Computer Science
Scientific paper
Jan 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998lpico.957...26m&link_type=abstract
Origin of the Earth and Moon, Proceedings of the Conference held 1-3 December, 1998 in Monterey, California. LPI Contribution N
Computer Science
Angular Momentum, Earth-Moon System, Mass Ratios, Moon, Planetary Nebulae, Protoplanets, Lunar Evolution, Planetary Mass, Planetary Orbits, Planetary Evolution
Scientific paper
Fundamental dynamical constraints for the origin of the Moon are the large mass ratio of the Moon to the Earth (1/80) and the large angular momentum of the Earth-Moon system. The large angular momentum has been explained only by the giant impact model. Ohtsuki and Ida, however, showed that planetary spin angular momentum supplied from planetesimals with gaps around planetary orbits (wherein random velocity is much lower than the escape velocity of the planet) is comparable to the Earth-Moon system. And the mass ratio of the Moon is too large to be explained by the giant impact model. From these results, we investigate the coaccretion process of a planet-satellite system under the swarm of planetesimals with some specific random velocity dispersion to clarify the condition in which the satellite embryos could have grown as large as the present Moon. We examine the evolution of the mass ratio of the satellite relative to the planet and the semimajor axis of the satellite by evaluating the planetesimal accretion rate of mass and geocentric orbital angular momentum to the satellite using the three-body numerical simulation under the Hill coordinates. The mass accretion rate of the satellite is enhanced by gravitational focusing of the planet. The mass ratio of the small satellite increases with growth while the mass ratio of the large satellite decreases. This is because larger cross sections relative to their mass ratio. Accretional torque drives the satellite to spiral into the planet, but tidal torque prevents it if the planetary spin is fast enough. As result, we find there exists a stable equilibrium point in the semimajor axis vs. mass-ratio plane. When the relative strength of the tidal torque becomes weaker, the equilibrium point moves to higher mass ratio and lower semimajor axis. It is difficult for the mass ratio of the equilibrium point applied standard value for the parameters to exceed the mass ratio of the Moon in the circumstances shown by Ohtsuki and Ida, in which the random velocity of accreted planetesimals is lower. If the product of quality factor relative to that of the present Earth and column density of planetesimals relative to the minimum -mass model of solar nebula are about 102 times larger it is possible to exceed the mass ratio of the equilibrium point always exceeds the mass ratio of the Moon while the angular momentum supplied form such planetesimals is nearly zero. If the planet satellite system with the large angular momentum is formed by the giant impact in the middle of the planetary accretion, the satellite can grow as large as the Moon.
Morishima Ryuji
Watamabe S.
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