Publication Date
7-6-1977
Abstract
Two planar, fixed-orbit models of the rotation of the planet Mercury are studied using the method of averaging. The first model includes only the solar torques on the planet's permanent asymmetry and on its solar tidal bulge. For this model, it is shown that the zero of the averaged tidal torque corresponds to an asymptotically stable periodic solution of the second kind which, for two tidal torque representations, is close to the asymptotically stable equilibrium point corresponding to an exact 3:2 spin-orbit resonance. This periodic solution restricts the possible initial rotation states of Mercury, and it may account for the currently observed rotation period of the planet. A conjecture that the current rotation state of Mercury is due to transfer from capture by the zero of the averaged tidal torque to 3:2 resonance capture with changes in the eccentricity of the planet's orbit is discussed. The second model of Mercury's rotation is a refinement of the first which includes the additional effects of core-mantle coupling. It is shown that a number of results which are valid for the first model are also valid for the refined model.
Degree Name
Mathematics
Level of Degree
Doctoral
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Walter Thomas Kyner
Second Committee Member
Richard Crenshaw Allen
Third Committee Member
Steven Arthur Pruess
Language
English
Document Type
Dissertation
Recommended Citation
Burns, Timothy John. "Nonlinear Resonance In Celestial Mechanics With Applications To The Rotation Of Mercury." (1977). https://digitalrepository.unm.edu/math_etds/221
