II. Early history of the Moon - Dynamical capture of the Moon by the Earth

Abstract

The process of extracting the Moon from the Earth through some mechanism of rotational instability, and one that can also set it into orbital motion round the Earth, has nowadays come to be widely recognized as almost certainly dynamically impossible. Accordingly ideas have turned towards the notion that the Moon originated as a separate planet and was later captured by the Earth. It is reasonable to conjecture beforehand that this could happen in a three-body system consisting of the Sun, Earth, and Moon, but nevertheless it is of interest and importance to establish that such a capture is possible within the laws of dynamics, and moreover we should like to have some numerical indications of the initial dimensions that the lunar orbit would have on the basis of such an origin. Dissipative action may well be operative upon the planetary orbits to a minute extent, and there may have been eras in the history of the solar system when such dissipation was greater than average, but it seems certain that the main geometrical features of the process of capture of a satellite must in the final stages be governed purely by dynamical forces arising only from the mutual attractions of the bodies. Thus the first stage towards demonstrating the possibility of capture will be to study motions under purely conservative dynamical forces. Considerations of a phase-space or ergodic nature suggest that if the moon were captured in such a way it would eventually escape again, but we cannot on such a basis form any notion of the period of time for which the body might remain a satellite before escaping again. Actual numerical instances are needed to determine this.