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

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, 3.5 times more than 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. The isotopic correspondence. Since planet B supplies no material, the Moon is made of terrestrial material: the Earth–Moon isotopic identity (O, Ti, Cr, ¹⁸²W) and the depletions in V, Cr, Mn are expected from the outset, where the giant impact has to explain them after the fact. Angular momentum. The bound system holds 0.21 L_EM more than the present Earth–Moon pair. Braking by planet B, the solar tide and the evection resonance each remove only part of it; computed together on a single trajectory, they 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 conditions that the text states: a weak terrestrial tide early in the history, as befits a soft body, and a slow contraction of the proto-Earth. These percentages describe the parameter grid studied, 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. Relation to earlier records. In the earlier records listed under “Related works”, the flyby is described as prograde. In the present work the sense of the flyby is defined relative to the rotation of the Earth, and the flyby that keeps the disk bound to the Earth is the retrograde one (against the rotation): 18.5 % of the reservoir reaches the lunar window in the retrograde case against 4 % in the prograde case. These are the figures of the earlier records with the sense labels interchanged: the earlier records defined the sense of the flyby differently, whereas the present work defines it relative to the rotation of the Earth. The sense labels of the present work supersede those of the earlier records. The deposit contains the French and English versions (PDF), their LaTeX source and some figures.