Two problems pertaining to the dynamics of the origin of the moon, and its subsequent orbital evolution

Two problems are studied, both of which are related to the orbital history of the moon. The first problem deals with the accretional capture of the moon by the earth. It is assumed that originally the moon was in an independent helocentric orbit near earth's. It is further assumed that during a time of close approach the earth ws in the final stage of planetary growth where the remaining debris in earth's neighborhood was being accreted onto it. The equations of motion were integrated numerically to indicate that during a close two-body interaction, capture could occur if the mass of the central body (the earth) were increasing. The eccentricity of the moon's initial heliocentric orbit, its separation from earth at perihelion, and the time scale of accretion were varied. It was found that, within the framework of a two-body problem, a significant window for capture exists if a large portion of the earth is accreted in less than 100 years. It was also found that accretional capture is favored by both rapid accretion rates and an eccentric heliocentric lunar orbit. The second, and major, problem deals with the orbital evolution of a dumbbell shaped satellite with linear flexibility and damping in order to model the orbital effects of tides raised on the moon. The motion of this satellite will be described, approximately, by an ellipse as in the classic two-body problem. The perturbing effects of the satellite's shape, energy storage, and dissipation will cause small deviations from the elliptical path as well as causing the orbital elements which describe the ellipse to slowly change in time. It was found that an initial eccentric orbit will evolve into a slightly smaller, circular one with the satellite locked in synchronous rotation