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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. https://doi.org/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. https://doi.org/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 different geometries of space-time influence on solutions in astrophysical phenomena.
Keywords
perihelion; gravity
Subject
Physical Sciences, Astronomy and Astrophysics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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