Physics
Scientific paper
Feb 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976cemec..13...75b&link_type=abstract
Celestial Mechanics, vol. 13, Feb. 1976, p. 75-88.
Physics
1
Elliptical Orbits, Orbital Mechanics, Space Probes, Trajectory Analysis, Two Body Problem, Cartesian Coordinates, Cycloids, Eccentric Orbits, Kepler Laws, Polar Coordinates, Prolateness, Space Stations
Scientific paper
The motion of an unpowered probe ejected into an elliptical orbit in the orbital plane of a space station in circular orbit is investigated from a reference system attached to the space station. Existing approximate solutions to this relative trajectory problem of two bodies in Keplerian orbits about the same primary are restricted to small relative displacements. A first-order solution is derived from an exact solution; no restriction is placed on the relative displacement, and the solution osculates with the exact solution at points corresponding to the perigee and apogee of the probe's orbit. A geometric description of the trajectories is given in terms of prolate cycloids plotted in a curvilinear coordinate system.
Berreen T. F.
Crisp D. C. J.
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