Approximate Analytical Solutions for the Circular Restricted Three-Body Problem Including Non-Hamiltonian Solar Radiation Pressure

Abstract: 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 a starshade mission since the starshade's attitude will inherently vary from the configuration that corresponds to Hamiltonian dynamics. This paper presents the derivation of the equations of motion for CR3BP with SRP that permit the application of the Lindstedt-Poincare method, such that approximate solutions are produced, which may serve as invaluable trajectory design tools. Examples of periodic orbits and manifolds corresponding to three sets of attitude angles are shown and the accuracy of their seventh-order approximations is considered.