Numerical Investigation for 3D Branches of the Lyapunov Families in the Hill’s Problem with Radiation Pressure

Hill’s problem plays an important role in analyzing the local dynamics of an infinitesimal body under the gravitational influence of a distant massive primary and a nearby secondary body of smaller mass. When radiation pressure is included, the resulting model becomes particularly relevant for studying the motion of dust particles and solar-sail spacecraft in the vicinity of minor celestial bodies, such as planets or asteroids. This inclusion breaks the symmetry with respect to the Oy axis that characterizes the configurations of motion in the classical Hill’s problem. Thus, the location of the collinear equilibrium points, and the evolution of the Lyapunov families must be studied independently. Although the planar dynamics of the photogravitational Hill’s problem have been extensively investigated, its three-dimensional structure remains largely unexplored. The present study undertakes a systematic numerical investigation of branches of spatial periodic orbits that bifurcate from the planar Lyapunov families. Specifically, we compute all three-dimensional bifurcations up to multiplicity four and classify them according to their symmetry properties. The analysis reveals that these families exhibit distinct evolutionary patterns in the space of initial conditions, with most of them terminating in collision orbits with the secondary body.