SOLUTION OF THE N-BODY PROBLEM EXPANDED INTO TAYLOR-SERIES OF HIGH ORDERS - APPLICATIONS TO THE SOLAR-SYSTEM OVER LARGE TIME RANGE

A method for numerical integration of the N-body problem is carried ou t and described in this paper, the solution obtained being expanded in to Taylor series of high orders with the aid of recurrent formulae. An easy to use Fortran program having been written, the accuracy of this method is then tested integrating some planetary problems with respec t to time, in a direction and its reverse, such as: (a) The nine major planets in translation around the Sun are integrated over intervals o f 40 000 d with a near constant integration step-size of 4 d. The resu lts are compared 'to the ephemeris DE200 of the JPL (Standish 1982a), to which the relativistic perturbations and those due to the Moon and minor planets were first subtracted. Differences of about 10(-10) AU a re obtained on the rectangular coordinates of all the planets. (b) In the same way, the eight first major planets (Pluto is excluded) are in tegrated over intervals of 1000 yr and the results especially estimate d on the mean longitudes. An accuracy of 0.0025'' is reached on Mercur y. (c) The four outer planets (Jupiter, Saturn, Uranus, Neptune) are i ntegrated over intervals of 6000 yr with a near constant integration s tep-size of 400 d. It is shown here that the results got by the numeri cal integrations of Schubart & Stumpff (1966) are improved by a factor of about 15.