Perturbations of the orbital elements due to the magnetic-like part of the field of a plane gravitational wave

TL;DR

This paper investigates how the magnetic-like component of a gravitational wave affects the orbital elements of planets, revealing that these effects are significantly smaller than the electric-like effects.

Contribution

It introduces the analysis of the gravito-magnetic force on orbital elements, which was previously overlooked in studies of gravitational wave effects.

Findings

Gravito-magnetic effects depend on particle velocity.

These effects are much smaller than gravito-electric effects.

Approximate results are obtained for orbital eccentricities.

Abstract

We focus on the secular changes of the orbital elements of a planet in the solar system, determined by the magnetic-like part of a gravitational wave field. Using Fermi coordinates we show that the total force acting on a test particle is made of two contributions: a gravito-electric one and a gravito-magnetic one. While the electric-like force has been thoroughly discussed in the past, the effect of the gravito-magnetic force, which depends on the velocity of the test particle, has not been considered yet. We obtain approximated results to some orders in the orbital eccentricity and show that these effects are much smaller than the corresponding gravito-electric ones.