Origin of the Moon — Capture by gas drag of the Earth's primordial atmosphere

We propose a new scenario of the lunar origin, which is a natural extension of planetary formation processes studied so far by us in Kyoto. According to these studies, the Earth grew up in a gaseous solar nebula and, consequently, the sphere of its gravitational influence (i.e., the Hill sphere of the Earth) was filled by a gas forming a dense primordial atmosphere of the Earth. In the later stages, this atmosphere as well as the solar nebula was dissipated gradually, owing to strong activities of the early-Sun in a T Tauri-stage.In the present and the subsequent papers, we study a series of dynamical processes where a lowenergy (i.e., slightly unbound) planetisimal is trapped within the terrestrial Hill sphere, under the above-mentioned circumstances that the gas density of the primordial atmosphere is gradually decreasing. It is clear that two conditions must be satisfied for the lunar origin: first, an unbound planetesimal entering the Hill sphere have to dissipate its kinetic energy and come into a bound orbit before it escapes from the Hill sphere and, second, the bound planetisimal never falls onto the surface of the Earth.In this paper we study the first condition by calculating the oribital motion of a planetesimal in the Hill sphere, which is affected both by solar gravity and by atmospheric gas drag. The results show that a low-energy planetisimal with the lunar mass or less can be trapped in the Hill sphere with a high probability, if it enters the Hill sphere at stages before the atmospheric density is decreased to about 1/50 of the initial value.In the subsequent paper, the second condition will be studied and it will be shown that a tidal force, among other forces, is very important for a trapped planetesimal to avoid collision with the Earth and stay eternally in the Hill sphere as a satellite.