Analytical series representing the DE431 ephemerides of the outer planetsстатья
Статья опубликована в высокорейтинговом журнале
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Аннотация:This paper presents a new development of orbital elements for the four outer planets in analytical series. These series complete the series DEA431, for which the terms for the terrestrial planets are given in an earlier paper. As the source of planetary coordinates, the development uses the latest long-term numerical ephemerides DE431, which are valid over 30 000 yr [−13 000, 17 000]. The author's modification of the frequency analysis method is used as the expansion tool. The obtained results are compared with those given by recent analytical theories of planetary motion, namely VSOP2013 and TOP2013. The number of terms in DEA431 is about one order of magnitude lower than that in either VSOP2013 or TOP2013. The extensive analytical theories of the motion of the outer planets are more precise than the compact DEA431 series over time intervals of several hundreds of years; the three compared analytical series are of about the same accuracy over time intervals of a few thousand years; and DEA431 has a higher accuracy than both VSOP2013 and TOP2013 when representing the coordinates of the outer planets over longer time intervals, such as tens of thousands of years. Over 24 000 yr centred at epoch J2000, the maximum difference between the mean orbital longitudes of the outer planets given by the DE431 numerical ephemerides and the DEA431 analytical series is 0.08" for Jupiter, 0.22" for Saturn, 0.10" for Uranus, and 0.05" for Neptune. The coefficients of the DEA431 series for all the outer planets and the corresponding FORTRAN routines for calculating the orbital elements and rectangular coordinates of the planets are available on the SAI web-server.