Analytical three-dimensional propulsion process of electric sail with fixed pitch angle

This paper proposes an analytical three-dimensional propulsion process of electric sail considering constant thrust angle. Due to the small characteristic acceleration of electric sails, its dimensionless form is defined as a perturbation parameter. For an electric sail with a determined initial state, an analytical approximate three-dimensional trajectory consisting of a primary term and perturbation terms can be derived by considering a reasonable approximation in the equation of motion. Furthermore, rectification steps are introduced to minimize approximation error caused by reasonable approximation and continuous changes in elements of osculating orbit. Despite the addition of fixed step rectification, the analytical estimation time is much shorter than the integration time, as the entire approximation process, including the rectification step, is analytical. The time required for analytical approximation is much lower than that for integration. Significantly, the parking orbit of the electric sail required for analytical approximation can be arbitrary. Based on the characteristics, the proposed analytical approximate three-dimensional trajectory is suitable for fast trajectory prediction of various complex deep-space exploration missions, especially for splicing trajectories with different pitch angles to solve problems with fixed targets.