A Gravitomagnetic Effect on the Orbit of a Test Body due to the Earth's Variable Angular Momentum

TL;DR

This paper investigates how changes in Earth's angular momentum affect satellite orbits through gravitomagnetic effects, extending the classical Lense-Thirring effect, but finds the effects are too small for current detection methods.

Contribution

It introduces the theoretical analysis of orbital effects caused by Earth's variable angular momentum, expanding the understanding of gravitomagnetic influences beyond constant angular momentum scenarios.

Findings

Orbital effects due to Earth's changing angular momentum are extremely small.

Detection of such effects with current satellites like LAGEOS is not feasible.

The effect is analogous to inertial accelerations in accelerated frames.

Abstract

The well known general relativistic Lense-Thirring drag of the orbit of a test particle in the stationary field of a central slowly rotating body is generated, in the weak-field and slow-motion approximation of General Relativity, by a gravitomagnetic Lorentz-like acceleration in the equations of motion of the test particle. In it the gravitomagnetic field is due to the central body's angular momentum supposed to be constant. In the context of the gravitational analogue of the Larmor theorem, such acceleration looks like a Coriolis inertial term in an accelerated frame. In this paper the effect of the variation in time of the central body's angular momentum on the orbit of a test mass is considered. It can be shown that it is analogue to the inertial acceleration due to the time derivative of the angular velocity vector of an accelerated frame. The possibility of detecting such effect in the gravitational field of the Earth with LAGEOS-like satellites is investigated. It turns out that the orbital effects are far too small to be measured.