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SOME PERIODIC TRAJECTORIES IN CISLUNAR SPACE VERY RESTRICTED FOUR BODY APPROXIMATION.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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The possibility of existence of periodic or nearly periodic trajectories in cislunar space is investigated. In cislunar space, the motion is determined by the gravitational fields of the earth, moon, and sun. The problem is studied using the very restricted four body approximation. It is assumed that the earth and moon revolve in circular paths about their barycenter and the barycenter of the earth and moon moves in a circle about the sun. The motion of the infinitesimal fourth body is restricted to the plane of the three finite bodies. The equations of motion are integrated numerically using a digital computer. A class of periodic or nearly periodic trajectories is found in cislunar space. The period of each trajectory is approximately 29.53 days with respect to a coordinate system centered at the earth-moon barycenter and rotating at the rate the moon rotates about the earth. Periodic trajectories are found which circle the earth, the moon, and the earth-moon L libration point. Author
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