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**Session 29 - Planets, Asteroids and Comets.**

*Oral session, Monday, June 08*

*De Anza/Mesa, *

## [29.02] Resonance Lock and Planetary Dynamics

*N. Haghighipour (U. Missouri-Columbia)*
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**