Mathematics – Probability
Scientific paper
Jan 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998lpico.957q..20k&link_type=abstract
Origin of the Earth and Moon, Proceedings of the Conference held 1-3 December, 1998 in Monterey, California. LPI Contribution N
Mathematics
Probability
Many Body Problem, Moon, Simulation, Agglomeration, Gravitational Binding Energy, Lunar Evolution, Selenology, Roche Limit, Solar System Evolution, Accretion Disks
Scientific paper
We present the high-resolution N-body calculation of the lunar accretion from a circumterrestrial disk of debris generated by a giant impact on Earth. Our calculation is inspired by pioneering work, which was the first published N-body calculation of lunar accretion from an impact-generated disk. They modeled the disk by 1000 1500 particles, which were not enough to see the evolution of the spatial structure of the disk. By using the special-purpose computer for N-body problem HARP, we use 10,000 30,000 particles for the disk. The particle disk is modeled by the power-law surface density distribution and the power-law mass distribution. We use the 4th- order Hermite integrator for time integration. Mutual gravitational interactions among all particles are calculated by HARP. The normal and tangential components of the coefficient of restitution are 0.01-0.1 and 1, respectively. When two particles collide, we merge them if their rebound velocity is less than their surface escape velocity and the sum of their radii is smaller than 70% of their Hill radii, which corresponds to the fact that the two particles are outside their Roche limit. We also perform simulations without artificial accretion in which large bound particle aggregates are formed outside the Roche limit. The aggregates are often deformed or sometimes disrupted by Earth's tidal force. The results of our simulations suggest that the approximate treatment of accretion is generally valid. We follow the evolution of the disk for 1000 TK about 10 months, where TK is the Kepler period at the distance of the classical Roche limit. The typical outcome of the simulation is the formation of one large moon on a nearly circular orbit just outside the Roche limit. The result hardly depends on the initial condition of the disk as long as the disk is compact; in other words, most of the disk's mass exists inside the Roche limit. The evolution of f the dis is summarized as follows: (1) The disk shrinks through the mutual collisions of particles. (2) Gravitational instability takes place and particle clumps grow inside the Roche limit. 3) The clumps are elongated by the Kepler shear, which forms spiral arms with m=5-10 modes. (4) Particles are transferred to the outside of the Roche limit through the spiral arms. When a spiral arm is extended beyond the Roche Limit, the tip of the spiral arm is detached from the arm to form a small aggregate. The rapid accretion of these small aggregates form a lunar seed. (5) The seed grows by sweeping up particles transferred over the Roche Limit. (6) When the moon becomes large enough to gravitationally dominate the disk it shepherds the rest of the disk to the earth. The moon is almost completed by stage 5. Our result shows that the timescale up to stage 5 is about 100 TK (about a month). The efficiency of incorporation of disk material into a moon is 20-50% which increases the initial specific angular momentum of the disk. The results of the high-resolution simulations give a larger moon mass and probability of a single moon. The lunar mass is more consistent with the analytical argument.
Ida Shigeru
Kokubo Eiichiro
Makino Junichiro
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