This page is 'work in progress'.
I have implemented the algorithm for finding the mean geocentric longitude and latitude of the Moon which forms chapter 30 of Jean Meeus' book Astronomical Formulas for Calculators. I have written a simple QBASIC program based on the algorithm, and modified the program to produce daily Moon positions for the whole of a 'Saros' cycle of about 18.6 years ending around J2000.
I compared values from the Meeus algorithm with a series generated using Manfred Ding's Ephtool Lite ephemeris program, together with his DLL implementing the full ELP-2000/82 analytical lunar theory.
The error in latitude when compared with ELP-2000/82 follows an expected pattern, but the error in longitude shows a systematic difference of 35 arcseconds (posibly part of a long period cycle) even after correction for nutation. The RMS error in longitude is 5 arcsec.
Below is the longitude error after applying a simple correction for nutation in longitude:
The error in latitude has an RMS of 3 arcsec, and the error curve looks symmetrical about zero error - there is no systematic error apparent.
Any ideas regarding the systematic error welcome. Otherwise, I shall produce a 'fudge factor' to keep the algorithm accurate for fifty years either side of J2000.0
Keith Burnett
1999 April 27th
keith@xylem.demon.co.uk