Geometrical parameters of the translunar Apollo orbit are derived from elementary equations relating to elliptical and hyperbolic orbits in an inverse-square force field. The simplification is to divide the problem into an elliptical orbit in the region where the earth's attraction dominates and a hyperbolic orbit (referred to a moving coordinate system attached to the moon) in the region where the moon dominates. The result shows that the orbit will return the spacecraft to earth (unless the propulsion system is fired), provided the spacecraft is properly incident on the leading side of the moon. The elementary results are compared with those of a computer simulation of the orbit.
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PAPERS| November 01 1969
Elementary Analysis of Translunar Apollo Orbit
R. W. Christy;
R. W. Christy, M. R. Mayhugh; Elementary Analysis of Translunar Apollo Orbit. Am. J. Phys. 1 November 1969; 37 (11): 1103–1109. https://doi.org/10.1119/1.1975224
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