The Lens-Thirring effect in the anomalistic period of celestial bodies

TL;DR

This paper investigates the influence of gravitomagnetic effects, derived from general relativity, on the orbital periods of celestial bodies, providing equations and numerical estimates for various astronomical objects.

Contribution

It derives new equations to approximate the periastron time variation due to gravitomagnetic forces and applies them to multiple celestial bodies, including artificial satellites.

Findings

Gravitomagnetic effects cause 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

In the weak field and slow motion approximation, the general relativistic field equations are linearized, resembling those of the electromagnetic theory. In a way analogous to that of a moving charge generating a magnetic field, a mass energy current can produce a gravitomagnetic field. In this contribution, the motion of a secondary celestial body is studied under the influence of the gravitomagnetic force generated by a spherical primary. More specifically, two equations are derived to approximate the periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period). Kinematically, this influence results to an apsidal motion. The aforementioned quantities are numerically estimated for Mercury, the companion star of the pulsar PSR 1913 plus 16, the companion planet of the star HD 80606 and the artificial Earth satellite GRACE A. The case of the artificial Earth satellite GRACE A is also considered, but the results present a low degree of reliability from a practical standpoint.