Approximate Solutions for the Non-Hamiltonian Restricted Three-Body Problem

The circular restricted three-body problem (CR3BP) with solar radiation pressure (SRP) has often been analyzed with assumptions made on a spacecraft’s attitude, such that the problem remains Hamiltonian. These assumptions are unsatisfactorily limiting for some missions, like a starshade mission, since the starshade’s attitude will inherently vary from the configuration corresponding to Hamiltonian dynamics. This paper presents the derivation of the equations of motion for the CR3BP with SRP that permit the application of the Lindstedt–Poincaré method such that approximate solutions are produced, which may serve as trajectory design tools. Examples of periodic orbits and manifolds corresponding to three sets of attitude angles are shown, and the accuracy of their ninth-order approximations is considered.