[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85932-en":3,"doc-seo-85932-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85932,7971461740909,"Levi","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Tulip-Shaped Orbits for Lunar South-Pole PNT and Direct-to-Earth Relay Missions","Geometric analysis 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. Tulip-shaped orbits are compared with elliptical lunar frozen orbit (ELFO) constellations within NASA LunaNet Service Volume II (SV2) south of −75°. A six-satellite tulip baseline and a minimum-cost five-satellite variant share a three-body orbit and differ only in phasing. Performance is assessed using three IOC-C metrics: LOS link availability, LANS GDOP \u003C 6 precision, and daily EVA usable-PNT windows, with both tulip options satisfying all metrics.","arXiv :2607 . 10482v1 [ ee ss . SY] 11 Jul 2026  \nTulip-Shaped Orbits for Lunar South-Pole PNT and Direct-to-Earth Relay Missions  \nDarin C. Koblick∗ and Michael Casey  \nCoorbital, Inc.  \nJuly 2026  \nAbstract  \nThis 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 II (SV2), covering lunar latitudes south of −75◦ . We compare a six-satellite tulip baseline with a minimum-cost five-satellite variant;  \nboth 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:  \nline-of-sight (LOS) link availability, Lunar Augmented Navigation System (LANS) geometric dilution of precision (GDOP) at GDOP \u003C 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 \u003C 6 availability and 18 h of daily EVA support. The five-satellite variant also passes, but with thinner margin: 44% availability and 10 h of EVA support. Unlike the ELFO configurations, each spacecraft in this tulip-shaped orbit configuration maintains continuous Earth line of sight, providing continuous geometric opportunity for direct single-hop Earth relay. This persistent Earth visibility is paired with a three-body orbit, reducing ∆V requirements for initial phasing andreconstitution maneuvers.  \n1 Introduction  \nNASA’s Artemis program, commercial lunar missions, and international lunar initiatives create immediate demand for lunar surface positioning, navigation, and timing (PNT) and communications relay services. South-polar users see Earth only a few degrees above the horizon [1], so reliable navigation and data return require orbiting infrastructure [2, 3, 4] . NASA’s LunaNet / Lunar Communications Relay and Navigation Systems (LCRNS) effort addresses this need through phased relay, PNT, and constellation-geometry requirements [5] .  \nThis paper evaluates constellations of tulip-shaped orbits against the Initial Operating Capability C (IOC-C) requirements because IOC-C is the first LunaNet increment that strongly drives constellation geometry. At IOC-C, the network must provide Service Volume II (SV2) coverage, multiple simultaneous relay links, and four geometrically diverse Augmented Forward Signal (AFS)/ Lunar Augmented Navigation System (LANS) links with GDOP below 6 [5] . Table 1 summarizes the SRD constellation-sizing requirements and highlights the IOC-C benchmark used in this study.  \n∗ Corresponding author: [Darin@coorbital.com](Darin@coorbital.com)  \nTable 1: Constellation sizing requirements from the NASA LCRNS SRD, with the IOC-C increment highlighted. “Min coverage” is the minimum coverage of the corresponding service volume specified by the SRD [5] .  \n\n| Service Type | IOC-A |  |  | IOC-B |  |  |  | IOC-C |  |  | EOC |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  | Ka | S | AFS | Ka | \u003Cbr>S | AFS |  | Ka | S AFS/LANS |  | Ka | S AFS/LANS |  |\n| Number of links | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 2 | \u003Cbr>2 | 4 | 2 | 2 | 5 |\n| Fwd / Rtn link | R | F+R | F | F+R | F+R | F | F | F+R | \u003Cbr>F+R | F | F+R | F+R | F |\n| Service volume |  | SV1 |  |  | SV1 |  |  |  | SV2 |  |  | SV3 |  |\n| Min coverage |  | 70% |  | 75% | 90% | 70% | 40% | 75% | \u003Cbr>90% | 40%† | 75% | 95% | 99% |\n\n† Minimum fraction of an Earth day with GDOP \u003C 6 over SV2; GDOP threshold TBR (LCRNS.3.0130) .  \n2 IOC-C Requirements and Evaluation Metrics  \nThe IOC-C requirements can be reduced to three constellation-geometry tests outlined in Table 2 . R1 and R2 use thresholds stated directly by t","cbCaigcQrjNQIC2t","https://ap.wps.com/l/cbCaigcQrjNQIC2t","pdf",2083615,1,9,"English","en",105,"# Introduction\n## IOC-C Requirements and Evaluation Metrics","[{\"question\":\"What problem does the study address for lunar south-pole operations?\",\"answer\":\"The study targets positioning, navigation, and timing (PNT) plus direct-to-Earth relay support for south-polar users, where Earth is only a few degrees above the horizon and requires reliable orbital infrastructure.\"},{\"question\":\"Which orbit constellations are compared in the evaluation?\",\"answer\":\"The evaluation compares tulip-shaped orbit constellations against elliptical lunar frozen orbit (ELFO) configurations, including reference Lunar Data Network (LDN) cases using five satellites in ELFO planes.\"},{\"question\":\"How are the IOC-C metrics used to judge whether a constellation passes?\",\"answer\":\"A constellation must satisfy three geometry-driven tests on SV2: LOS link availability with surface points having LOS to at least two relays for at least 90% of an Earth day, LANS coverage with GDOP \\u003c 6 for at least 40%, and two daily EVA-support windows per surface point scored at GDOP \\u003c 6.\"}]",1784207239,23,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"tulip-shaped-orbits-for-lunar-south-pole-pnt-and-direct-to-earth-relay-missions","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/tulip-shaped-orbits-for-lunar-south-pole-pnt-and-direct-to-earth-relay-missions/85932/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the study address for lunar south-pole operations?","Question",{"text":75,"@type":76},"The study targets positioning, navigation, and timing (PNT) plus direct-to-Earth relay support for south-polar users, where Earth is only a few degrees above the horizon and requires reliable orbital infrastructure.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which orbit constellations are compared in the evaluation?",{"text":80,"@type":76},"The evaluation compares tulip-shaped orbit constellations against elliptical lunar frozen orbit (ELFO) configurations, including reference Lunar Data Network (LDN) cases using five satellites in ELFO planes.",{"name":82,"@type":73,"acceptedAnswer":83},"How are the IOC-C metrics used to judge whether a constellation passes?",{"text":84,"@type":76},"A constellation must satisfy three geometry-driven tests on SV2: LOS link availability with surface points having LOS to at least two relays for at least 90% of an Earth day, LANS coverage with GDOP \u003C 6 for at least 40%, and two daily EVA-support windows per surface point scored at GDOP \u003C 6.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & 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