The thermal–orbital evolution of the Earth–Moon system with a subsurface magma ocean and fossil figure

Various theories have been proposed to explain the Moon's current inclined orbit. We test the viability of these theories by reconstructing the thermal–orbital history of the Moon. We build on past thermal–orbital models and incorporate the evolution of the lunar figure including a fossil figure component. Obliquity tidal heating in the lunar magma ocean would have produced rapid inclination damping, making it difficult for an early inclination to survive to the present-day. An early inclination is preserved only if the solid-body of the early Moon were less dissipative than at present. If instabilities at the Laplace plane transition were the source of the inclination, then the Moon had to recede slowly, which is consistent with previous findings of a weakly dissipative early Earth. If collisionless encounters with planetesimals up to 140 Myr after Moon formation excited the inclination, then the Moon had to migrate quickly to pass through the Cassini state transition at 33 Earth radii and reach a period of limited inclination damping. The fossil figure was likely established before 16 Earth radii to match the present-day degree-2 gravity field observations.