Stochastic behavior of a planet's orbits in the process of their accumulation

Astronomy and Astrophysics – Astronomy

Scientific paper

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Orbit Perturbation, Orbital Elements, Planetary Evolution, Planetary Orbits, Stochastic Processes, Fokker-Planck Equation, Gravitational Effects, Long Term Effects, Meteorite Collisions, Planetary Mass

Scientific paper

The evolution of the orbital elements of a growing planet during the accumulation process is considered. The planetary orbit undergoes perturbations as a result of random encounters and collisions with bodies of its accretion zone, as well as gravitational perturbations from an already formed massive planet (e.g., Jupiter). A Fokker-Planck equation describing the behavior of the distribution function of the growing planet's orbital elements is derived and solved. Present-day mean values of the eccentricities and inclinations of the orbits of the terrestrial planets are consistent with their accumulation at the final stage from a swarm of bodies with a mean mass of 0.01 solar mass and mean orbital eccentricities and inclinations of about 0.2.

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