Abstract
We use global data from the Lunar Orbiter Laser Altimeter (LOLA) to retrieve the lunar tidal Love number h_2 and find h_2 = 0.0387pm 0.0025. This result is in agreement with previous estimates from laser altimetry using crossover points of LOLA profiles. The Love numbers k_2 and h_2 are key constraints on planetary interior models. We further develop and apply a retrieval method based on a simultaneous inversion for the topography and the tidal signal benefiting from the large volume of LOLA data. By the application to the lunar tides, we also demonstrate the potential of the method for future altimetry experiments at other planetary bodies. The results of this study are very promising with respect to the determination of Mercury’s and Ganymede’s h_2 from future altimeter measurements.
Highlights
Geodetic measurements of a planetary body’s reaction to tidal forces, expressed by the tidal Love numbers k2 and h2, provide a key constraint on its interior
The lunar h2 has been determined by Lunar Laser Ranging (LLR, Williams et al 2013; Pavlov et al 2016; Viswanathan et al 2018 and by laser altimetry (Mazarico et al 2014), making the Moon the only planetary body other than Earth, for which measurements of both h2 and k2 exist (Fig. 1)
A single Lunar Orbiter Laser Altimeter (LOLA) observation of the topographic elevation consists of the static, time-invariant topography Tstat at that location, the radial displacement ur of the surface due to tides at time tk (Eq 9), and measurement and model errors, contained in the term ek: Tk = Tstat(θk, λk ) + ur(θk, λk, tk ) + ek . (10)
Summary
Geodetic measurements of a planetary body’s reaction to tidal forces, expressed by the tidal Love numbers k2 and h2, provide a key constraint on its interior. Measurements of k2 have contributed to the determination of the Moon’s core size (Williams et al 2014), the detection of a subsurface ocean on Titan (Iess et al 2012), and the rheological properties of Mercury’s mantle (Padovan et al 2014; Genova et al 2019). The lunar h2 has been determined by Lunar Laser Ranging (LLR, Williams et al 2013; Pavlov et al 2016; Viswanathan et al 2018 and by laser altimetry (Mazarico et al 2014), making the Moon the only planetary body other than Earth, for which measurements of both h2 and k2 exist (Fig. 1)
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