Abstract
The gravitational interaction of two small satellites, on initially close circular, coplanar orbits leads to a one-parameter family of solutions. When varying the parameter h of the family, the solution changes continuously on an interval and then undergoes a sudden change. The set of discontinuities has a Cantor-like structure.
Similar phenomena have been observed in other problems of scattering. Such a behavior is related to the presence of periodic orbits and homo- and heteroclinic points. It can be shown that in the vicinity of a homo- or heteroclinic point, one can define a symbolic dynamics (Moser, 1973).
The large eigenvalue (600) of the satellite problem limits the possibility of numerical exploration. A model problem, the inclined billiard (Hénon, 1988), was designed with a tunable eigenvalue, for which the symbolic dynamics can be analytically defined, thus fully elucidating the structure of the family.
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© 2002 Springer-Verlag Berlin Heidelberg
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Petit, JM. (2002). Chaotic Scattering in Planetary Rings. In: Benest, D., Froeschlé, C. (eds) Singularities in Gravitational Systems. Lecture Notes in Physics, vol 590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48009-9_8
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DOI: https://doi.org/10.1007/3-540-48009-9_8
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