Modulation of LISA free-fall orbits due to the Earth-Moon system

TL;DR

This paper analyzes how the Earth-Moon system's gravitational effects influence LISA's free-fall test masses, identifying resonances and perturbations that could serve as calibration signals for low-frequency gravitational wave detection.

Contribution

It provides a detailed calculation of Earth-Moon gravitational perturbations on LISA test masses and explores their potential use for calibration at very low frequencies.

Findings

Resonance at 1 yr^-1 frequency affects test masses.

Perturbations range from 3mm to 10pm across harmonics.

Some harmonics are detectable in LISA's Doppler data.

Abstract

We calculate the effect of the Earth-Moon (EM) system on the free-fall motion of LISA test masses. We show that the periodic gravitational pulling of the EM system induces a resonance with fundamental frequency 1 yr^-1 and a series of periodic perturbations with frequencies equal to integer harmonics of the synodic month (9.92 10^-7 Hz). We then evaluate the effects of these perturbations (up to the 6th harmonics) on the relative motions between each test masses couple, finding that they range between 3mm and 10pm for the 2nd and 6th harmonic, respectively. If we take the LISA sensitivity curve, as extrapolated down to 10^-6 Hz, we obtain that a few harmonics of the EM system can be detected in the Doppler data collected by the LISA space mission. This suggests that the EM system gravitational near field could provide an absolute calibration for the LISA sensitivity at very low frequencies.