41
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Three-body-interaction effects on the relativistic perihelion precession for the Sun-Jupiter-Saturn system

      Preprint
      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          The relativistic perihelion precession due to the three-body interaction is derived. We consider a hierarchical coplanar three-body system, such as the Sun, Jupiter and Saturn, in which both the secondary object as the largest planet corresponding to Jupiter (mass \(m_2\)) and the third one corresponding to Saturn (mass \(m_3\)) orbit around the primary object corresponding to Sun (mass \(m_1 \gg m_2 \gg m_3\)), where the mean orbital radius of the third body is larger than that of the secondary one (denoted as \(\ell\)). We investigate the post-Newtonian effects on the motion of the third body (semimajor axis a, eccentricity e for the Keplerian orbital elements). Under some assumptions with a certain averaging, the relativistic perihelion precession of the third mass by the post-Newtonian three-body interaction is expressed as \(6 G m_2 \ell^2 c^{-2} a^{-3} n (1+9e^2/16) (1-e^2)^{-3} \), where G and c denote the gravitational constant and the speed of light, respectively, and the mean motion for the third body is denoted as \(n = 2\pi a^{3/2} G^{-1/2} (m_1+m_2)^{-1/2}\). For the Sun-Jupiter-Saturn system, it is \(7.8 \times 10^{-6}\) arcsec/cy. This is larger than the Lense-Thirring effect by Sun but it cannot yet explain the recently reported value for the anomalous perihelion precession of Saturn as \(-0.006 \pm 0.002\) arcsec/cy by Iorio (2009) based on the analyses by Pitjeva with the EPM2008 ephemerides.

          Related collections

          Author and article information

          Journal
          16 May 2011
          2012-03-23
          Article
          1105.2998
          64c049c9-8563-4026-b598-d990608f829a

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          This paper has been withdrawn by the authors, because the motivation (Saturn's perihelion anomaly problem) has disappeared
          gr-qc astro-ph.EP

          Comments

          Comment on this article