{"ID":6536525,"CreatedAt":"2026-07-14T01:21:01.169441415Z","UpdatedAt":"2026-07-14T21:15:48.6971638Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.10482","arxiv_id":"2607.10482","title":"Tulip-Shaped Orbits for Lunar South-Pole PNT and Direct-to-Earth Relay Missions","abstract":"This geometric study evaluates a compact seven-petal, 6:5-resonant tulip-shaped orbit constellation for lunar south-pole positioning, navigation, and timing (PNT) and direct-to-Earth relay services. The tulip-shaped orbits are compared against elliptical lunar frozen orbit (ELFO) constellations over the NASA LunaNet Service Volume 2 (SV2), covering lunar latitudes south of -75 degrees. We compare a six-satellite tulip baseline with a minimum-cost five-satellite variant; both use the same shared three-body orbit and differ only in satellite count and along-track phasing. Performance is scored against three Initial Operating Capability C (IOC-C) metrics: line-of-sight (LOS) link availability, Lunar Augmented Navigation System (LANS) geometric dilution of precision (GDOP) below 6, and daily extravehicular activity (EVA) usable-PNT windows. Both tulip constellations satisfy all three IOC-C metrics across SV2. The six-satellite configuration meets requirements with wide margin: 75% worst-point daily GDOP availability and 18 hours of daily EVA support. The five-satellite variant also passes, but with thinner margin: 44% availability and 10 hours of EVA support. Unlike the ELFO configurations, each spacecraft in the tulip-shaped constellation maintains continuous Earth line of sight, providing persistent geometric opportunity for direct single-hop Earth relay. Because all spacecraft share a single three-body orbit, initial phasing and post-failure reconstitution reduce to along-track drift maneuvers between neighboring orbits, with screening-level estimates indicating low maneuver cost.","short_abstract":"This geometric study evaluates a compact seven-petal, 6:5-resonant tulip-shaped orbit constellation for lunar south-pole positioning, navigation, and timing (PNT) and direct-to-Earth relay services. The tulip-shaped orbits are compared against elliptical lunar frozen orbit (ELFO) constellations over the NASA LunaNet Se...","url_abs":"https://arxiv.org/abs/2607.10482","url_pdf":"https://arxiv.org/pdf/2607.10482v1","authors":"[\"Darin C. Koblick\",\"Michael Casey\"]","published":"2026-07-11T21:28:05Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"astro-ph.EP\",\"math.OC\"]","methods":"[]","has_code":false}