Аннотация:The files contain numerical coefficients of the Poisson series representing the geocentric ecliptic spherical coordinates of the Moon R, V and U where R is the geocentric distance, V is the spherical longitude, U is the spherical latitude. The series are obtained by spectral analysis of the long-term numerical ephemeris of the Moon LE-405/406 (Standish 1998: JPL IOM 312.F-98-048).
There are two versions of the Poisson series for lunar coordinates R, V, U: - the complete series, LEA-406a, include 42270 terms of minimal amplitude equivalent to 1 cm and are valid over 1500-2500. - the simplified series, LEA-406b, include 7952 terms of minimal amplitude equivalent to 1 m and are valid over 3000BC-3000AD.
The formulation of the series is: R = {SUM}[k=1,Records;i=0,2](A_{ki}*t_i*cos(Arg_{ki})) V = V0(t) + {SUM}[k=1,Records;i=0,2](A_{ki}*t_i*sin(Arg_{ki})) U = {SUM}[k=1,Records;i=0,2](A_{ki}*t_i*sin(Arg_{ki})),
where t is the time (TDB) in thousands of Julian years from J2000: t=(JulianDate-2451545.0)/365250.0; V0(t) is the mean longitude of the Moon referred to the moving ecliptic and mean equinox of date as given by Simon et al. (1994A&A..282..663S); A_{ki} is the amplitude of the "k"th Poisson term of the order i; Arg_{ki} is the four-degree time polynomial argument defined as linear combination of integer multipliers of 14 variables (Arg_j, j=1,14): Delaunay variables l, l', F, D; mean longitude of the ascending node of the Moon {Omega}; mean longitudes of eight major planets {lambda}pl; and the general precession in longitude p_A. So that Arg_{ki}={SUM}[j=1,14](m_{kj}*Argj+phi_{ki}), where m_{kj} are the integer multiplies and phi_{ki} are the phases. The expressions for Arg_j are given by Simon et al. (1994A&A..282..663S).
The lunar coordinates R, V and U given by the series are referred to the moving ecliptic and mean equinox of date. Transformation of the coordinates to the reference frame of the numerical ephemeris LE-405/406 (defined by the mean geoequator and equinox of epoch J2000) should be performed with use of the precession quantities as given by Simon et al. (1994A&A..282..663S).
A Fortran 77 subroutine for calculation of lunar rectangular coordinates on the base of the suggested Poisson series and two test examples are also given.