Dynamics and control of displaced periodic orbits using solar-sail propulsion

Solar-sail propulsion to generate families of displaced periodic orbits at planetary bodies is considered. These highly non-Keplerian orbits are achieved using the constant acceleration from the solar sail to generate an artificial libration point, which then acts as a generator of periodic orbits. The orbit is modeled first using two-body and then three-body dynamics including solar radiation pressure effects. A two-body stability condition for the orbits is derived using both a linear and nonlinear analysis and a Jacobi-type integral to identify zero-velocity surfaces that bound the orbital motion. A new family of highly perturbed orbits is then identified resulting in a set of useful manifolds, which can be used for orbit insertion. A closed-form solution to the two-body case is derived using parabolic coordinates, which allows separation of the Hamiltonian of the problem. It is demonstrated that the manifolds are bound to the surface of a paraboloid. A three-body analysis is performed by using Hill's equations as an approximation to the circular restricted three-body problem. Stationkeeping techniques are also investigated to prevent escape after arrival at the desired highly non-Keplerian orbit.