Impossibility of the capture of retrograde satellites in the restricted three-body problem

Details Impossibility of the capture of retrograde satellites in the restricted three-body problem Impossibility of the capture of retrograde satellites in the restricted three-body problem

Apr 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..29..367t&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 29, April 1983, p. 367-402.

Physics

9

Capture Effect, Natural Satellites, Orbital Mechanics, Three Body Problem, Circular Orbits, Equations Of Motion, Jupiter (Planet), Particle Motion

Scientific paper

Employing the method of surfaces of section, the impossibility of capture of retrograde satellites in the framework of the restricted three-body problem is demonstrated. Equations of motion are described in the physical variables as well as in Birkhoff's regularizing variables. Each transition of points on the surfaces of section is shown to occur by the operation of surface transformations during a bounded time interval. Intersections and orders of intersection of orbits with curves in Birkhoff's plane are defined, introducing various kinds of retrograde orbits. The motion of the particle is considered in the phase space, introducing the manifold of states of motion and defining the surfaces of section and surface transformations. Sets of representative points of orbits which revolve retrogradely round one of the primaries successively at least once in the future are defined, and surface transformations are shown to be homeomorphic and measure-preserving on these sets. The measure of the set of representative points of captured retrograde orbits is shown to be zero.

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