Leveraging Resonant-Orbit Manifolds to Design Transfers Between Libration-Point Orbits

Resonant orbits have been widely employed in mission design for planetary flyby trajectories (Jupiter Europa Orbiter) and, more recently, as a source of long-term stability (Interstellar Boundary Explorer). Yet, resonant orbits have not been explored extensively as transfer mechanisms between nonresonant orbits in multibody systems. To highlight the benefit of employing resonant orbits for transfers and given the increased interest in employing libration-point orbits for a variety of purposes, planar and three-dimensional transfers from a low Earth orbit to the vicinity of the Earth–moon libration points via resonant arcs are constructed. Solutions are efficiently generated in the circular restricted three-body model, and transitioned to a higher-fidelity model for validation. Direct optimization techniques are applied to further reduce the propellant requirements, and a system translation process is defined to allow for the quick translation of Earth–moon transfers to other three-body systems.

[1]  Gregory J. Whiffen,et al.  Exploration of distant retrograde orbits around Europa , 2005 .

[2]  Victor Szebehely,et al.  Chapter 1 – Description of the Restricted Problem , 1967 .

[3]  Alessio Di Salvo,et al.  Novel spaceways for reaching the Moon: an assessment for exploration , 2008 .

[4]  K. Howell,et al.  Transfer Design Exploiting Resonant Orbits and Manifolds in the Saturn-Titan System , 2013 .

[5]  Kathleen C. Howell,et al.  Exploration of bounded motion near binary systems comprised of small irregular bodies , 2015 .

[6]  E. Butcher,et al.  Transfers to Earth-Moon L3 halo orbits , 2012 .

[7]  V. Szebehely,et al.  Theory of Orbits: The Restricted Problem of Three Bodies , 1967 .

[8]  Martin W. Lo,et al.  The role of invariant manifolds in lowthrust trajectory design (part III) , 2004 .

[9]  Morad Nazari,et al.  Optimal transfers with guidance to the earth-moon L1 and L3 libration points using invariant manifolds: A preliminary study , 2012 .

[10]  George H. Born,et al.  Direct lunar halo orbit transfers , 2008 .

[11]  C. Murray,et al.  Solar System Dynamics: Expansion of the Disturbing Function , 1999 .

[12]  E. Macau,et al.  Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5 , 2012 .

[13]  David J. McComas,et al.  A new class of long‐term stable lunar resonance orbits: Space weather applications and the Interstellar Boundary Explorer , 2011 .

[14]  Randy C. Paffenroth,et al.  Elemental Periodic orbits Associated with the libration Points in the Circular Restricted 3-Body Problem , 2007, Int. J. Bifurc. Chaos.

[15]  Diane C. Davis,et al.  Application of Periapse Maps for the Design of Trajectories Near the Smaller Primary in Multi-Body Regimes , 2012 .

[16]  Vaquero Escribano,et al.  Poincare sections and resonant orbits in the restricted three-body problem , 2010 .

[17]  Unstable Resonant Orbits near Earth and Their Applications in Planetary Missions , 2004 .

[18]  Z. Olikara.  Computation of quasi-periodic tori in the circular restricted three-body problem , 2010 .

[19]  P. Gurfil,et al.  Transfer to Distant Retrograde Orbits Using Manifold Theory , 2007 .

[20]  Kathleen C. Howell,et al.  Evolution of the out-of-plane amplitude for quasi-periodic trajectories in the Earth–Moon system , 2012 .

[21]  Rodney L. Anderson,et al.  Comparison of low-energy lunar transfer trajectories to invariant manifolds , 2013 .

[22]  Rodney L. Anderson,et al.  Role of Invariant Manifolds in Low-Thrust Trajectory Design , 2004 .