Journal Article

Post-Newtonian effects of planetary gravity on the perihelion shift

Kei Yamada and Hideki Asada

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 423, issue 4, pages 3540-3544
Published in print July 2012 | ISSN: 0035-8711
Published online July 2012 | e-ISSN: 1365-2966 | DOI:
Post-Newtonian effects of planetary gravity on the perihelion shift

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We consider a coplanar system comprising of a massive central body (a star), a less massive secondary (a planet) on a circular orbit, and a test particle on a bound orbit exterior to that of the secondary. The gravitational pull exerted on the test particle by the secondary acts as a small perturbation, wherefore the trajectory of the particle can be described as an ellipse of a precessing perihelion. While the apsidal motion is defined overwhelmingly by the Newtonian portion of the secondary’s gravity, the post-Newtonian portion, too, brings its tiny input. We explore whether this input may be of any astrophysical relevance in the next few decades. We demonstrate that the overall post-Newtonian input of the secondary’s gravity can be split into two parts. One can be expressed via the orbital angular momentum of the secondary and another via its orbital radius. Despite some moderately large numerical factors showing up in the expressions for these two parts, the resulting post-Newtonian contributions from the secondary’s gravity into the apsidal motion of the test particle turn out to be small enough to be neglected in the near-future measurements.

Keywords: gravitation; methods: analytical; celestial mechanics; planets and satellites: general

Journal Article.  2197 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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