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

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 (sime 3.92 × 10^-7 Hz). We then evaluate the effects of these perturbations (up to the 6th harmonics) on the relative motions between each test mass couple, finding that they range between 3 mm and 10 pm for the 2nd and 6th harmonic, respectively. If we take the LISA sensitivity curve, as extrapolated down to 10^-6 Hz in Bender (2003 Class. Quantum Grav. 20 301-10), 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 additional crosscheck to the calibration of LISA, as extended to such low frequencies.