Computer Science
Scientific paper
Jun 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phdt........43m&link_type=abstract
Ph.D. Thesis Wisconsin Univ., Madison.
Computer Science
5
Celestial Mechanics, Jupiter Satellites, Three Body Problem, Eccentricity, Gravitational Effects, Mass Ratios, Orbits
Scientific paper
This is a general numerical study of satellite capture in the gravitational Planer restricted three-body problem. The understanding of the probable capture origin of the irregular Jovian satellites is sought. The scope is broadened in order to develop a foundation for understanding gravitational capture in general. The two most important parameters are the mass ratio mu and the primary eccentricity e sub p. Each is varied separately, in order to isolate effects on capture by the smaller mass from the larger mass. The main results are summarized as follows: (1) In C sub 0-x sub 0 space, the capture time is an exceedingly complex function. (2) The complexity is due to an infinite number of periodic orbit families. (3) The capture time is intimately connected to the periodic orbit families. (4) The structure of the periodic orbit families in the C sub 0-x sub 0 plane is self-similar, indicating that it is fractal. (5) The C sub 0-x sub 0 structure is very sensitive to e sub p. (6) There are two well-defined distributions in semimajor axis/eccentricity space of orbits around m sub 1 (the more massive primary) that get captured by m sub 2. The changes in a and e of these distributiuons are shown as a function of mu and e sub p. (7) Capture into retrograde motion is much less probable than capture into prograde motion. (8) There is no distinction in semimajor axis, eccentricity, or orbit orientation between prograde and retrograde capture. (9) Capture occurs near primary pericenter. (10) For the current Jupiter-Sun system, capture occurs for heliocentric elements a approximately equal 3.74 to 4.06 AU, and e approximately equal 0.06 to 0.29 AU.
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