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Session 29 - Planets, Asteroids and Comets.
Oral session, Monday, June 08
The results of a series of extensive numerical experiments as well as analytical arguments on the dynamics of a planetary system consisting of a star and two planets are presented. A planar circular restricted three- body system has been used to model this planetary system. The motion of the star has been neglected and the motions of the planets are affected by an interplanetary medium. This medium is freely rotating around the star and its inhomogeneity is neglected. It is assumed that after taking the effects of all resistive forces into account, the motion of the inner planet is uniformly circular so that we focus attention on the motion of the outer planet. The numerical integrations indicate a resonance capture which results in a constant ratio for the orbital periods of the two planets and also a nearly constant eccentricity , semi major axis and angular momentum for the orbital motion of the outer planet.
A newly developed averaging technique has been used to elucidate the results of the numerical integrations. By writing the equations of motion in terms of Delaunay variables and partially averaging them near the resonance, the equations of motion of the outer planet are reduced to a pendulum-like equation with external torques. The solutions to this equation indicate the existence of a nearly periodic solution whose frequency is related to the characteristics of the system such as the ratio of the masses of the planets and the density of the interplanetary medium. It will be shown how the orbital elements of the resonant orbit such as the eccentricity and the semi major axis will depend on the characteristics of the system. The application of these calculations to the problem of formation and evolution of the planetary systems will be discussed.
Program listing for Monday