Quantum and Post-Newtonian Effects in the Anomalistic Period and the Mean Motion of Celestial Bodies

TL;DR

This paper investigates how quantum and relativistic corrections to gravity influence the orbital periods and mean motion of celestial bodies, providing equations and numerical analysis for specific satellites and planets.

Contribution

It derives new equations to approximate orbital period variations caused by quantum and post-Newtonian gravitational effects.

Findings

Quantum and relativistic effects cause measurable changes in orbital periods.

Numerical results demonstrate the significance of these corrections for specific celestial bodies.

The study offers a framework for analyzing gravitational effects beyond classical Newtonian theory.

Abstract

We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We study the effect of quantum and relativistic corrections to the gravitational potential of a primary body acting on the orbiting body. More specifically, two equations are derived to approximate the perigee/perihelion/periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period) under the influence of the quantum as well as post- Newtonian accelerations. Numerical results have been obtained for the artificial Earth satellite Molnya, Mercury, and, finally, the for the HW Vir c, planetary companion.