Mathematics
Scientific paper
May 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..24...83r&link_type=abstract
Celestial Mechanics, vol. 24, May 1981, p. 83-107.
Mathematics
5
Celestial Mechanics, Gravitational Effects, Ground State, Mathematical Models, Mercury (Planet), Orbital Resonances (Celestial Mechanics), Spin-Orbit Interactions, Conformal Mapping, Equations Of Motion, Motion Stability, Perturbation, Resonant Frequencies
Scientific paper
This paper forms a sequel to that by Murdock (1978), which examined the hypotheses of the model used to account for the fact that the spin period of Mercury is almost exactly 2/3 of the orbital period. Some of the problems left open in the earlier paper are resolved. It is noted that the model assumes that the spin axis is normal to the orbital plane and that the spin angle theta (the angle between a ray fixed in the planet and a ray fixed with respect to the stars, both lying in the orbit plane) satisfies a particular differential equation. It is shown that the results obtained for the averaged equations near an active resonance are valid for the original (unaveraged) system itself, that is, the particular differential equation. In addition, the behavior near a ground state is studied for certain cases. A small parameter approach to these equations is used; hence the resonant frequency or ground state frequency is fixed first and then it is determined how small epsilon (the small parameter in the original differential equation) must be for the theorems to apply.
Murdock James
Robinson Christian
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