Ambitious lunar missions, such as a proposed mission to construct, from multiple CubeSats, a large aperture radio telescope behind the Moon, shielded from Earth’s radiation, to detect emissions from exoplanets, will benefit from, or even be enabled by, improved performance in transferring CubeSats from the Earth to the Moon. Low-energy transfers, leveraging solar gravity to reduce significantly the propellant required, are a flight-proven solution for Earth-to-Moon transfers. However, the long transfer times, and large distances from Earth during transfers, associated with low-energy transfers, can be problematic for small satellites such as CubeSats.
In this dissertation, an approach for expediting low-energy Earth-to-Moon transfers is proposed and characterized. A key element of the approach is electrospray propulsion, which is under development and promises to meet the needs of CubeSats, including providing low-thrust for Earth-to-Moon orbital transfer. Starting with the current ballistic low-energy transfer that minimizes propellant usage, we investigate using low-thrust during the transfer to shorten the transfer time. The transfer problem is posed as an optimal control problem to minimize a weighted combination of propellant usage and transfer time. This problem has a one-parameter family of solutions, where the parameter determines the relative weighting of propellant usage and transfer time.
Using the patched-circular-restricted-three-body model to account for the Sun, Earth, and Moon gravitational forces acting on the CubeSat, the idealized low-energy strategy of constructing an Earth-to-Moon transfer as a chain of invariant manifold arcs provides the conceptual starting point; the manifolds are associated with the unstable periodic libration orbits. Ballistic shadowing of the manifold arc chain yields a finite-time transfer; however, the transfer time reduction is limited by the requirement to satisfy the initial conditions for the transfer. Thus, the use of low-thrust during the transfer is considered. Using the patched-three-body model augmented with the low-thrust force provided by electrospray propulsion, it is shown that the transfer time can be reduced at the expense of using some propellant for a low-thrust arc. Using the solution for the thrust-augmented patched-three-body model as an initial guess, the optimal transfer problem is solved for the thrust-augmented bicircular-restricted-four-body model using the General Pseudospectral Optimization Software and for a thrust-augmented ephemeris model using the General Mission Analysis Tool. The higher-fidelity models confirm the results from the thrust-augmented patched-three-body model.
The primary contribution of the dissertation is to determine the trade-offs between Earth-to-Moon transfer time and propellant usage for CubeSat with electrospray propulsion. For the CubeSat with the specifications assumed herein, our results show that by using 26\% of the onboard propellant, the transfer time can be reduced by a month relative to the best ballistic low-energy transfer of about 4 months. A second contribution of the research is providing evidence that electrospray propulsion is viable for expediting low-energy Earth-to-Moon transfer for CubeSats.
