Mercury's Cassini state from co-registration of MESSENGER laser profiles

Abstract

Like our Moon, Mercury is assumed to be driven by dissipative torques into an equilibrium Cassini state 1, where its spin axis, its orbit normal, and the Laplace pole remain coplanar during the precessional cycle. The orientation of Mercury’s spin axis has been determined independently based on observations from Earth-based radar (Margot et al., 2007, 2012), camera and/or laser altimeter (Stark et al., 2015; Bertone et al., 2021), and radio tracking (Mazarico et al., 2014; Verma and Margot, 2016; Genova et al., 2019; Konopliv et al., 2020). The obliquity, the separation angle between the spin axis and the orbital normal, is constrained to be approximately 2 arcmin and deviation of the spin axis from coplanarity is limited to a phase lag of around 10 arcsec.

If Mercury is indeed forced into an equilibrium Cassini state and the whole planet precesses as a rigid body (Dumberry, 2021), its obliquity can be used to infer its normalized polar moment of inertia which depends on Mercury’s radial mass distribution (e.g., Peale, 1981; Baland et al., 2017). In addition, a precise estimate of the angular offset of Mercury’s spin axis to the Cassini state can place a constraint on its tidal quality factor Q and thus on the bulk viscosity of its mantle (Baland et al., 2017; MacPherson and Dumberry, 2022).

In this study, we look into Mercury’s Cassini state by applying the co-registration techniques to the MESSENGER Mercury Laser Altimeter (MLA) profiles. First, we reprocess the profiles (Xiao et al., 2021) and self-register them to maximize their self-consistency by shifting the profiles in both lateral and radial directions (Xiao et al., 2022; Xiao et al., 2025). After that, we build a reference terrain model out of these self-registered profiles. Finally, we merge all original profiles and co-register them as a whole to the reference terrain model by solving for corrections to the mismodeling in the orientation angles. We have carried out some preliminary experiments at various zonal bands and with different a priori orientation angles (Figure 1). In these cases, the prime meridian angle is fixed and set to match our measured annual and long-period libratons (Xiao et al., this meeting). We can see that our estimates converge well and place Mercury within 2 arcsec (0.0006 degree) of the Cassini state although some yet-to-be-explained dependence on latitude can be observed.

We will further refine the proposed approach and carry out simulations using realistic synthetic profiles to validate our approach and quantify the uncertainty. Once the assessment of Mercury’s Cassini state is finalized, we will combine it with our estimated annual and long-term librations of Mercury (Xiao et al., this meeting), and its tidal Love number h2 (Xiao et al., 2025) to shed comprehensive insights into the planet’s interior structure and compositions (e.g., Dumberry and Rivoldini, 2015; Briaud et al., this meeting; Rivoldini et al., this meeting; Yseboodt et al., this meeting). This information can critically constrain the thermal evolution of Mercury and its magnetic dynamo.