Preprint Article Version 1 This version is not peer-reviewed

Effective Apsidal Precession in Oblate Coordinates

Version 1 : Received: 8 November 2018 / Approved: 12 November 2018 / Online: 12 November 2018 (04:20:50 CET)

How to cite: Capistrano, A.J.S.; Seidel, P.T.Z..; Cabral, L.A.. Effective Apsidal Precession in Oblate Coordinates. Preprints 2018, 2018110257 (doi: 10.20944/preprints201811.0257.v1). Capistrano, A.J.S.; Seidel, P.T.Z..; Cabral, L.A.. Effective Apsidal Precession in Oblate Coordinates. Preprints 2018, 2018110257 (doi: 10.20944/preprints201811.0257.v1).

Abstract

We use oblate coordinates to study its resulting orbit equations. Their related solutions of Einstein's vacuum equations can be written as a linear combination of Legendre polynomials of positive de nite integers $l$. Starting from solutions of the zeroth order $l=0$ in a nearly newtonian regime, we obtain a non-trivial formula favoring both retrograde and advanced solutions for the apsidal precession depending on parameters related to the metric coecients, particularly applied to the apsidal precessions of Mercury and asteroids (Icarus and 2 Pallas). As a realization of the equivalence problem in general Relativity, a comparison is made with the resulting perihelion shift produced by Weyl cylindric coordinates and the Schwarzschild solution analyzing how diff erent geometries of space-time influence on solutions in astrophysical phenomena.

Subject Areas

perihelion; gravity

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