Reachable Domain Under J₂ Perturbation for Satellites with a Single Impulse

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 J₂ 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 J₂ effect. First, the reachable domain under J₂ 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 J₂ perturbation assumption is valid. Finally, the dynamical evolution of the reachable domain from a toroid to a band, driven by the J₂ perturbation, is successfully modeled.