Analytical series representing DE431 ephemerides of terrestrial planets

Abstract

This paper describes the new analytical series DEA431, which comprise orbital elements of terrestrial planets obtained from the long-term numerical ephemerides DE431. The series are obtained from a modified frequency analysis of the ephemerides over 30 000 yr [-13 000, 17 000], the total time interval covered by DE431. Unlike the procedure involving classical Fourier analysis, the development here is made to trigonometric series in which both the amplitudes and the arguments of the series terms are high-degree polynomials of time. A comparison of the new series with those given by the most accurate analytical theory of planetary motion VSOP2013 is performed. The two analytical solutions find very similar major fundamental frequencies of planetary motion; however, the number of terms for orbital elements in the DEA431 development is about one order of magnitude lower than that in the VSOP2013 theory. VSOP2013 is still the best analytical solution when predicting the motion of terrestrial planets over 100 years or so, but DEA431 gives a much better prediction over long intervals, up to several tens of thousands of years. Over 24 000 yr centred at epoch J2000, the maximum differences between the rectangular ecliptic coordinates of terrestrial planets calculated using the DEA431 analytical series and the corresponding coordinates given by DE431 numerical ephemerides are 0.5 km for Mercury, 14.0 km for Venus, 12.7 km for the Earth-Moon barycentre, and 76.5 km for Mars. All coefficients of the DEA431 series and fortran routines for calculating both orbital elements and rectangular coordinates of the terrestrial planets on the basis of the new series are available on the SAI web-server.