I am trying to write an app to determine planetary positions, using Jean Meeus' Astronomical Algorithms as a reference. His guidance on using the VSOP87D data is straightforward, as are many other sources that I googled. But all of these talk only about the last three columns of that data. What is the purpose of the preceding columns? Some are self explanatory (e.g., the simple numbering of each row), but others seem to have no explanation either in the file itself or the 'read me' documents that accompany it on the FTP site. I want to ensure I fully understand the data.

Here is an example of the third row of VSOP87D for the planet Jupiter:

4510, 3, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, -0.00566632795, -0.00089195704, 0.00573610145, 1.44406205976, 7.11354700080

where I have replaced the various spaces with commas to save space.

I will note that the term .00573610145, for example, differs by by several orders of magnitude from that listed in Meeus' table, as do some other terms. But this does not seem to correspond to any of the numbers in the other columns, unless I'm missing the obvious.

The data is taken from the FTP website: ftp://cdsarc.u-strasbg.fr/pub/cats/VI%2F81/VSOP87D.jup


  • 1
    $\begingroup$ ftp.imcce.fr/pub/ephem/planets/vsop87/vsop87.doc may or may not be helpful. You can find text versions by googling this phrase: google.com/… (a description of the columns in FORTRAN). $\endgroup$ – barrycarter Jan 26 '17 at 19:16
  • $\begingroup$ In fact, that is VERY helpful. Although I don't yet grasp the meaning of each term, at least now I have a starting point to begin learning what each term means. It also appears that these 'leading' columns are not necessary for calculating planetary positions using Meeus's instructions. Thanks barrycarter! $\endgroup$ – Aloft Jan 26 '17 at 19:40

First, the data in most of these columns is not required for the computation of planetary positions using the theory if the 'second' form equation is used. The terms are, using the order of the example of Jupiter VSOP 87D's third line ...

4510 ...

"4" means the 'version code', i.e., this is the "D" version of the theory which allows computation of the heliocentric rectangular coordinates of the planet for the ecliptic of date. A "3" would be for the spherical heliocentric coordinates for the ecliptic of date.

"5" is the 'body' code, Jupiter being the FIFTH planet. Mercury would be planet '1', for example.

"1" is the 'index of coordinate', meaning in this example that this line is part of the 'longitude' coordinate calculation. Later lines show a '2' for the B (or latitude) coordinate or '3' for the R (radial or distance) coordinate)

"0" is the 'degree' or power of the time variable. Here, terms are multiplied by T to the ZERO power (or 1). Later terms are multiplied by successively higher powers of T.

3 ... is simply the sequential number of this line in this series. Jupiter has 5 series (each multiplied by a higher power of T), so this number 'resets' for each series.

The next 12 terms, mostly zeros in this example, are the 'coefficients of mean longitude'. As near as I can tell, these coefficients are used to correct mean longitude quantities for secular perturbations. They are used only in the first form of the equation as shown below with the next two terms:

The next two terms are amplitudes S and K, used in the first form of the positional equation:

T**alpha * (S sin phi + K cos phi)

where phi = sum[i, 1 thru 12] [a(i) * lambda(i)] and lambda(i) values are given for each solar system body in the explanatory text.

The final 3 terms are Amplitude A, Amplitude B and Phase C for use in the second form of the equations to calculate position:

T**alpha * A * cos(B + CT)

... with T being time in Julian centuries, and alpha the 'power' of T.

My comment in the original question about the terms being 'off' by several orders of magnitude is moot ... for convenience either in calculating or printing, Meeus multiplied the terms by 10**8, then corrects for it later. This probably facilitated better computation on machines of the time it was written and also made for neater printing in the book.

The document provided by barrycarter, along with some other study of planetary motion allowed me to finally understand this, thanks!


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