| A novel method to evaluate the trajectory dynamics of low-thrust spacecraft is developed. Using a two-body Newtonian model, the spacecraft thrust vector components are represented by Fourier series in terms of eccentric anomaly, and Gauss's variational equations are averaged over one orbit to obtain a set of secular equations. These secular equations are a function of 14 of the thrust Fourier coefficients, regardless of the order of the original Fourier series, and are sufficient to determine a low-thrust spiral trajectory with significantly reduced computational requirements as compared with integration of the full Newtonian problem.;This method is applied to orbital targeting problems. The targeting problems are defined as two-point boundary value problems with fixed endpoint constraints. Average low-thrust controls that solve these problems are found using the averaged variational equations and a cost function represented also as a Fourier series. The resulting fuel costs and dynamic fidelity of the targeting solutions are evaluated.;Low-thrust controls with equivalent average trajectory dynamics but different thrust profiles are also studied. Higher-order control coefficients that do not affect the average dynamics are used to reduce fuel costs and transform time-varying controls into controls with constant thrust arcs, which can be implemented more easily by low-thrust propulsion systems.;These methods have applications to low-thrust mission design and space situational awareness. Example problems based on past missions and potential future scenarios demonstrate the effectiveness of these methods. |
