This paper discusses a trajectory synthesis for low thrust Lunar orbiter travelling between a low Earth circular orbit and a low Lunar one. The low thrust trajectory discussed here is made up of three phases which are the Earth spiral ascending phase, the Lunar capture phase and the Lunar spiral descending phase, each of which plays proper roles in the transfers to the Lunar orbit. The Lunar capture phase is the most important one in which the orbiter is guided from a parking orbit of around 150, 000km radius to an elliptical orbit with the eccentricity of about 0.3 by thrusting only in the one side of the orbital arc, attracted by the Lunar gravitational force and put into the Lunar sphere of influence on the conditions to achieve near circular but unstable Lunar orbit, and finally transferred to a stable circular orbit by using the low thrust with acceleration levels of the order of 10
-5G. In this paper, the conditions to establish the Lunar capturing are considered and expressed as numerical relations of the entry radius and velocity into the Lunar sphere of influence. Such relations are derived from trajectory simulations. Also typical trajectories to the Moon are shown as samples to evaluate the time of flights, consumed propellant weights and the orbital control capabilities.
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