Orbital motion in uniformly rotating second degree and order gravity fields.

摘要

This dissertation studies the orbital motion of a spacecraft about a rotating second degree and order gravity field, with its main application to orbital motion about uniformly rotating, irregular-shape asteroids. Such dynamical systems are non-integrable in general. Our goal is to understand how the orbital dynamics change as a function of the central body's rotation rate and mass distribution. To carry out this analysis we use three different approaches: averaging, resonance analysis, and periodic orbit computation. By using these analyses, we can better understand the character of a spacecraft's motion around an asteroid, which is much different from spacecraft motion around the Earth or other planets in the Solar system.; Specifically, the main contributions of this dissertation are as follows. First a definition for size-shape stability of orbital motion is proposed and two facts are presented, which are related to the orbital stability of spacecraft motion in the rotating second degree and order gravity field. Second, the secular motions of a spacecraft are studied for three cases: when the central body does not rotate, rotates slowly, and rotates rapidly. The averaged Lagrange equations are derived and analyzed for these cases. Third, the short-period motions related to resonance are analyzed using the elliptic expansions of semi-major axis and eccentricity, and averaging near a resonance between the asteroid rotational and orbital motion. Fourth, periodic orbits are studied, including search methods, existence and stability analyses; five basic families of periodic orbits are found. Finally, a summary of the results in this dissertation is given, and their relations to our size-shape stability definition are discussed.