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It is natural to ask whether the feasibility property implies an optimality property. t. the Earth-Moon axis has the property of being an optimal Moon-Earth trajectory. To supply an answer to the above question, we present in this paper a systematic study of optimal Earth-Moon and Moon-Earth trajectories under the following scenario. The optimization criterion is the total characteristic velocity; the class of two-impulse trajectories is considered; the parameters being optimized are four: initial phase angle of spacecraft Design of Moon Missions 33 with respect to either Earth or Moon, flight time, velocity impulse at departure, velocity impulse at arrival.

2 for counterclockwise LMO arrival. Major comments are as follows: the accelerating velocity impulse is nearly independent of the orbital altitude over the Moon surface (see Ref. 18); decreases as the orbital (ii) the braking velocity impulse altitude over the Moon surface increases (see Ref. 2 days, depending on the mission); (iv) the optimal trajectories with counterclockwise arrival to LMO are slightly superior to the optimal trajectories with clockwise arrival to LMO in terms of characteristic velocity and flight time.

3. , Optimal Ascent Trajectories for TSTO Spacecraft: Extensions, Aero-Astronautics Report 277, Rice University, 1997. Design of Rocket-Powered Orbital Spacecraft 29 4. , Optimal Ascent Trajectories for SSSO, SSTO, and TSTO Spacecraft: Extensions, Aero-Astronautics Report 278, Rice University, 1997. 5. ANONYMOUS, N. , Access to Space Study, Summary Report, Office of Space Systems Development, NASA Headquarters, 1994. 6. FREEMAN, D. C, TALAY, T. , STANLEY, D. , LEPSCH, R. , and WIHITE, A. 241-249, 1995.

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