Abstract
Using a solar sail, a spacecraft orbit can be offset from a central body such that the orbital plane is displaced from the gravitational center. Such a trajectory might be desirable for a single-spacecraft relay to support communications with an outpost at the lunar south pole. Although trajectory design within the context of the Earth-Moon restricted problem is advantageous for this problem, it is difficult to envision the design space for offset orbits. Numerical techniques to solve boundary value problems can be employed to understand this challenging dynamical regime. Numerical finite-difference schemes are simple to understand and implement. Two augmented finite-difference methods (FDMs) are developed and compared to a Hermite-Simpson collocation scheme. With 101 evenly spaced nodes, solutions from the FDM are locally accurate to within 1740 km. Other methods, such as collocation, offer more accurate solutions, but these gains are mitigated when solutions resulting from simple models are migrated to higher-fidelity models. The primary purpose of using a simple, lower-fidelity, augmented finite-difference method is to quickly and easily generate accurate trajectories.
Highlights
When a permanent outpost on the Moon to support extended human expeditions is eventually established, the astronauts at the facility will require a continual communications link with the Earth
A generous maximum-altitude constraint of one Earth-Moon distance (384,400 km) is selected to establish the constraints in (42)
It is instructive to demonstrate the finite-difference methods (FDMs) with characteristic accelerations for sail spacecraft that may be available with near-future technological improvements
Summary
When a permanent outpost on the Moon to support extended human expeditions is eventually established, the astronauts at the facility will require a continual communications link with the Earth. In contrast to a constellation of multiple spacecraft, alternative communications strategies that rely on only one satellite do exist, using current or near-future technology Advanced propulsion concepts, such as low-thrust ion engines, as well as solar sails, supply a force in addition to gravity and can offset an orbit from the Moon [2,3,4], that is, the orbit plane is displaced from the gravitational center and the spacecraft appears to hover above the surface. Once the analyst is familiar with the feasible options, higher-fidelity methods for solving the BVP can be used to refine trajectories or combined with optimization techniques to produce optimal trajectories Another option is to employ the FDM technique to generate trajectories that fit path constraints to quickly explore a broad design space. A separate study uses these FDMs for surveying the solution space and assessing the required solar sail and spacecraft characteristics necessary for the lunar south pole (LSP) coverage problem [32]
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