Making the Terrestrial Planets: N-Body Integrations of Planetary Embryos in Three Dimensions

Details Making the Terrestrial Planets: N-Body Integrations of Planetary Embryos in Three Dimensions Making the Terrestrial Planets: N-Body Integrations of Planetary Embryos in Three Dimensions

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998icar..136..304c&link_type=abstract

Icarus, Volume 136, Issue 2, pp. 304-327.

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183

Scientific paper

We simulate the late stages of terrestrial-planet formation using N-body integrations, in three dimensions, of disks of up to 56 initially isolated, nearly coplanar planetary embryos, plus Jupiter and Saturn. Gravitational perturbations between embryos increase their eccentricities, e, until their orbits become crossing, allowing collisions to occur. Further interactions produce large-amplitude oscillations in e and the inclination, i, with periods of ~10^5 years. These oscillations are caused by secular resonances 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, but accretion proceeds by orderly growth. The simulations typically produce two large planets interior to 2 AU, whose time-averaged e and i are significantly larger than Earth and Venus. The accretion rate falls off rapidly with heliocentric distance, and embryos in the ``Mars zone'' (1.2 < a < 2 AU) are usually scattered inward and accreted by ``Earth'' or ``Venus,'' or scattered outward and removed by resonances, before they can accrete one another. The asteroid belt (a > 2 AU) is efficiently cleared as objects scatter one another into resonances, where they are lost via encounters with Jupiter or collisions with the Sun, leaving, at most, one surviving object. Accretional evolution is complete after 3 x 10^8 years in all simulations that include Jupiter and Saturn. The number and spacing of the final planets, in our simulations, is determined by the embryos' eccentricities, and the amplitude of secular oscillations in e, prior to the last few collision events.

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