Coplanar multi-turn rendezvous in near-circular orbit using a low-thrust engine

The authors describe an algorithm that allows calculating the parameters of maneuvers performed on several turns by the low-thrust engine, which ensure the flight of the active spacecraft to the specified vicinity of the target space object. The movement takes place in the vicinity of a circular orbit. Linearized equations of motion are used in solving the problem. The influence of the non-centrality of the gravitational field and the atmosphere is not taken into account. The determination of maneuver parameters takes place in three stages. At the first and third stages, the parameters of the pulse transition and the transition performed by the low-thrust engine, are determined analytically. At the second stage, the distribution of maneuvering between turns, which provides a solution to the meeting problem, is carried out by iterating over one variable. This method of solving the problem provides simplicity and high reliability of determining the parameters of maneuvers, which allows it to be used on board the spacecraft. The paper investigates the dependence of the total characteristic speed of solving the meeting problem on the number of turns of the flight and the magnitude of the engine thrust.