The tracking laws relative to Earth-Moon of spacecrafts on the Lissajous orbits around L₂ point

The Lissajous orbit about L₂ point of Earth and Moon system can be employed to explore the lunar farside which is beyond our view, so the tracking laws from Tracking and Data Relay Satellites (TDRS) on the orbit to the Moon and Earth is presented in this paper. The scheme of spacecraft's attitude description is proposed to model the motions of the antenna large maneuvering with two freedoms. The tracking angles and angular velocities of the antenna are derived, associated with the probability of TDRS pointing to Earth with no eclipse by the Moon. Then the relations between the parameters of Lissajous orbit and the tracking laws are provided, and the mission alternation between different TDRSS for the separating by the Moon is conducted. Finally, the influence of beam angle on the pointing accuracy is analyzed. All the results have been validated numerically.