign(movement_settings_t *settings, void *context) {
+    (void) settings;
+    (void) context;
+}
+
diff --git a/movement/watch_faces/complication/tomato_face.h b/movement/watch_faces/complication/tomato_face.h
new file mode 100644
index 00000000..5404ad11
--- /dev/null
+++ b/movement/watch_faces/complication/tomato_face.h
@@ -0,0 +1,63 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Wesley Ellis
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#ifndef TOMATO_FACE_H_
+#define TOMATO_FACE_H_
+
+#include "movement.h"
+
+typedef enum {
+    tomato_ready,
+    tomato_run,
+    // to_pause, // TODO implement pausing
+} tomato_mode;
+
+typedef enum {
+    tomato_break,
+    tomato_focus,
+} tomato_kind;
+
+typedef struct {
+    uint32_t target_ts;
+    uint32_t now_ts;
+    tomato_mode mode;
+    tomato_kind kind;
+    uint8_t done_count;
+} tomato_state_t;
+
+void tomato_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr);
+void tomato_face_activate(movement_settings_t *settings, void *context);
+bool tomato_face_loop(movement_event_t event, movement_settings_t *settings, void *context);
+void tomato_face_resign(movement_settings_t *settings, void *context);
+
+#define tomato_face ((const watch_face_t){ \
+    tomato_face_setup, \
+    tomato_face_activate, \
+    tomato_face_loop, \
+    tomato_face_resign, \
+    NULL, \
+})
+
+#endif // TOMATO_FACE_H_
+
diff --git a/movement/watch_faces/sensor/thermistor_readout_face.c b/movement/watch_faces/sensor/thermistor_readout_face.c
index b97c8432..28106022 100644
--- a/movement/watch_faces/sensor/thermistor_readout_face.c
+++ b/movement/watch_faces/sensor/thermistor_readout_face.c
@@ -63,7 +63,7 @@ bool thermistor_readout_face_loop(movement_event_t event, movement_settings_t *s
         case EVENT_LIGHT_BUTTON_DOWN:
             movement_illuminate_led();
             break;
-        case EVENT_ALARM_BUTTON_UP:
+        case EVENT_ALARM_BUTTON_DOWN:
             settings->bit.use_imperial_units = !settings->bit.use_imperial_units;
             _thermistor_readout_face_update_display(settings->bit.use_imperial_units);
             break;
diff --git a/movement/watch_faces/sensor/thermistor_testing_face.c b/movement/watch_faces/sensor/thermistor_testing_face.c
new file mode 100644
index 00000000..f50e0567
--- /dev/null
+++ b/movement/watch_faces/sensor/thermistor_testing_face.c
@@ -0,0 +1,88 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Joey Castillo
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include <stdlib.h>
+#include <string.h>
+#include "thermistor_testing_face.h"
+#include "thermistor_driver.h"
+#include "watch.h"
+
+// This watch face is designed for testing temperature sensor boards.
+// It displays temperature readings at a relatively fast rate of 8 Hz,
+// and disables low energy mode so my testing device doesn't sleep.
+// You more than likely want to use thermistor_readout_face instead.
+
+static void _thermistor_testing_face_update_display(bool in_fahrenheit) {
+    thermistor_driver_enable();
+    float temperature_c = thermistor_driver_get_temperature();
+    char buf[14];
+    if (in_fahrenheit) {
+        sprintf(buf, "%4.1f#F", temperature_c * 1.8 + 32.0);
+    } else {
+        sprintf(buf, "%4.1f#C", temperature_c);
+    }
+    watch_display_string(buf, 4);
+    thermistor_driver_disable();
+}
+
+void thermistor_testing_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr) {
+    (void) watch_face_index;
+    (void) context_ptr;
+    // force one setting: never enter low energy mode.
+    // I'm using this watch face to test the temperature sensor boards; there's no need for it.
+    settings->bit.le_interval = 0;
+}
+
+void thermistor_testing_face_activate(movement_settings_t *settings, void *context) {
+    (void) settings;
+    (void) context;
+    watch_display_string("TE", 0);
+    movement_request_tick_frequency(8);
+}
+
+bool thermistor_testing_face_loop(movement_event_t event, movement_settings_t *settings, void *context) {
+    (void) context;
+    switch (event.event_type) {
+        case EVENT_MODE_BUTTON_UP:
+            movement_move_to_next_face();
+            break;
+        case EVENT_ALARM_BUTTON_DOWN:
+            settings->bit.use_imperial_units = !settings->bit.use_imperial_units;
+            _thermistor_testing_face_update_display(settings->bit.use_imperial_units);
+            break;
+        case EVENT_ACTIVATE:
+        case EVENT_TICK:
+            _thermistor_testing_face_update_display(settings->bit.use_imperial_units);
+            break;
+        default:
+            break;
+    }
+
+    return true;
+}
+
+void thermistor_testing_face_resign(movement_settings_t *settings, void *context) {
+    (void) settings;
+    (void) context;
+}
diff --git a/movement/watch_faces/sensor/thermistor_testing_face.h b/movement/watch_faces/sensor/thermistor_testing_face.h
new file mode 100644
index 00000000..656f58d5
--- /dev/null
+++ b/movement/watch_faces/sensor/thermistor_testing_face.h
@@ -0,0 +1,43 @@
+/*
+ * MIT License
+ *
+ * Copyright (c) 2022 Joey Castillo
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#ifndef THERMISTOR_TESTING_FACE_H_
+#define THERMISTOR_TESTING_FACE_H_
+
+#include "movement.h"
+
+void thermistor_testing_face_setup(movement_settings_t *settings, uint8_t watch_face_index, void ** context_ptr);
+void thermistor_testing_face_activate(movement_settings_t *settings, void *context);
+bool thermistor_testing_face_loop(movement_event_t event, movement_settings_t *settings, void *context);
+void thermistor_testing_face_resign(movement_settings_t *settings, void *context);
+
+#define thermistor_testing_face ((const watch_face_t){ \
+    thermistor_testing_face_setup, \
+    thermistor_testing_face_activate, \
+    thermistor_testing_face_loop, \
+    thermistor_testing_face_resign, \
+    NULL, \
+})
+
+#endif // THERMISTOR_TESTING_FACE_H_
diff --git a/movement/watch_faces/settings/set_time_face.c b/movement/watch_faces/settings/set_time_face.c
index f0e7dc6c..af5421f1 100644
--- a/movement/watch_faces/settings/set_time_face.c
+++ b/movement/watch_faces/settings/set_time_face.c
@@ -102,8 +102,8 @@ bool set_time_face_loop(movement_event_t event, movement_settings_t *settings, v
             sprintf(buf, "%s  %2d%02d%02d", set_time_face_titles[current_page], date_time.unit.hour, date_time.unit.minute, date_time.unit.second);
         } else {
             sprintf(buf, "%s  %2d%02d%02d", set_time_face_titles[current_page], (date_time.unit.hour % 12) ? (date_time.unit.hour % 12) : 12, date_time.unit.minute, date_time.unit.second);
-            if (date_time.unit.hour > 12) watch_set_indicator(WATCH_INDICATOR_PM);
-            else watch_clear_indicator(WATCH_INDICATOR_PM);
+            if (date_time.unit.hour < 12) watch_clear_indicator(WATCH_INDICATOR_PM);
+            else watch_set_indicator(WATCH_INDICATOR_PM);
         }
     } else if (current_page < 6) {
         watch_clear_colon();