On the figure of the planet Mercury

Abstract

The figure of Mercury is estimated in terms of an isostatic form of equilibrium which tends to be controlled by the situation near perihelion passage at the 3∶2 resonance spin rate. The ratios of the principal moments of inertia for Mercury are: (1)(C−A)/C≥7×10−5; (2)(C−B)/C≥5×10−5 and (3)(B−A)/C≥2×10−5. The thermal effect on Mercury's figure during solidification forces Mercury's rotation to be trapped in the 3∶2 resonance lock as its spin rate is being slowed by tidal effects. It is shown that the process of trapping of Mercury has been naturally affected by the instantaneous solidification of Mercury into a shape with two thermal bulges, and that the two permanent thermal bulges stabilize the planet's rotation.