Lunar Obliquity History Revisited

In preparation for a LRO (Lunar Reconnaissance Orbiter) related study of possible lunar polar volatiles, we re- examined the lunar orbital and rotational history, with primary focus on the obliquity history of the Moon. Though broad models have been made of lunar obliquity, a cohesive obliquity history was not found. We report on a new model of lunar obliquity including secular changes in inclination of the lunar orbit, tidal dissipation, lunar moments of inertia, and details for periods outside of the stable configurations known as Cassini states. For planets, the obliquity, or angle between the spin and orbit poles, is the dominant control on incident solar radiation. For planetary satellites, the radiation pattern can be more complex, as it depends on the mutual inclinations of three poles; the satellite spin and orbit poles, and the planetary heliocentric orbit pole. Presently, the lunar spin pole and orbit pole co-precess about the ecliptic pole, in a stable situation known as a Cassini state. As a result, permanently shadowed regions near the poles are expected to exist and act as cold traps, retaining water or other volatiles delivered to the surface by comets, solar wind, or via outgassing of the lunar interior. However, tidally driven secular changes in the lunar semimajor axis cause changes in precession rates of the spin and orbit poles, and thereby alter or destabilize the Cassini states. Only one prograde Cassini state exists at present (state 2). In the standard Cassini state model of Ward [1975], two other such states would have existed in the past (states 1 and 4) with the Moon starting in the low obliquity state 1, and remaining there until states 1 and 4 merged and disappear, at roughly half the present Earth-Moon distance. At that point, the Moon transitioned into the currently occupied state 2, and briefly attained very high obliquity values during the transition, and then stayed in state 2 until the present. If correct, this model implies that the transition from state 1 to state 2 is the most important event in the histories of lunar obliquity and polar volatiles, as it separates two periods in which current lunar cold traps could have existed with a period of high polar insolation which could have mobilized volatiles into space or to greater depths in the lunar near surface. If incorrect, lunar cold traps may prove only a very recent phenomenon. By including secular orbit changes, our model should help determine if this Cassini state stability really dominated in the past and allow detailed examination of extra-Cassini state periods.