Making the terrestrial planets: N-body integrations of planetary embryos in three dimensions

Ne simulate the late stages of terrestrial-planet formation using N-body in tegrations, in three dimensions, of disks of up to 56 initially isolated, n early coplanar planetary embryos, plus Jupiter and Saturn. Gravitational pe rturbations between embryos increase their eccentricities, e, until their o rbits become crossing, allowing collisions to occur. Further interactions p roduce large-amplitude oscillations in e and the inclination, i, with perio ds of similar to 10(5) years. These oscillations are caused by secular reso nances between embryos and prevent objects from becoming re-isolated during the simulations. The largest objects tend to maintain smaller e and i than low-mass bodies, suggesting some equipartition of random orbital energy, b ut accretion proceeds by orderly growth. The simulations typically produce two large planets interior to 2 AU, whose time-averaged e and i are signifi cantly larger than Earth and Venus. The accretion rate falls off rapidly wi th heliocentric distance, and embryos in the "Mars zone" (1.2 < a < 2 AU) a re usually scattered inward and accreted by "Earth" or "Venus," or scattere d outward and removed by resonances, before they can accrete one another. T he asteroid belt (a > 2 AU) is efficiently cleared as objects scatter one a nother into resonances, where they are lost via encounters with Jupiter or collisions with the Sun, leaving, at most, one surviving object. Accretiona l evolution is complete after 3 x 10(8) years in all simulations that inclu de Jupiter and Saturn. The number and spacing of the final planets, in our simulations, is determined by the embryos' eccentricities, and the amplitud e of secular oscillations in e, prior to the last few collision events. (C) 1998 Academic Press.