Viscoelastic Relaxation within the Moon and the Phase Lag of its Cassini State

The Cassini state of the Moon requires that the lunar orbit normal and the lunar figure axis remain co-planar with the ecliptic normal. However, Lunar Laser Ranging (LLR) observations conducted in the decades following the Apollo missions unequivocally demonstrate the existence of a small 0.26 arc-second phase lag between the theoretical state (as described by Cassini) and the observed state of the Moon. This fact is suggestive of the existence of a dissipation mechanism within the Moon itself. The objective of this study is to explain this phase lag in terms of viscoelastic relaxation occurring in the solid regions of the Moon. This hypothesis is analyzed from the perspective of the angular momentum dynamics of the Moon and its constituent layers; a numerical model of the Moon is constructed, consisting of 5 homogeneous regions (a solid inner core, a fluid outer core, a low seismic velocity zone at the base of the mantle, a mantle and a crust). The model is constrained by the observed lunar mass, the moment of inertia of the solid Moon and other selenodetic and seismic observations. Viscoelastic deformations are incorporated into the angular momentum dynamics of the Moon in terms of compliances which depend on viscosity. The goal is to recreate the observed phase lag solely from the effects of viscoelasticity in the appropriate lunar regions. Our approach enables us to determine the viscosity of the low seismic velocity zone, or that of the inner core, which is compatible with the observed phase lag.