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The paper outlines the optimization of the L1-L2 and L2-L1 missions using electric propulsion. The variational problem of the low thrust spacecraft transfer optimization with the optimization criterion as the total flight time is considered. The optimal control programs were obtained by using the Pontryagin's maximum principle. The optimization results were as follows: for a certain value of acceleration and exhaust velocity of the propulsion system, we determined optimal control programs, corresponding trajectories and minimal total flight times.

This paper examines the formation of halo-orbits by a spacecraft around L1 and L2 libration points of the Earth-Moon system. Perturbations from the gravitation of the Sun and the non-centrality of the gravitational fields of the Moon and the Earth are taken into account (LP165p model). The proposed perturbed model is an intermediate stage between the dynamic model of the three bodies of the Earth-Moon system and the high-precision non-periodic ephemeris model. The paper proposes two strategies for maintaining halo orbits. The first is to use a small impulse performed on each half of the orbit. The second is to use continuation methods to form a periodic orbit that does not require additional corrections. The essence of the second strategy is to use the perturbation periodicity to generate a special multi-circular halo orbit resonating with the perturbation period. The results of these two approaches are presented for various perturbed models.

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