Models of evolutionary tracks of the planets

Statistics – Computation

Scientific paper

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Gas Giant Planets, Planetary Evolution, Protoplanets, Terrestrial Planets, Computational Astrophysics, Gas Dynamics, Natural Satellites, Planetary Mass, Planetary Nebulae

Scientific paper

A discontinuous model for the surface density or rock and ice in the protoplanetary nebula is derived, and improved differential equations models of evolutionary tracks of the planets showing accretion time intervals, masses, and relative velocities in the accretion bands of the planets. Accretion time intervals of Mercury, Venus and earth are about 30 million yr, and for Mars 300 million yr. Gas accretion starting at a core mass of ten earth masses yields formation intervals of Jupiter, Saturn, Uranus, and Neptune of 80 million, 30 million, 1.3 billion, and 1.8 billion yr, respectively. Uranus and Neptune can accrete only with a two and three times increased surface density of rock and ice of about 0.5 g/sq cm. Without gas accretion the cores of Jupiter and Saturn accrete during 200 million yr and 400 million yr, whereas the formation intervals of Uranus and Neptune increase insignificantly. Inward spiraling of small planetesimals due to gas drag at the planet's heliocentric distance is of order 1.2, 2.0, 6.3 and 9.8 AU for the accretion bands of Jupiter, Saturn, Uranus, and Neptune, respectively.

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