Effects in the Anomalistic Period of Celestial Bodies due to a Logarithmic Correction to the Newtonian Gravitational Potential

TL;DR

This paper investigates how a logarithmic correction to Newtonian gravity affects celestial bodies' orbital precession, providing equations and numerical estimates for Mercury, pulsar companions, and Earth satellites.

Contribution

It introduces a method to quantify the impact of logarithmic gravitational corrections on orbital dynamics, extending previous models.

Findings

Logarithmic correction causes measurable apsidal motion in celestial orbits.

Numerical estimates show significant effects for Mercury and pulsar companions.

Results for Earth satellites are less reliable due to practical limitations.

Abstract

We study the motion of a secondary celestial body under the influence of the logarithmic corrected gravitational force of a primary one. This kind of correction was introduced by Fabris et al. (2009). We derive two equations to compute the rate of change of the periastron w.r.t. the eccentric anomaly and its total variation over one revolution, In a kinematical sense, this influence produces an apsidal motion. We perform numerical estimations for Mercury and for the companion star of the pulsar PSR 1913+16. We also consider the case of the artificial Earth satellite GRACE-A, but the results present a low degree of reliability from a practical standpoint