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  • 1
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    Adiabatic invariants and phase equilibria for first-order orbital resonances (1975)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: In the planar circular restricted three-body problem, the evolution of near-commensurable orbits is studied under change in the mass ratio, mu. The evolution involves preservation of two adiabatic invariants. Transition from circulation to libration may occur; such transitions are of two types. Type I transition occurs when the evolutionary track in phase space passes through near-zero eccentricity; as in the ordinary case (no transition), pre- and post-evolutionary states are linked by solution of a two-point boundary-value problem. Type II transition occurs when the evolutionary track encounters an unstable phase equilibrium or periodic orbit. There is then a discontinuous change in one adiabatic invariant, and pre- and post-evolutionary states are linked by solution of a three-point boundary-value problem. No evolutionary track can encounter a stable phase equilibrium, but the class of all stable phase equilibria is mapped into itself under mu change.
    Keywords: ASTRONOMY
    Type: Astronomical Journal; 80; June 197
    Format: text
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  • 2
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    New contributions to the problem of capture (1977)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: Libration-point capture is analyzed in the framework of the restricted three-body problem in order to obtain general results capable of predicting the major features of an arbitrary postcapture orbit, with specific reference to capture as the presumed mode of origin of Jupiter's outer satellites. Some examples of libration-point capture are computed, the time a body remains captured is estimated, and a long-term numerical integration of orbits is carried out which shows that the equation used to estimate capture lifetimes is quite conservative. An extended capture criterion is proposed and used to demonstrate that direct postcapture orbits lie outside retrograde ones. Mass change involving one or both primaries is evaluated as a means of producing permanent capture, it is found that mass-change effects can produce 'pull-down capture', and consideration is given to the orbital evolution of Jupiter's outer satellites. The effect of drag in the solar nebula or in a nebula around proto-Jupiter on the capture process is briefly investigated. It is concluded that a capture origin for the outer satellites is improbable within the last 4.6 billion years but that either mass change or nebula drag could have been effective in producing capture.
    Keywords: ASTRONOMY
    Type: Icarus; 30; Feb. 197
    Format: text
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