On the Design of Transfers to Solar-Sail Displaced Orbits in the Earth-Moon System

This paper presents the design of solar-sail transfer trajectories to solar-sail displaced libration point orbits in the Earth- Moon system. The existence of families of solar-sail displaced libration point orbits in the Earth-Moon system has recently been demonstrated. These families originate from complementing the dynamics of the classical Earth-Moon circular restricted three-body problem with a solar-sail induced acceleration. Previous work has furthermore demonstrated the applicability of these orbits for high-latitude observation of the Earth and Moon. To not only demonstrate the existence and applicability of these orbits, but also their accessibility, this paper investigates the design of solar-sail transfers from Earth-bound parking orbits to a subset of these orbits. Initial guesses for the transfers are generated using reverse time propagation of the dynamics, where the control is provided by a locally optimal steering law. These initial guesses are subsequently used to initialize a 12th-order Gauss-Lobatto collocation method to satisfy a large number of constraints: departure from specific high Earth orbits, a minimum altitude with respect to the Earth and the Moon, and a maximum rotation rate of the solar sail. As an application of the developed methodology, this paper shows results for transferring two spacecraft to a constellation of displaced vertical Lyapunov orbits at the Earth-Moon L2 point. This constellation has been shown to provide continuous coverage of the lunar Aitken Basin and the lunar South Pole while maintaining a continuous line of sight with Earth. Sets of feasible trajectories for both spacecraft with identical launch conditions are produced in order for the constellation to be initiated using a single Soyuz launch. Such a Soyuz launch can deliver two 1160-kg spacecraft into the found transfer trajectories. One of the spacecraft subsequently requires a transfer time of 53.06 days to enter its constellation orbit, while the transfer of the other spacecraft takes 67.89 days. These results prove the accessibility of solar-sail displaced libration point orbits in the Earth-Moon system, thereby reaffirming the potential of solar-sail technology to enable novel scientific missions in the Earth-Moon system