The Lunar Fossil Figure in a Cassini State

The present ellipsoidal figure of the Moon requires a deformation that is significantly larger than the hydrostatic deformation in response to the present rotational and tidal potentials. This has long been explained as due to a fossil rotational and tidal deformation from a time when the Moon was closer to Earth. Previous studies constraining the orbital parameters at the time the fossil deformation was established find that high orbit eccentricities (e ≳ 0.2) are required at this ancient time, which is difficult to reconcile with the freezing of a fossil figure owing to the expected large tidal heating. We extend previous fossil deformation studies in several ways. First, we consider the effect of removing South Pole−Aitken (SPA) contributions from the present observed deformation using a nonaxially symmetric SPA model. Second, we use the assumption of an equilibrium Cassini state as an additional constraint, which allows us to consider the fossil deformation due to nonzero obliquity self-consistently. A fossil deformation established during Cassini state 1, 2, or 4 is consistent with the SPA-corrected present deformation. However, a fossil deformation established during Cassini state 2 or 4 requires large obliquity and orbit eccentricity (ϵ ∼ 68° and e ∼ 0.65), which are difficult to reconcile with the corresponding strong tidal heating. The most likely explanation is a fossil deformation established during Cassini state 1, with a small obliquity (ϵ ∼ −0.2°) and an orbit eccentricity range that includes zero eccentricity (0 ≤ e ≲ 0.3).

Cassini state of Galilean Moons: Influence of a subsurface ocean

<p>Large moons such as the Galilean satellites are thought to be in an equilibrium rotation state, called a Cassini state (Peale, 1969). This state is characterized by a synchronous rotation and a precession rate of the rotation axis that is equal to the precession rate of the normal to its orbit. It also implies that the spin axis, the normal to the orbit and the normal to the Laplace plane are coplanar with a (nearly) constant obliquity.</p><p>For rigid bodies, up to 4 possible Cassini states exist, but not all of them are stable. It is generally assumed that the Galilean satellites are in Cassini State I for which the obliquity is close to zero (see e.g. Baland et al. 2012). However, it is also theoretically possible that these satellites occupy or occupied another Cassini state.</p><p>We here investigate how the interior structure, and in particular the presence of a subsurface ocean, influences the existence and stability of the different possible Cassini states.</p><p><em>References :</em></p><p>Baland, R.M., Yseboodt, M. and Van Hoolst, T. (2012). Obliquity of the Galilean satellites: The influence of a global internal liquid layer. Icarus 220, 435-448.</p><p>Peale, S. (1969). Generalized Cassini’s laws. Astron. J. 74 (3), 483-489.</p>