The Tethered Moon

Abstract: We address the thermal history of the Earth after the Moon-forming impact, taking tidal heating and thermal blanketing by the atmosphere into account. The atmosphere sets an upper bound of ~100 W/m^2 on how quickly the Earth can cool. The liquid magma ocean cools over 2-10 Myrs, with longer times corresponding to high angular-momentum events. Tidal heating is focused mostly in mantle materials that are just beginning to freeze. The atmosphere's control over cooling sets up a negative feedback between viscosity-dependent tidal heating and temperature-dependent viscosity of the magma ocean. While the feedback holds, evolution of the Moon's orbit is limited by the modest radiative cooling rate of Earth's atmosphere. Orbital evolution is orders of magnitude slower than in conventional constant Q models, which promotes capture by resonances. The evection resonance is encountered early, when the Earth is molten. Capture by the evection resonance appears certain but unlikely to generate much eccentricity because it is encountered early when the Earth is molten and Q_Earth >> Q_Moon. Tidal dissipation in the Earth becomes more efficient (Q_Earth << Q_Moon) later when the Moon is between ~20 R_Earth and ~40 R_Earth. If lunar eccentricity grew great, this was when it did so, perhaps setting the table for some other process to leave its mark on the inclination of the Moon.