Three-dimensional Evolution of Mercury's Spin-orbit Resonance

WITHDRAWN AR IES ACKNOWLEDGEMENTS I would like to thank my two advisors, Professors Shapiro and Counselman, for their assistance in choosing and in carrying out this thesis research. I would also like to thank my wife, but this is impossible, as I am single. ABSTRACT Previous investigations of the evolution of the 3:2 spin-orbit resonance state of the planet Mercury have used simplified mathematical models in which the rotation axis of the planet has been assumed to remain perpendicular to the orbital plane. This thesis investigates the evolution of both the spin rate and the orientation of the rotation axis under tidal and permanent-asymmetry torques applied by the Sun. It is found that as the spin rate decreases, the inclination of the equatorial to the orbital plane increases. For initial inclinations of less than 500, the maximum inclination is never greater than 600, and is attained when the spin rate is about three times the orbital mean motion. The effect of such a substantial inclination upon the resonance capture probability depends upon the tidal-friction model. For a viscous friction model, the capture probability is less at each resonance for non-zero inclination than for the previously studied, zero inclination, case. However, for a model in which the tidal torque undergoes a discrete change with passage through the resonant rotation rate, the capture probability is less for non-zero inclination for the odd-half-integer resonances (3:2, 5:2, etc.), and larger for the even resonances (2:1, 3:1, etc.). Also, the capture probabilities for the discrete-change model are consistently larger (approximately one) than probabilities for the viscous model. If for this reason, the step model should be preferred to the viscous model, the question is raised: why was not Mercury trapped in the 2:1 or 3:1 resonance state?