Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth.

In the giant-impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however, the current lunar orbital inclination of five degrees requires a subsequent dynamical process that is still unclear. In addition, the giant-impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition. Here we show that tidal dissipation due to lunar obliquity was an important effect during the Moon's tidal evolution, and the lunar inclination in the past must have been very large, defying theoretical explanations. We present a tidal evolution model starting with the Moon in an equatorial orbit around an initially fast-spinning, high-obliquity Earth, which is a probable outcome of giant impacts. Using numerical modelling, we show that the solar perturbations on the Moon's orbit naturally induce a large lunar inclination and remove angular momentum from the Earth-Moon system. Our tidal evolution model supports recent high-angular-momentum, giant-impact scenarios to explain the Moon's isotopic composition and provides a new pathway to reach Earth's climatically favourable low obliquity.

Making the Moon from a fast-spinning Earth: a giant impact followed by resonant despinning.

A common origin for the Moon and Earth is required by their identical isotopic composition. However, simulations of the current giant impact hypothesis for Moon formation find that most lunar material originated from the impactor, which should have had a different isotopic signature. Previous Moon-formation studies assumed that the angular momentum after the impact was similar to that of the present day; however, Earth-mass planets are expected to have higher spin rates at the end of accretion. Here, we show that typical last giant impacts onto a fast-spinning proto-Earth can produce a Moon-forming disk derived primarily from Earth's mantle. Furthermore, we find that a faster-spinning early Earth-Moon system can lose angular momentum and reach the present state through an orbital resonance between the Sun and Moon.

Excitation of lunar eccentricity by planetary resonances.

The origin of the Moon's nonnegligible orbital eccentricity of 0.053 has no theoretical explanation. Lunar laser ranging indicates that tides on Earth are currently increasing the Moon's eccentricity. However, ocean tides were likely much weaker during the first billion years, allowing lunar tides to damp any primordial lunar eccentricity very early on. During the tidally driven expansion of its orbit, the Moon must have been affected by two substantial resonances related to Jupiter and Venus, passage through which may have generated today's lunar eccentricity.