Cislunar tulip orbits: Robust construction and applications in deep-space missions

Cislunar tulip orbits exhibit rich geometry, favorable stability, and multi-directional lunar coverage, offering substantial potential for diverse cislunar mission applications. Previous studies have shown that these orbits bifurcate from the ultra-low-perilune branch of the L2 Near-Rectilinear Halo Orbit (NRHO) subset. However, numerical continuation of their entire orbit families is challenging due to the enhanced singularity induced by the non-monotonic variation in the perilune distance. This study focuses on the efficient construction of tulip orbit families and systematically explores their potential applications. First, period-multiplying bifurcation points within the L2 NRHO subset are identified using the Broucke stability diagram, with the initial post-bifurcated orbits obtained through an orbit family switching algorithm. Then, a hybrid continuation protocol that incorporates the Kustaanheimo-Stiefel (KS) transformation is proposed, enabling robust continuation across the highly sensitive near-singular region, followed by the construction of the complete orbit family. Finally, systematic mission evaluations identify two tulip candidates that surpass the 9:2 NRHO and 2:1 Distant Retrograde Orbit (DRO) in global coverage and eclipse-free geometry, while offering diverse transfer options and comparable station-keeping costs. Consequently, these orbits represent robust alternatives for future cislunar infrastructure, particularly as strategic nodes for lunar navigation constellations and thermally sensitive platforms such as cryogenic propellant depots.