Prospect for Measuring Lunar Tidal Deformation and Displacement Love Numbers With Earth-Based Radar

Abstract

Lunar tidal deformation (LTD), characterized by the vertical (${{{\bm{h}}}_2}$) and horizontal (${{{\bm{l}}}_2}$) displacement Love numbers, is a key to deciphering the interior structure of the Moon. However, the small deformation amplitude of only up to 10 cm makes their measurements very challenging. In this article, we propose a novel method named Earth-based repeat-pass SAR interferometry (EBRP-InSAR) to measure the LTD and displacement Love numbers. We analyzed the potential and performance of EBRP-InSAR in detail based on the LTD model and existing planetary radar capabilities. The error budget and simulation results show that the relative measurement accuracy of LTD could be better than 2 mm. Furthermore, compared with lunar laser ranging (LLR) and lunar orbiter laser altimeter (LOLA), the two-pass EBRP-InSAR cannot only directly estimate ${{{\bm{h}}}_2}$ but also ${{{\bm{l}}}_2}$ with accuracies better than ${{\text{10}}^{ - 3}}$ and${{\text{10}}^{ - 4}}$, respectively, which is comparable to that of LLR and LOLA methods. In addition, through long-term time-series observations, it will be possible to assess the spatial inhomogeneity of LTD response to the forcing potential in the near side with time-series EBRP-InSAR. After spatial smoothing, a space variation as small as on the order of ${{\text{10}}^{ - 4}}$ and ${{\text{10}}^{ - 5}}$ in ${{{\bm{h}}}_2}$ and ${{{\bm{l}}}_2}$, respectively, can be distinguished on the lunar near side. As another measurement technology independent of LLR and LOLA, the EBRP-InSAR is expected to explain the difference between the observations from LLR and LOLA and the modeled lunar interior structure, and first estimate the lunar horizontal displacement Love number.

Keywords

• Earth-based radar
• interferometry
• Moon
• repeat-pass
• spatial and temporal baseline