Analysis of a distant retrograde orbit in the Hill three-body problem

In this study, spacecraft orbital motion in the Hill three-body problem is considered. When the secondary body moves in a circular orbit whose center is the primary body, a distant retrograde orbit (DRO) exists on the plane of revolution of the secondary body. In this study, a three-dimensional DRO including an out-of-plane motion is investigated. First, the motion in each direction is assumed as a simple trigonometric motion, and relations between the ratios of the amplitudes and the ratios of the angular velocities are derived. Then, a stability criterion of the three-dimensional DRO is obtained from the maximum eigenvalues of the monodromy matrix. A comparative study is executed between the present analytical results and the numerical simulations, and it validates the analytical results.