The Influence of a Fluid Core and a Solid Inner Core on the Cassini State of Mercury

Abstract

Mercury is expected to be in a Cassini state (Figure 1) whereby its orbit normal and spin-symmetry axis are both coplanar with, and precess about, the normal to the Laplace plane (Colombo, 1966; Peale, 1969, 2006). The orientation of the Laplace plane varies on long time scales, but its present-day orientation can be reconstructed from ephemerides data (Baland et al., 2017; Yseboodt & Margot, 2006). Likewise, the rate of precession is also not observed directly, but is reconstructed by ephemerides data. The latest estimate is a retrograde precession period of 325,513 years with an inclination angle of I = 8.5330° between the orbit and Laplace plane normals (Baland et al., 2017). Measurements of the obliquity ɛ m , defined as the angle of misalignment between the spin-symmetry axis and the orbit normal, have been obtained by different techniques, including ground-based radar observations (

Deriving Mercury Geodetic Parameters With Altimetric Crossovers From the Mercury Laser Altimeter (MLA)

“…Our solution puts Mercury in a precise Cassini state, as predicted by dynamical models (Peale, 1988), without any explicit constraints to place it in this state. While deviations from the Cassini state of the order of a few arc‐seconds are expected (e.g., due to the precession of perihelion or to tidal dissipation, see Baland et al., 2017), these are of the order of our error bars and significantly smaller than offsets presented by most previous solutions (also see, e.g., Dumberry, 2020). Compared to the gravity measurements provided by Genova et al.…”

“…Our solution puts Mercury in a precise Cassini state, as predicted by dynamical models (Peale, 1988), without any explicit constraints to place it in this state. While deviations from the Cassini state of the order of a few arc-seconds are expected (e.g., due to the precession of perihelion or to tidal dissipation, see Baland et al, 2017), these are of the order of our error bars and significantly smaller than offsets presented by most previous solutions (also see, e.g., Dumberry, 2020). Compared to the gravity measurements provided by Genova et al (2019) (also in agreement with a Cassini state), we get a higher obliquity ϵ = 2.031 ± 0.03 arcmin, consistent with a normalized polar moment of inertia C/MR 2 = 0.343 ± 0.006 (with C, M, and R the polar moment of inertia, mass, and radius of Mercury, respectively).…”

Evaluation of Recent Measurements of Mercury’s Moments of Inertia and Tides Using a Comprehensive Markov Chain Monte Carlo Method

“…This has already been suggested by Verma & Margot (2016), and the possibility is also raised by Bertone et al (2021). The existence of a solid inner core itself can also influence the Cassini state (Peale et al 2016;Baland et al 2017;Dumberry 2021), yet the effects may be small, below the current error levels. It is outside the scope of this analysis to try and resolve this discrepancy.…”

Core Eigenmodes and their Impact on the Earth’s Rotation

“…Also note that we have neglected in Equations ( 5) the external gravitational torque such as that from a star (planet) around which a planet (moon) orbits. While the influence of this torque on the internal modes for Earth is negligible, for bodies in synchronous rotation or with a rotation period approaching the orbital period, the free precession modes are altered by the external torque, e.g., Varadi et al (2005), Baland et al (2019), Dumberry (2021). Lastly, we have also neglected the influence of surface fluid layers such as oceans and the atmosphere.…”