Prospects for measuring Mercury’s tidal Love number h₂ with the BepiColombo Laser Altimeter

¹ Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
e-mail: thor@mps.mpg.de
² Technische Universität Berlin, Institute of Geodesy and Geoinformation Science, Straße des 17, Juni 135, 10623 Berlin, Germany
³ DLR Institute of Planetary Research, Rutherfordstraße 2, 12489 Berlin, Germany
⁴ Department of Geophysics, Stanford University, 397 Panama Mall, Stanford, CA 94305, USA
⁵ Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Via Eudossiana, 18, 00184 Roma, RM, Italy

Received: 16 August 2019
Accepted: 13 December 2019

Abstract

Context. The Love number h₂ describes 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 number k₂. 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 number h₂ can 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’s h₂ and global topography from the synthetic data through a joint inversion.

Results. Our results suggest that h₂ can 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 of h₂ depends strongly on the assumed scaling behavior of the topography at small scales and on the periodic misalignment of the instrument.