Near Ballistic Halo-to-Halo Transfers between Planetary Moons

Intermoon transfers are important components of planetary tour missions. However, these transfers are challenging to design due in part to the chaotic environment created by the multi-body dynamics. The specific objective of this work is to develop a systematic methodology to find fuel optimal, near ballistic Halo-to-Halo trajectories between planetary moons, and we achieve this goal by combining dynamical systems theory with a variety of nonlinear programming techniques. The spacecraft is constrained to start at a Halo orbit of a moon and end at another Halo orbit of a second moon. Our approach overcomes the obstacles of the chaotic dynamics by combining multiple “resonant-hopping” gravity assists with manifolds that control the low-energy transport near the Halo orbits of the moons. To help construct good initial guesses, contours of semimajor axes that can be reached by falling off a Halo orbit are presented. An empirical relationship is then derived to find quickly the boundary conditions on the Halo orbits that lead to ballistic capture and escape trajectories, and connect to desired resonances. The overall optimization procedure is broken into four parts of increasing fidelity: creation of the initial guess from unstable resonant orbits and manifolds, decomposition and optimization of the trajectory into two independent ideal three-body portions, end-to-end refinement in a patched three-body model, and transition to an ephemeris model using a continuation method. Each step is based on a robust multiple shooting approach to reduce the sensitivities associated with the close approach trajectories. Numerical results of an intermoon transfer in the Jovian system are presented. In an ephemeris model, using only 55 m/s and 205 days, a spacecraft can transfer between a Halo orbit of Ganymede and a Halo orbit of Europa.

[1]  Edward Ott,et al.  Targeting in Hamiltonian systems that have mixed regular/chaotic phase spaces. , 1997, Chaos.

[2]  Martin W. Lo,et al.  The InterPlanetary Superhighway and the Origins Program , 2002, Proceedings, IEEE Aerospace Conference.

[3]  J Llibre,et al.  Dynamics and Mission Design Near Libration Points: Volume II: Fundamentals: The Case of Triangular Libration Points , 2001 .

[4]  Orbit Transfer via Tube Jumping in Planar Restricted Problems of Four Bodies , 2005 .

[5]  R. Russell,et al.  Computation of a Science Orbit About Europa , 2007 .

[6]  J. Masdemont,et al.  High-order expansions of invariant manifolds of libration point orbits with applications to mission design , 2005 .

[7]  P. Falkner,et al.  SYSTEM CONCEPTS AND ENABLING TECHNOLOGIES FOR AN ESA LOW-COST MISSION TO JUPITER/EUROPA , 2004 .

[8]  P. Penzo,et al.  Trajectory Design for a Europa Orbitter Mission: A Plethora of Astrodynamic Challenges , 1997 .

[9]  Grebogi,et al.  Using chaos to direct trajectories to targets. , 1990, Physical review letters.

[10]  Ryan P. Russell,et al.  Designing Ephemeris Capture Trajectories at Europa Using Unstable Periodic Orbits , 2007 .

[11]  Timothy Edward Dowling,et al.  Jupiter : the planet, satellites, and magnetosphere , 2004 .

[12]  Shane D. Ross,et al.  Design of a multi-moon orbiter , 2003 .

[13]  Shane D. Ross,et al.  Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design , 2001 .

[14]  R. Woolley.  Endgame strategies for planetary moon orbiters , 2010 .

[15]  Nathan J. Strange,et al.  Cycler Trajectories in Planetary Moon Systems , 2009 .

[16]  Joaquim R. R. A. Martins,et al.  The complex-step derivative approximation , 2003, TOMS.

[17]  Shane D. Ross,et al.  The Lunar L1 Gateway: Portal to the Stars and Beyond , 2001 .

[18]  Nathan J. Strange,et al.  Automated Design of the Europa Orbiter Tour , 2000 .

[19]  Shane D. Ross,et al.  Multiple Gravity Assists, Capture, and Escape in the Restricted Three-Body Problem , 2007, SIAM J. Appl. Dyn. Syst..

[20]  Pini Gurfil,et al.  Quasi-periodic orbits of the restricted three-body problem made easy , 2007 .

[21]  Ryan P. Russell,et al.  Optimization of low-energy resonant hopping transfers between planetary moons , 2009 .

[22]  Ryan P. Russell,et al.  A Unied Framework for Robust Optimization of Interplanetary Trajectories , 2010 .

[23]  Anastassios E. Petropoulos,et al.  Low-Thrust Transfers using Primer Vector Theory and a Second-Order Penalty Method , 2008 .

[24]  Nathan J. Strange,et al.  A fast tour design method using non-tangent v-infinity leveraging transfer , 2010 .

[25]  K. Howell,et al.  Trajectory Design Using a Dynamical Systems Approach With Application to Genesis , 1997 .

[26]  James M. Longuski,et al.  V8 Leveraging for Interplanetary Missions: Multiple-Revolution Orbit Techniques , 1997 .

[27]  L. D'Amario,et al.  Europa Orbiter Mission Trajectory Design , 1999 .

[28]  Evan S. Gawlik,et al.  Invariant manifolds, discrete mechanics, and trajectory design for a mission to Titan , 2009 .

[29]  K. Howell,et al.  Representations of Invariant Manifolds for Applications in Three-Body Systems , 2006 .

[30]  Stefano Campagnola,et al.  END-TO-END MISSION ANALYSIS FOR A LOW-COST, TWO- SPACECRAFT MISSION TO EUROPA , 2009 .

[31]  Shane D. Ross,et al.  Connecting orbits and invariant manifolds in the spatial restricted three-body problem , 2004 .

[32]  Kathryn E. Davis.  Locally optimal transfer trajectories between libration point orbits using invariant manifolds , 2009 .

[33]  David D. Morrison,et al.  Multiple shooting method for two-point boundary value problems , 1962, CACM.

[34]  Piyush Grover,et al.  Designing Trajectories in a Planet-Moon Environment Using the Controlled Keplerian Map , 2009 .

[35]  Nathan J. Strange,et al.  Planetary moon cycler trajectories , 2007 .

[36]  Ryan P. Russell,et al.  Endgame Problem Part 2: Multibody Technique and the Tisserand-Poincare Graph , 2010 .

[37]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[38]  B. Barden,et al.  Application of Dynamical Systems Theory to Trajectory Design for a Libration Point Mission , 1997 .

[39]  Ryan P. Russell,et al.  Endgame Problem Part 1: V-Infinity-Leveraging Technique and the Leveraging Graph , 2010 .

[40]  Nathan J. Strange,et al.  Automated Design of the Europa Orbiter Tour , 2000 .

[41]  J. Marsden,et al.  Dynamical Systems, the Three-Body Problem and Space Mission Design , 2009 .

[42]  G. Floquet,et al.  Sur les équations différentielles linéaires à coefficients périodiques , 1883 .