For full details, consult Planetary theories in rectangular and spherical variables - VSOP 87 solutions
The VSOP87 theory provides methods of computing the planet positions in several different coordinate systems, and each solution may or may not a particular body. The table below outlines what each solution provides and the coordinate system the results are in.
|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|
Further, each solution is broken up into different accuracy levels in each file. In the repository you will see files named vsop87x_vvvvvv.ppp, where x is the solution in the table above, vvvvvv is the accuracy level, and ppp is the extention for a given programming language. You will only need one of these files. If you plan to implement abberation, you will also need the corresponding _velocities file. Since most solutions don't include the positon of the Sun, the coordinate system for those is Heliocentric. So the positon of the Sun, relative to Earth, can be computed by just negating the position vectors for the Earth. The example above shows how to perform this task.
If you're at a loss for where to start, vsop87a_full is likely worth trying first. If it turns out not to be fast enough for your application, consider one of the smaller vsop87a versions.
Eacy library version will contain functions named similar to getEarth(), getMars(), getJupiter(), etc. And VSOP87a contains the special function getMoon() (explained below). Each of these functions accepts one parameter T. T is the number of days in Julain Centuries passed since the year 2000 in the TDB time scale, again, the example above shows how to compute this value.
The special function getMoon() in VSOP87A accepts two parameters, the positon of the Earth, and the Earth-Moon Baryrcenter. It returns the position of the moon in the same coordinate system as VSOP87A.
This short example shows how a typical call to get the positon of the Earth and Moon might go:
const jd=2457987.267731481; //TDB time scale const t=(jd - 2451545.0) / 365250.0; const earth=vsop878a.getEarth(t); const emb=vsop87a.getEmb(t); const moon=vsop87a.getMoon(earth,emb);
The result is the varialbes earth, emb, and moon will contain an array of three Doubles which are the J2000 rectangular coordinates of each body in units of AU. Such coordinates are of little use to most people directly, so the example above shows how to convert them into more useful coordinates.
The interactive graph below is populated with precomputed data from 2000BC to 3000AD. Use the checkboxes to get an idea for the accuracy over a given time period. Note the Moon is unchecked by default, as the "pico", "nano", and "micro" versions are essentially unusable for the Moon for any date range. Keep in mind that you may copy the functions for computing one body into other versions, essentially mixing and matching accuracy editions.
The Y-axis is the error, in degrees, as viewed from the center of the Earth, compared to the full VSOP87a version.