Abstract
Context.The Love numberh2describes the radial tidal displacements of Mercury’s surface and allows constraints to be set on the inner core size when combined with the potential Love numberk2. Knowledge of Mercury’s inner core size is fundamental to gaining insights into the planet’s thermal evolution and dynamo working principle. The BepiColombo Laser Altimeter (BELA) is currently cruising to Mercury as part of the BepiColombo mission and once it is in orbit around Mercury, it will acquire precise measurements of the planet’s surface topography, potentially including variability that is due to tidal deformation.Aims.We use synthetic measurements acquired using BELA to assess how accurately Mercury’s tidal Love numberh2can be determined by laser altimetry.Methods.We generated realistic, synthetic BELA measurements, including instrument performance, orbit determination, as well as uncertainties in spacecraft attitude and Mercury’s libration. We then retrieved Mercury’sh2and global topography from the synthetic data through a joint inversion.Results.Our results suggest thath2can be determined with an absolute accuracy of ± 0.012, enabling a determination of Mercury’s inner core size to ± 150 km given the inner core is sufficiently large (>800 km). We also show that the uncertainty ofh2depends strongly on the assumed scaling behavior of the topography at small scales and on the periodic misalignment of the instrument.
Highlights
Knowledge of Mercury’s interior is key to understanding its formation and thermal evolution
The BepiColombo Laser Altimeter (BELA) is currently cruising to Mercury as part of the BepiColombo mission and once it is in orbit around Mercury, it will acquire precise measurements of the planet’s surface topography, potentially including variability that is due to tidal deformation
At resolutions lower than 16 grid points per degree, there is a noticeable bias in the results that can be explained by our usage of the MDIS topography model up to degree L = 900
Summary
Knowledge of Mercury’s interior is key to understanding its formation and thermal evolution. Stark et al (2015a) used a MESSENGER-based digital elevation model (DEM) and MLA data to find a very similar result of φ0 = 38.9 ± 1.3 arcsec, equivalent to 460 ± 15 m at the equator While these two methods are based on surface observations and directly assess the libration of the solid outer shell, gravity allows for the measurement of the libration amplitude of the whole planet, with a larger uncertainty, of 2.9 arcsec (Genova et al 2019). The amplitude of this sinusoid is estimated as a global parameter for the full one-year data set (Iafolla et al 2007) This approach, followed in Imperi et al (2018), shall suppress the residual systematic accelerations to a level below 2 × 10−8 m s−2, which corresponds to a range rate signal well below the expected accuracy (Iess et al 2009). Residual nongravitational accelerations at these levels would not introduce A85, page 4 of 8
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