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Stochastic Behaviour of Planetary Orbits During the Accumulation Process

Published online by Cambridge University Press:  12 April 2016

I.N. Ziglina  and
O.Yu. Schmidt
I.N. Ziglina
Affiliation:
Institute of Earth Physics, Russian Academy of Sciences, Moscow, Russia
O.Yu. Schmidt
Affiliation:
Institute of Earth Physics, Russian Academy of Sciences, Moscow, Russia

Abstract

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The evolution of orbital elements of a growing planet during the accumulation process is considered. The planetary orbit undergoes perturbations because of random encounters and collisions with bodies of its accretion zone and also because of gravitational interaction with an already formed massive planet (“Jupiter”). The mass and velocity distributions of the swarm bodies are assumed to be given time-dependent functions. The Fokker-Planck equation describing the behaviour of the distribution function of orbital elements of the growing planet is worked out and solved. The present mean values of the eccentricities and inclinations of orbits of the terrestrial planets can be explained in the case of their accumulation from a single swarm of bodies with mean mass ~ 10−2 M⊕ and with mean eccentricities and inclinations ~ 0.2.

Type
Part II Ergodic and Stochastic Motion
Information
International Astronomical Union Colloquium , Volume 132: Instability, Chaos and Predictability in Celestial Mechanics and Stellar Dynamics , 1993 , pp. 137 - 148
Copyright
Copyright © Nova Science Publishers 1993

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