Towards a Consistent Calculation of the Lunar Response to Gravitational Waves

Abstract

The recent increasing interest in detecting gravitational waves (GWs) by lunar seismic measurement urges us to have a clear understanding of the response of the moon to passing GWs. In this paper, we clarify the relationship between two seemly different response functions which have been derived previously using two different methods, one taking the field-theory approach and the other using the tidal force induced by GWs. We revisit their derivation and prove, by both analytical arguments and numerical calculations, that the two response functions are equivalent. Their apparent difference can be attributed to the choice of different coordinates. Using the correct response function, we calculate the sensitivities (to GWs) of several designed lunar seismometers, and find that the sensitivity curves between $10^{-3}$ and $0.1$ Hz are much flatter than the previous calculations based on normal-mode model. Our results will help clarifying the scientific objectives of lunar GW observation, as well as provide important constraints on the design of lunar GW detectors.

Accepted for publication in Physical Review D

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Cited by in corpus (6)

• The Lunar Gravitational-wave Antenna: Mission Studies and Science Case
• Modeling lunar response to gravitational waves using normal-mode approach and tidal forcing
• Constraining the stochastic gravitational wave background using the future lunar seismometers
• Probing intermediate-mass black hole binaries with the Lunar Gravitational-wave Antenna
• Identifying the Quadrupolar Nature of Gravitational Wave Background through Space-based Missions
• The new generation lunar gravitational wave detectors: sky map resolution and joint analysis