Long-term harmonic development of lunar ephemeris^*

Sternberg Astronomical Institute of Moscow State University, Universitetsky Pr. 13, Moscow, 119992, Russia e-mail: ksm@sai.msu.ru

Received: 29 March 2007
Accepted: 28 May 2007

Abstract

Aims.The aim of this study is to develop new analytical series representing lunar coordinates to accuracy compatible with the accuracy of the modern numerical ephemeris of the Moon.

Methods.An improved method of spectral analysis of tabulated function is used to make harmonic development of the latest long-term numerical ephemeris of the Moon LE-406 which covers a six thousand-year interval. A feature of the method is that the development is made directly to Poisson series where both amplitudes and arguments of the series' terms are high-degree polynomials of time.

Results.The new analytical development includes 42 270 Poisson series' terms of minimal amplitude equivalent to 1 cm and is valid over 1500–2500. A simplified version of the development includes 7952 series' terms of minimal amplitude equivalent to 1 m and is valid over 3000BC–3000AD. Over 1500–2500 the maximum difference between lunar coordinates calculated by means of the new analytical series and numerical ephemeris LE-406 is 3.2 m in geocentric distance, 00056 in ecliptic longitude, and 00018 in ecliptic latitude. This is 9–70 times better than the accuracy of the latest analytical theory of lunar motion ELP/MPP02, and the number of terms in the new development is less than that in ELP/MPP02.