Reachable Domain Under Perturbation for Satellites with a Single Impulse

Abstract

The conventional reachable domain problem for satellites with a single impulse under the ideal two-body dynamical environment was extended to a more realistic scenario that takes perturbation into account. Such an extension enables the reachable domain to model the medium-term evolution of a debris cloud and to facilitate the orbit maneuver planning by exploiting the effect. First, the reachable domain under perturbation is defined as the collection of osculating orbits. To solve the boundary surface of the reachable domain, the three-dimensional reachable domain is reduced to a two-dimensional problem by discretization onto cross-sectional meridian planes of the central body. In this manner, the two-dimensional cross-sectional reachable domain can be expressed as a family of two-variable parameterized curves. Then, the reachable domain boundary is formulated by using envelope theory. A rigorous algorithm is proposed to solve the reachable domain boundary. The computational efficiency and accuracy of the algorithm are also analyzed. The results show that the computational time of a reachable domain is at the level of seconds on a personal desktop. The accuracy can be guaranteed as long as the perturbation assumption is valid. Finally, the dynamical evolution of the reachable domain from a toroid to a band, driven by the perturbation, is successfully modeled.