Long-term harmonic development of lunar ephemeris

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, 0. 0056 in ecliptic longitude, and 0. 0018 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.

Accurate analytical representation of Pluto modern ephemeris

“…For solving similar tasks we earlier suggested a new modification of the spectral analysis method (Kudryavtsev 2004(Kudryavtsev , 2007. The new method makes a harmonic development of a tabulated function directly to Poisson series, so that amplitudes and arguments of the series' terms are time polynomials.…”

Harmonic development of tide-generating potential of terrestrial planets

“…We made harmonic development of the TGP for the three terrestrial planets with help of a new modification of the spectral analysis method (Kudryavtsev 2004(Kudryavtsev , 2007. According to this method, the development is directly made to Poisson series where both amplitudes and frequencies of the series' terms are high-degree polynomials of time (as opposite to the classical Fourier analysis where both amplitudes and frequencies of the resulting series' terms are constants).…”

“…The arguments (15) are obtained as linear combinations of integer multipliers of various frequencies specific to motion of the main planet (for which we calculate the TGP) and of the attracting bodies (such as the planetary moons or other major planets). The degree of argument (15) is chosen equal to 4 as it is the maximum degree of polynomials for Delaunay variables widely used in developing terrestrial planets' TGP and nutation series [more details about the selection procedure for arguments (15) can be found in Kudryavtsev (2007)]. …”

“…The new developments of the terrestrial planets' TGP can be further used in improvement of the planets' nutation series, tidal models, gravity variations, and internal structure (see Roosbeek 1999;Van Hoolst et al 2003, 2007.…”

“…The latest long-term numerical planetary/lunar ephemerides DE/LE-406 (which are the extension of DE/LE-405 over 6,000 years) are used as the source of the Sun, Moon and major planets' coordinates. The expansion of the planetary TGP is made with use of a new modification of the spectral analysis method (Kudryavtsev 2004(Kudryavtsev , 2007.…”