Mercury's Love number h2: Expected error range throughout the BepiColombo mission

Introduction: Mercury, the innermost planet in the Solar System, remains an enigma due to significant gaps in our understanding of its internal structure. Recent advancements in planetary science have highlighted the potential of tidal Love numbers, specifically k2 and h2, to provide critical insights into the size of Mercury's inner core [1]. The Love number k2 represents a gravitational parameter, while h2 characterizes the radial deformation of the planet's surface. The determination of h2 can be achieved through techniques such as laser altimetry. The upcoming BepiColombo mission, set to arrive at Mercury in late 2026 [2], will enhance our understanding of Mercury's interior. A key instrument aboard BepiColombo, the Laser Altimeter (BELA), will enable the mapping of time-dependent surface elevations, providing crucial data for calculating h2 [3,4].

This study simulates BepiColombo's measurements using an orbit, observation, and tides model [5,6,7] to examine how the uncertainty in h2 decreases over the observation period. The BepiColombo Mercury Planetary Orbiter (MPO) offers significantly better coverage of Mercury's tidal potential compared to the MESSENGER mission [8,9], suggesting that the BepiColombo mission will yield more precise measurements of the h2 parameter. However, the simulation kernels used in this study are based on outdated mission parameters due to the revised arrival schedule of BepiColombo. To ensure the accuracy and relevance of our findings, we plan to update the simulations with the most recent kernel data.

To further explore the potential of the BepiColombo mission in constraining Mercury's internal structure, we will employ a simulation-based approach using planning kernels provided by the European Space Agency (ESA). Our model will simulate observations of Mercury's surface topography, incorporating tidal signals to model the planet's response to external gravitational forces. Additionally, observational errors and potentially different rotation states of Mercury will be introduced to reflect the expected noise levels from the BELA laser altimeter. These simulated observations will be used to calculate the Love number h2 and its associated uncertainty for different observation durations. This will allow us to assess how the mission's length influences the precision of the h2 measurement.

Acknowledgments: This work is supported by DLR under grant 50QW2301. PDS data used in this work: Neumann G. (2016), urn:nasa:pds:mess_mla_calibrated::1.0, 10.17189

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