A retrodictive theory of the origin of the Moon: a secondary circumterrestrial disk redistributed by the retrograde flyby of a rocky planet

Michel DEBAILLEUL 

The Moon is a datum, and the question is retrodictive: which physical pathways lead to it without a giant impact? The pathway examined starts from a young, hot proto-Earth, soft but never liquid, flattened and inflated by a 6 h rotation, surrounded by a disk of material that has not yet formed a satellite.

A second rocky planet, planet B, passes close to the Earth against its rotation, without touching it and without giving it any material: it acts by gravity alone. It reworks the disk (about 47 % stays bound to the Earth, against 14 % for a flyby in the sense of the rotation), tilts the Earth's axis and carries away some of the angular momentum of its rotation.

The bound material assembles into a body of about one lunar mass in every realization computed; it is kept in four realizations out of ten, when its orbit settles beyond the corotation radius, and tides carry it to the present lunar distance in 4.5 billion years. Since planet B supplies no material, the Moon is made of terrestrial material, and the Earth-Moon isotopic identity (O, Ti, Cr, 182W) is expected from the outset. The bound system holds 0.21 L_EM more angular momentum than the present Earth-Moon pair. Braking by planet B, the solar tide and the evection resonance, computed together on a single trajectory, close the budget at +/-0.05 L_EM in about a quarter to a third of the trajectories explored, and at +/-0.08 L_EM in about two fifths to two thirds, under two stated conditions: a weak early terrestrial tide and a slow contraction of the proto-Earth.

These shares describe the parameter grid, not a probability. The appendices give a three-body check of the evection model, the duration of capture in the resonance, the sensitivity of the budget closure, and collision speeds and merging thresholds in the assembly phase. The results are necessary conditions or families of solutions, not facts; the limits are stated section by section.