Mathematics
Scientific paper
Jan 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998lpico.957....4c&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
Earth-Moon System, Gravitational Instability, Planetary Evolution, Protoplanets, Solar System, Terrestrial Planets, Solar System Evolution, Lunar Evolution, Selenology, Many Body Problem, Mathematical Models, Monte Carlo Method, Simulation, Planetary Geology
Scientific paper
The leading paradigm for the origin of the terrestrial planets is the planetesimal hypothesis, which proposes that mutual collisions between objects in the protoplanetary disk resulted in the accretional growth of increasingly massive bodies, ending with the formation of planets in the 0.5 - 1.5-AU region. Two decades of analytical modeling and numerical simulation have revealed three general stages in the terrestrial accretion process: an early stage that commences with dust grains in a gas-rich nebula and ends with the formation of kilometer-sized "planetesimals"; an intermediate stage in which planetestimals experience runaway growth and form lunar sized "planetary embryos" in -105-106 yr; and a final stage dominated by mutual gravitational perturbations between planetary embryos, resulting in large, stochastic impact events and the formation of the final terrestrial planets after -108 yr. The prediction of a final impact-dominated phase coincides nicely with observed features in our solar system that are believed to be the result of giant impact events, including the Earth-Moon system. The first stage of plnetesimals is perhaps still the least understood phase of planetary accretion. Early models suggested that gravitational instability played a dominant role, while recentwork has suggested that low-velocity collisions and nongravitational sticking mechanisms may be required. Geochemical evidence suggest there was widespread melting and differentiation of planetesimals in the terrestrial region by the ned of this stage, perhaps a result of some event associated with solar activity. The intermediat stage opf collisional growth of roughly lunar sized embryos has been extensively studied using statistical methods. Recent work has modeled the accretional evolution of initially kilometer-sized bodies throughout the entire terrestrial region. Results from this work suggest that a few tens of planetary embryos with masses <1026 g (a lunar mass = 7.35 X 10 23 g) form after about a million years and contain nearly all of the total mass in the system. The final stage of terrestrial planet formation thus likely commences with a few tens of lunar-sized bodies on fairly circular orbits,which must then experience mutual pertubations and collisions to yield the final planets. Until recently, modeling of this stage had been limited to staitstical methods, as the timescales involved preculdued simulation using direct n-body orbit integrations. Multiple works by Wetherill using a Monte Carlo approach found on average about one impact between a body of nearly Earth size and an impactor with at least a Mars mas per simulation. This is the approximate type of impact tha tappears to be required to yield the Earth-moon system in the giant impact scenario. Estimates of the thermal effects of accretion suggest that melting and differentiation of bodies due to impact heating would have occurred by the time bodies were Mars sized (or 10% of Earth's mass.)
Agnor Craig
Canup Robin M.
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