Prospects for measuring Mercury’s tidal Love numberh₂with the BepiColombo Laser Altimeter

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.

Geodesy, Geophysics and Fundamental Physics Investigations of the BepiColombo Mission

“…For detection of the reflected laser pulses an APD (Avalanche Photo Diode) is used. Details of the instrument design can be found in Thomas et al (this issue) and in Thomas et al (2019).…”

“…Mercury's spin rate, obliquity, as well as amplitude and phase of the physical librations will be adjusted by using techniques that were developed for the MESSENGER mission (Stark et al 2015). Time-varying perturbations will also be estimated, including a key objective as the tidal Love number h 2 that informs on the deformation of the planet due to tides raised by the strong gravity field of the Sun (Steinbrugge et al 2018;Thor et al 2020).…”

“…To accurately determine the Love number h 2 , BELA will probably have to collect data over two years. Because of orbital and operational constraints, an extended one-year mission will enable spatial and temporal distributions of the BELA data that are well-suited to detect the surface tides (Steinbrügge et al 2018;Thor et al 2020). Altimetric measurements collected over intersecting ground-tracks at different tidal phases (i.e., crossovers) will be processed to precisely determine the tidal radial deformation.…”

“…4 Maximum tidal amplitudes (peak-to-peak) on Mercury's surface over one tidal cycle of 89 days, i.e., one revolution around the Sun. Here a typical Love number h 2 = 0.85 is assumed data by using cubic B-splines to model the local static topography for a measurement point (Koch et al 2010;Thor et al 2020). Thor et al (2020) show that the processing of the BELA measurements through this novel technique will yield an h 2 accuracy of 0.012, which may be subject to uncertainties in periodic misalignment behavior of the instrument.…”

Gravity, Geodesy and Fundamental Physics with BepiColombo’s MORE Investigation

“…Furthermore, the precise orbit determination of the MPO through the analysis of MORE data will greatly help the determination of the Love number h 2 , which measures the physical displacement of the planetary surface. Thor et al (2020) indicate that h 2 may be determined with a formal uncertainty of 0.012 by using BELA laser altimetric measurements that are opportunely processed with a refined orbit reconstruction. A combined knowledge of the Love numbers k 2 and h 2 will result in outstanding refinements of the interior modeling (Steinbrügge et al 2018) and composition (Van Hoolst and Jacobs 2003).…”