<p>Over a dozen new families of periodic ’tulip-shaped’ orbits are introduced, offering significant opportunities for lunar exploration and mission designers. Utilizing numerical simulations and bifurcation analysis in the Circular Restricted Three-Body Problem (CR3BP), these orbits are derived from bifurcating near rectilinear halo orbits (NRHOs) around the Earth-Moon <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40295_2025_510_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> Lagrange point, and their existence validated in the Elliptic Restricted Three-Body Problem (ER3BP). With petal counts ranging from 2 to 15, many tulip-shaped orbits enable full lunar surface coverage, continuous Earth communication, and efficient polar access for both human and robotic landing systems. Unlike traditional NRHOs and frozen lunar orbits, these orbits balance dynamical complexity and operational utility, with configurations that avoid lunar occultation,&#xa0;a critical mission advantage for navigation, surveillance, and infrastructure. Their altitude variability and repeating lunar ground tracks can provide persistent surface visibility, while their two-impulse transfer <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40295_2025_510_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta V\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>V</mi> </mrow> </math></EquationSource> </InlineEquation> costs to the poles are within modern human landing system capabilities. This work presents a novel class of orbit families, opening new pathways for efficient and versatile mission strategies.</p>

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Novel Three-body Tulip-Shaped Orbit Families for Lunar Missions

  • Darin C. Koblick,
  • Patrick Kelly

摘要

Over a dozen new families of periodic ’tulip-shaped’ orbits are introduced, offering significant opportunities for lunar exploration and mission designers. Utilizing numerical simulations and bifurcation analysis in the Circular Restricted Three-Body Problem (CR3BP), these orbits are derived from bifurcating near rectilinear halo orbits (NRHOs) around the Earth-Moon \(L_2\) L 2 Lagrange point, and their existence validated in the Elliptic Restricted Three-Body Problem (ER3BP). With petal counts ranging from 2 to 15, many tulip-shaped orbits enable full lunar surface coverage, continuous Earth communication, and efficient polar access for both human and robotic landing systems. Unlike traditional NRHOs and frozen lunar orbits, these orbits balance dynamical complexity and operational utility, with configurations that avoid lunar occultation, a critical mission advantage for navigation, surveillance, and infrastructure. Their altitude variability and repeating lunar ground tracks can provide persistent surface visibility, while their two-impulse transfer \(\Delta V\) Δ V costs to the poles are within modern human landing system capabilities. This work presents a novel class of orbit families, opening new pathways for efficient and versatile mission strategies.