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Description
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. The addition of this acceleration makes the problem non-autonomous, but by constraining the orbital period in a differential correction scheme, closed orbits can be found that are periodic with the Sun's synodic motion about the Earth-Moon system. These orbits can be catalogued into traditional orbit families such as solar-sail displaced Lyapunov, halo, and vertical Lyapunov orbits where different families can be generated for different solar-sail steering laws. 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 to a subset of solar-sail displaced libration point orbits in the Earth-Moon system.
Initial guesses for the transfers are generated using reverse time propagation of the dynamics starting from a grid of state-vectors along the targeted periodic orbits. The backwards propagated transfers are truncated at close approach to Earth. Furthermore, the control is provided through a locally optimal steering law that maximises the solar-sail acceleration component along the inertial velocity vector. These near-feasible initial guesses are subsequently transferred into a highly constrained 12${^{th}}$-order Gauss-Lobatto collocation scheme to improve their feasibility. Constraints are included that ensure linkage between the start of the transfer and commonly used Earth parking orbits, a minimum altitude with respect to the Earth and the Moon, as well as a realistic maximum rotation rate of the solar sail of 20 deg per day.
The paper provides sets of feasible trajectories for realistic- near-term solar-sail technology. In particular, transfers to a solar-sail displaced Lyapunov orbit at $L_1$ and a halo orbit at $L_2$ are provided as well as a two-spacecraft transfer to a constellation of solar-sail displaced vertical Lyapunov orbits at $L_2$. This constellation achieves continuous coverage of both the lunar South Pole and the center of the Aitken Basin, while maintaining an uninterrupted communication link with Earth. The Aitken Basin is of great scientific interest as it is believed to hold clues to the history of the Moon and allows access to the deeper layers of the lunar crust. The lunar South Pole is often mentioned as a potential location for a human outpost because it is an area of near-permanent sunlight, providing access to power, and water ice is most likely present in the continuously shaded areas of the crater interior.
For the two-spacecraft transfer to the constellation of vertical Lyapunov orbits at $L_2$, identical launch conditions for both spacecraft are sought for, such that the constellation can be initiated using a single launch by a Soyuz launch vehicle. The resulting transfers allow two 1160-kg spacecraft to be launched into standard highly elliptical Earth parking orbits from where the solar sail is deployed to transfer the spacecraft to their respective orbits at $L_2$. These transfers take 53.1 and 67.9 days to complete before the spacecraft enter their respective constellation orbits. 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.
