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| author | joeycastillo <joeycastillo@utexas.edu> | 2022-03-04 14:52:49 -0600 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2022-03-04 14:52:49 -0600 |
| commit | ccdf08da876d2c66bbc54cc246443676c4f9bf2e (patch) | |
| tree | 77473da9df40f9b1f7cec5f8bd03c1b52c26b8e7 /movement/lib/vsop87 | |
| parent | ea988208e10dbcf62eff65522ec9f92231d880e9 (diff) | |
| download | Sensor-Watch-ccdf08da876d2c66bbc54cc246443676c4f9bf2e.tar.gz Sensor-Watch-ccdf08da876d2c66bbc54cc246443676c4f9bf2e.tar.bz2 Sensor-Watch-ccdf08da876d2c66bbc54cc246443676c4f9bf2e.zip | |
Movement: Astronomy and Orrery watch faces (#55)
Diffstat (limited to 'movement/lib/vsop87')
| -rwxr-xr-x | movement/lib/vsop87/LICENSE.txt | 5 | ||||
| -rwxr-xr-x | movement/lib/vsop87/README.md | 143 | ||||
| -rwxr-xr-x | movement/lib/vsop87/vsop87a_micro.c | 1019 | ||||
| -rwxr-xr-x | movement/lib/vsop87/vsop87a_micro.h | 17 | ||||
| -rwxr-xr-x | movement/lib/vsop87/vsop87a_milli.c | 2048 | ||||
| -rwxr-xr-x | movement/lib/vsop87/vsop87a_milli.h | 17 |
6 files changed, 3249 insertions, 0 deletions
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
+
+
+### Venus
+
+
+### Earth-Moon Barrycenter
+
+
+### Earth-Moon Barrycenter (zoomed)
+
+
+### Mars
+
+
+### Jupiter
+
+
+### Saturn
+
+
+### Saturn (zoomed)
+
+
+### Uranus
+
+
+### Uranus (zoomed)
+
+
+### Neptune
+
+
+### Neptune (zoomed)
+
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
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