XI^{th} International Astronautical Congress Stockholm 1960 / XI. Internationaler Astronautischer Kongress / XI^{e} Congrès International D’Astronautique
pp 385-391 |
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# Theorem of Image Trajectories in the Earth-Moon Space

## Abstract

The motion of a small vehicle in the Earth-Moon space is considered using the mathematical model of the restricted three-body problem. Two theorems associated with this motion are established: the Irreversibility Theorem and the Theorem of Image Trajectories. The *Irreversibility Theorem* states that, if a trajectory is physically possible in the Earth-Moon space, the reverse trajectory is not physically possible. The *Theorem of Image Trajectories* states that, if a trajectory is physically possible in the Earth-Moon space, three image trajectories are also physically possible: (*a*)the image with respect to the plane which contains the Earth-Moon axis and is perpendicular to the axis of rotation of the Earth-Moon system; (*b*) the image with respect to the plane which contains the Earth-Moon axis and the axis of rotation of the Earth-Moon system; and (*c*) the image with respect to the Earth-Moon axis. The first of these image trajectories must be flown in the same sense as that of the basic trajectory, while the other two must be flown in the opposite sense. As a conclusion, the time required for the parametric study of lunar trajectories is reduced considerably, since, once a basic set of trajectories is calculated, three additional sets can be obtained by simple transformations of coordinates.

## Keywords

Rand Corporation Opposite Sense Geometric Image Inertial Coordinate System Absolute Motion## Preview

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