Optimal two-impulse Earth-to-Moon trajectories based on elliptic patched-conic approximation

Sandro da Silva Fernandes¹; Marcus Vinicius Cardoso Macêdo¹; Luiz Arthur Gagg Filho¹

¹ Instituto Tecnológico de Aeronáutica

Resumo

In this paper, the problem of transferring a space vehicle from a circular low Earth orbit (LEO) to a circular low Moon orbit (LMO) with minimum fuel consumption is studied. The class of two impulse trajectories is considered: a first accelerating velocity impulse tangential to the space vehicle velocity relative to Earth is applied at a circular LEO and a second braking velocity impulse tangential to the space vehicle velocity relative to Moon is applied at a circular LMO. The dynamical model used to describe the motion of the space vehicle is based on a new version of the patched-conic approximation which includes the eccentricity of the orbit of the Moon. The optimization problem has been solved by means of a gradient algorithm in conjunction with Newton-Raphson method. Numerical results are compared to other ones that use the classical patched-conic approximation or the classical circular restricted three-body problem.

Palavras-chave: Earth-to-Moon trajectories; optimal space trajectories; minimum fuel trajectories