The restricted Hill four-body problem

Details The restricted Hill four-body problem The restricted Hill four-body problem

Aug 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992wadc.iafcv....s&link_type=abstract

IAF, International Astronautical Congress, 43rd, Washington, Aug. 28-Sept. 5, 1992. 13 p.

Astronomy and Astrophysics

Astronomy

Earth-Moon System, Four Body Problem, Hill Method, Lagrange Coordinates, Spacecraft Motion, Degrees Of Freedom, Equations Of Motion, Orbital Mechanics, Three Body Problem

Scientific paper

With the four-body problem as a point of departure, a generalization of both the restricted three-body problem and the Hill three-body problem is derived. The present model exhibits motions described by previous researchers using more general and complicated models with specified parameter values. The model is used to numerically investigate the structure of motions around the geometric position of the triangular Lagrange points for values of the parameter nu in the neighborhood of the earth-moon value as m increases from 0 to 0.195 at which the Hill variation orbit becomes unstable. The stable and unstable manifolds of the unstable periodic orbits are investigated, and motions which expand and contract around the triangular points and which remain bounded over long time periods are found. The way in which these results help explain phenomena observed by previous investigators is shown.

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