  A restricted planar circular three-body system, consisting of the Sun and two
planets, is studied as a simple model for a planetary system. The mass of the
inner planet is considered to be larger and the system is assumed to be moving
in a uniform interplanetary medium with constant density. Numerical
integrations of this system indicate a resonance capture when the dynamical
friction of the interplanetary medium is taken into account. As a result of
this resonance trapping, the ratio of orbital periods of the two planets
becomes nearly commensurate and the eccentricity and semimajor axis of the
orbit of the outer planet and also its angular momentum and total energy become
constant. It appears from the numerical work that the resulting
commensurability and also the resonant values of the orbital elements of the
outer planet are essentially independent of the initial relative positions of
the two bodies. The results of numerical integrations of this system are
presented and the first-order partially averaged equations are studied in order
to elucidate the behavior of the system while captured in resonance.
