Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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 coecients, 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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