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PDF document - Orbital and Celestial Mechanics Website

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Park orbit RAANFor a given TLI injection time, there are two possible locations on the initial park orbit at which toperform the propulsive maneuver. One opportunity occurs during the ascending part of the park orbit<strong>and</strong> the other during the descending motion. The park orbit RAAN at these two locations can bedetermined from spherical trigonometry relationships involving the park orbit inclination <strong>and</strong> the rightascension <strong>and</strong> declination of the moon at encounter.1ascending p 180 m sin tanm tan ip1descending p m sin tanm tanippwheremmi pright ascension of the moon at encounterdeclination of the moon at encounterpark orbit inclinationThese opportunities are valid whenever m ip.B-plane targetingThe derivation of B-plane coordinates is described in the classic JPL reports, “A Method of DescribingMiss Distances for Lunar <strong>and</strong> Interplanetary Trajectories” <strong>and</strong> “Some <strong>Orbital</strong> Elements Useful in SpaceTrajectory Calculations”, both by William Kizner. The following diagram illustrates the fundamentalgeometry of the B-plane coordinate system.page 22

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