VSOP87 -- I hope I am wrong ...

[molecule]

edit-

PRoblem solved by Hank! -- bug potential not worth your reading time -- I just blanked out about the rho (Doh!) in the ecliptic plane!

subsequent comparisions (with the right formula this time) of VSOP versions show that they are hot, hot H-O-T. comparisons of full comp values between A,B,C,D for the same date do not vary by more than 0.00x arc sec.

Thanks hank.

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I'm trying to code up some old fashioned "Ptolomaic" path charts, so I chose VSOP87, thinking ~0.1" accuracy would be nice.

I coded up VSOP87 in oOO macroBasic for the rectangular VSOP97"C" tables and the spherical "D" tables. Both are equinox of date. When output is compared to the values given in the VSOP checksheet, they to all decimals given (10th decimal ~ .000I arcsec).

The VSOP checksheet file, "vsop98.chk", is available from ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/

I thought that, since the D-tables are much smaller and converge faster, I would use the D-tables for a spherical solution, and then compute rectangular coords on my own, from which I could then compute the apparent geocentric positions.

Ouch!!

[code]From the VSOP check sheet for Saturn on JD 2305445.0
SATURN -- JD 2305445.0 (29/12/1599)
-VSOP97C: Lon= 3.5217555199 rd, Lat= 0.0437035058 rd, Dist= 9.7571035629 au
-VSOP87D: X = -9.0518360159 au, Y = -3.6171280351 au, Z = 0.4262838732 au

If I compute X from the spherical solution, I get quite a shock
if X = Dist * cos(Long) then X = 9.7571035629 * cos(3.5217555199) = -9.0604874734 au

The difference between VSOP87C and D is 9.0604874734 - 9.0518360159 = 0.0086515 au. At the given radius, this is approximately 183 secs of arc.[/code]

183 arcsecs is not quite the ~0.1 arcsec accuracy (consistency?) that VSOP87 is reported to have ...

BTW, the check sheet values above are "full solution" values -- that is that evey coordinate is included no matter how small in the 10 decimal printouts. (Default solution drops coordinates at approx the 8th decimal -- there is a default precision for each planet below which remaining terms are considered not significant. The default precision for Saturn is 70.0e-8, which corresponds to 0.14 arcsec. Still well below the 183 arcsec internal discrepance between version C and D. Both C and D are ecliptic and equinox of date.

Am I computing X from Distance and Longitude wrong?

(If I am not -- and I hope that I am -- then this 180 arcsec discrepancy is not aytpical of the comparative C to D values on the VSOP checksheet -- many are greater than 300 arcsec, and some go over 600 arcsec (for Mercury and Venus)

Can anyone explain this?

Which version of VSOP87 does Celestia use?

I understand from the author's original report, found at
http://articles.adsabs.harvard.edu/cgi- ... etype=.pdf
that the D (spherical, ecliptic and equinox of date) was computed from C (rectangular, ecliptic and equinox of date), which was computed from A (rectangular, J2000), which was computed from the original elliptical solution after applying correctives for motion of the ecliptic and the equator.

183 arcsec seems too large to be an internal discrepancy -- am I computing X incorrectly -- I hope I am! Otherwise this might be the tipside of a very deep bug?

[hank]

Am I computing X from Distance and Longitude wrong?

Yes, I think so. I believe you need to multiply your result by the cosine of the latitude. (The length of a degree of longitude varies with the latitude.)

- Hank