Optimal Earth–Moon trajectories in elliptic models: part 1 round-trip missions

Resumo

© 2021, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering.In this paper, a preliminary study of optimal round-trip trajectories for Earth–Moon–Earth missions is presented. The outgoing mission consists in transferring a space vehicle from a circular low Earth orbit (LEO) to a circular low Moon orbit (LMO) with minimum fuel consumption. The class of two-impulse trajectories is considered: A first accelerating velocity impulse is applied to insert the space vehicle into an Earth–Moon transfer trajectory, and a second braking velocity impulse is applied to insert the space vehicle into the terminal LMO. It is assumed that the velocity increments are applied tangentially to the terminal orbits. The fuel consumption is defined by the arithmetic sum of the velocity increments. The return trip is similarly described with the initial orbit corresponding to LMO and the final orbit corresponding to LEO. Two dynamical models are considered: an extended version of the patched-conic approximation which includes the eccentricity of the Moon’s orbit and the planar elliptic restricted three-body problem. The optimization problem is solved by means of two gradient techniques: Newton–Raphson–gradient algorithm and sequential gradient–restoration algorithm. Clockwise and counterclockwise arrivals at LMO are considered for outgoing trips, and clockwise and counterclockwise departures from Moon are considered for return trips. The time of flight varies from 4.5 to 5.3 days for outgoing trips or for return trips. Numerical results show that the fuel can be saved if the initial position of the Moon is appropriately determined.

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