Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

TL;DR

This paper analytically investigates how ultra-low frequency monochromatic gravitational waves affect the long-term orbital parameters of a two-body system, revealing specific non-secular variations that could help detect such waves.

Contribution

It provides a general analytical framework for understanding orbital perturbations caused by ultra-low frequency gravitational waves without assuming wave direction or orbital configuration.

Findings

Semi-major axis remains unchanged.

Eccentricity, inclination, and orbital angles experience long-term variations.

Results may help constrain ultra-low frequency gravitational waves.

Abstract

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency is much smaller than the particle's orbital one. We make neither a priori assumptions about the direction of the wavevector nor on the orbital geometry of the planet. We find that, while the semi-major axis is left unaffected, the eccentricity, the inclination, the longitude of the ascending node, the longitude of pericenter and the mean anomaly undergo non-vanishing long-term changes. They are not secular trends because of the slow modulation introduced by the tidal matrix coefficients and by the orbital elements themselves. They could be useful to indepenedently constrain the ultra-low frequency waves which may have been indirectly detected in the BICEP2 experiment. Our calculation holds, in general, for any gravitationally bound two-body system whose characteristic frequency is much larger than the frequency of the external wave. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.