Solution of the N-Body Problem Expanded Into Taylor Series of High Orders. Applications to the Solar System Over Large Time Range

Details Solution of the N-Body Problem Expanded Into Taylor Series of High Orders. Applications to the Solar System Over Large Time Range Solution of the N-Body Problem Expanded Into Taylor Series of High Orders. Applications to the Solar System Over Large Time Range

May 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...272..687l&link_type=abstract

Astronomy and Astrophysics, vol. 272, 687-694. Article.

Astronomy and Astrophysics

Astrophysics

5

Celestial Mechanics, Numerical Integration, Solar System, Planets, Solar System, Celestial Mechanics, Numerical Methods, Velocity, Calculations, Position (Location), Orbital Elements, Ephemerides, Motion, Comparison, Theoretical Studies, Parameters, Computer Methods

Scientific paper

A method for numerical integration of the N- body problem is carried out and described in this paper, the solution obtained being expanded into 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 respect to time, in a direction and its reverse, such as:
(a) The nine major planets in translation around the Sun are integrated over intervals of 40000 d with a near constant integration step-size of 4 d. The results 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 are obtained on the rectangular coordinates of all the planets.
(b) In the same way, the eight first major planets (Pluto is excluded) are integrated over intervals of 1000 yr and the results especially estimated on the mean longitudes. An accuracy of 0"0025 is reached on Mercury.
(c) The four outer planets (Jupiter, Saturn, Uranus, Neptune) are integrated over intervals of 6000 yr with a near constant integration step-size of 400 d. It is shown here that the results got by the numerical integrations of Schubart & Stumpff (1966) are improved by a factor of about 15.

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