Bounds of relative motion for resonant solar-sail halo orbits in Earth–Moon system

This study discusses the relative motion among Earth–Moon resonant solar-sail halo orbits of the same period, which are promising candidates for formation-flying missions. Because the restricted multibody problem admits no closed-form solutions, this study proposes a semi-analytic method for the bound analysis of relative motion using the jet transport technique. In particular, the bounds on the coordinate components and inter-spacecraft distance are explicitly specified as high-order Taylor polynomials in terms of solar-sail parameters that characterize the families of resonant halo orbits. These semi-analytic closed-form solutions allow rapid evaluations of the maximum, minimum, and mean distances among nearby solar-sail halo orbits, which are crucial for formation configuration design and control. Based on illustrative examples, we verify the effectiveness of the proposed semi-analytic bound-analysis method.