โ Scribed by J.E. Chambers
No coin nor oath required. For personal study only.
The results of 16 new 3D N-body simulations of the final stage of the formation of the terrestrial planets are presented. These Nbody integrations begin with 150-160 lunar-to-Mars size planetary embryos, with semi-major axes 0.3 < a < 2.0 AU, and include perturbations from Jupiter and Saturn. Two initial mass distributions are examined: approximately uniform masses, and a bimodal distribution with a few large and many small bodies. In most of the integrations, systems of three or four terrestrial planets form within about 200 million years. These planets have orbital separations similar to the terrestrial planets, and the largest body contains 1/3-2/3 of the surviving mass. The final planets typically have larger eccentricities, e, and inclinations, i than the time-averaged values for Earth and Venus. However, the values of e and i are lower than in earlier N-body integrations which started with fewer embryos. The spin axes of the planets have approximately random orientations, unlike the terrestrial planets, and the high degree of mass concentration in the region occupied by Earth and Venus is not reproduced in any of the simulations. The principal effect of using an initially bimodal mass distribution is to increase the final number of planets. Each simulation ends with an object that is an approximate analogue of Earth in terms of mass and heliocentric distance. These Earth analogues reach 50% (90%) of their final mass with a median time of 20 (50) million years, and they typically accrete some material from all portions of the disk.
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