Analysis of the process of deployment of a lunar tether system taking into account the Earth's gravity

The development of space transport systems for the delivery of payloads and the study of the lunar surface is an important scientific and technical challenge. The article considers a near-lunar space tether system consisting of a station and a microsatellite. The station is considered as a rigid body having a cylindrical shape, and the microsatellite is considered as a spherical rigid body. The tether is considered as a weightless inextensible rod of variable length. The station moves in a near-lunar orbit, which is influenced by the Earth's gravity. The process of deployment of a radially directed near-lunar tether system is considered. The equations of motion of the space tether system are obtained using Newton's second law and the theorem on the change in the angular momentum. To release the tether and bring the orbital tether system to a working state, the article proposes to use the control program of tethers tension force, which ensures the deployment of the tether system to a position close to the vertical. A comparison of the motion of the tether system along the unperturbed lunar orbit and along the perturbed one, taking into account the gravitational influence of the Earth, is made. To substantiate the theoretical results, a numerical simulation was carried out, based on the results of which a conclusion was made about the influence of the Earth's gravity on the amplitude of oscillations of the microsatellite relative to the local vertical.