The orbital dust torus as an enveloping surface of a family of trajectories of isotropically ejected particles

Details The orbital dust torus as an enveloping surface of a family of trajectories of isotropically ejected particles The orbital dust torus as an enveloping surface of a family of trajectories of isotropically ejected particles

Apr 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008sosyr..42...91o&link_type=abstract

Solar System Research, Volume 42, Issue 2, pp.91-110

Mathematics

Logic

91.10.Sp, 96.15.Qr, Satellite Orbits, Impact Phenomena

Scientific paper

Meteorite impacts onto a small satellite lead to the ejection of a regolith mass, which is much greater than the impactor mass, into cosmic space. Assume that an isotropic ejection with velocities smaller than the maximum possible velocity b took place at the time moment t 0. Since the orbital periods are unequal, the particle trajectories will densely fill a certain domain D. The same domain will be filled after an explosion of an artificial satellite moving in a high orbit. One to three months later, the node and pericenter longitudes will be distributed over the entire circle and the domain D will become a body of revolution, a topological solid torus. We examine the domain of possible particle motion and its boundary S immediately after the impact event (an unperturbed case) and the same domain under the assumption that the initial longitudes of nodes and pericenters were already a result of considerable changes (a perturbed case). In both cases, we managed to construct the domain D and its boundary S analytically: parametric equations containing only relatively simple functions were obtained for S. The basic topologic and differential-geometric properties of S were studied completely.

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