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The Journal of the Astronautical Sciences

, Volume 63, Issue 3, pp 175–205 | Cite as

Computer Aided Ballistic Orbit Classification Around Small Bodies

  • Benjamin F. Villac
  • Rodney L. Anderson
  • Alex J. Pini
Article

Abstract

Orbital dynamics around small bodies are as varied as the shapes and dynamical states of these bodies. While various classes of orbits have been analyzed in detail, the global overview of relevant ballistic orbits at particular bodies is not easily computed or organized. Yet, correctly categorizing these orbits will ease their future use in the overall trajectory design process. This paper overviews methods that have been used to organize orbits, focusing on periodic orbits in particular, and introduces new methods based on clustering approaches.

Keywords

Trajectory design Periodic orbits Clustering Data mining Asteroid missions 

Notes

Acknowledgments

This research has been sponsored by the AMMOS technology development task. A portion of the research presented in this paper has been carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

References

  1. 1.
    Miller, J.K., Konopliv, A.S., Antreasian, P.G., Bordi, J.J., Chesley, S., Helfrich, C.E., Owen, W.M., Wang, T.C., Williams, B.G., Yeomans, D.K., Scheeres, D.J.: Determination of shape, gravity, and rotational state of asteroid 433 Eros. Icarus 155(1), 3–17 (2002)CrossRefGoogle Scholar
  2. 2.
    Laurettam, D.S.: Overview of the OSIRIS-REx Asteroid Sample Return Mission. 43rd Lunar and Planetary Science Conference, No. 2491 (2012)Google Scholar
  3. 3.
    Berry, K., Sutter, B., May, A., Williams, K., Barbee, B.W., Beckman, M., Williams, B.: (TAG) Mission Design and Analysis, Proceedings of the 36th Annual AAS Guidance, Navigation and Control Conference, Vol. Paper AAS 13-095 (2013)Google Scholar
  4. 4.
    Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments: Applications to Asteroid, Comet and Planetary Satellite Orbiters. Springer Praxis, Berlin Heidelberg (2012)Google Scholar
  5. 5.
    Villac, B., Liu, K.Y.-Y.: Long-term Stable Orbits for Passive Tracking Beacon Missions to Asteroids. In: Proceedings of the 2009 International Astronautical Congress (IAC), vol. IAC-09.C1.10.6 (2009)Google Scholar
  6. 6.
    Mondelo, J.-M., Broschart, S.B.: Ballistic Transfer Across the 1:1 Resonance Around Vesta Following Invariant Manifolds. J. Guid. Control Dyn. 36, 1119-1133 (2013)CrossRefGoogle Scholar
  7. 7.
    Rayman, M.D., Fraschetti, T.C., Raymond, C.A., Russell, C.T.: Dawn: A Mission in Development for Exploration of Main Belt Asteroids Vesta and Ceres. Acta Astronaut. 58(11), 605– 616 (2006)CrossRefGoogle Scholar
  8. 8.
    Doedel, E., Paffenroth, R., Keller, H.B., Dichmann, D.J., Galan-Vioque, J., Vanderbauwhede, A.: Computation of periodic solutions of conservative systems with application to the 3-body problem. Int. J. Bifurc. Chaos 6, 1–29 (2003)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Broschart, S.B., Villac, B.F.: Identification of Non-Chaotic Terminator Orbits Near 6489 Golevka. In: Segerman, A.M., Lai, P.C., Wilkins, M.P., Pittelkau, M.E. (eds.) Spaceflight Mechanics: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting held February 9-12, 2009, Savannah, Georgia. Vol. 134 of Advances in the Astronautical Sciences, San Diego, CA, American Astronautical Society, Univelt Inc. (2009)Google Scholar
  10. 10.
    Liu, K., Villac, B.: Periodic Orbit Families in the Hill’s Three-Body Problem with Solar Radiation Pressure. AAS Spaceflight Mechanics Meeting, No. AAS 10-118 (2010)Google Scholar
  11. 11.
    Garcia Yárnoz, D., Scheeres, D.J., McInnes, C.R.: On the a and g Families of Symmetric Periodic Orbits in the Photo-Gravitational Hill Problem and Their Application to Asteroids. AIAA/AAS Astrodynamics Specialist Conference, No. AIAA 2014-4119, San Diego, California (2014)Google Scholar
  12. 12.
    Anderson, R.L., Campagnola, S., Lantoine, G.: Broad Search for Unstable Resonant Orbits in the Planar Circular Restricted Three-Body Problem. AAS/AAIA Astrodynamics Specialist Conference, No. AAS 13-787, Hilton Head Island, South Carolina (2013)Google Scholar
  13. 13.
    Chow, C., Villac, B.: Mapping autonomous constellation design spaces using numerical continuation. J. Guid. Control Dyn. 35(5), 1426–1434 (2012)CrossRefGoogle Scholar
  14. 14.
    Giancotti, M., campagnola, S.: Families of periodic orbits in Hill’s problem with solar radiation pressure: application to Hayabusa 2. Cel. Mech. Dyn. Astron. 120(3), 269-286 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Anderson, R.L.: Tour Design Using Resonant Orbit Heteroclinic Connections in Patched Circular Restricted Three-Body Problems. 23rd AAS/AIAA Space Flight Mechanics Meeting, No. AAS 13-493, Kauai, Hawaii (2013)Google Scholar
  16. 16.
    Anderson, R.L., Lo, M.W.: Spatial approaches to moons from resonance relative to invariant manifolds. Acta Astronaut. 105, 355–372 (2014)CrossRefGoogle Scholar
  17. 17.
    Tsirogiannis, G.A., Perdios, E.A., Markellos, V.V.: Improved grid search method: an efficient tool for global computation of periodic orbits. Cel. Mech. Dyn. Astron. 1, 49–78 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Arnal Fort, E., Villac, B.: Exploration of a Graph Based Method for Orbital Transfers near Small Bodies, 2013 AAS/AIAA Astrodynamics Specialist Conference, No. AAS 13-81 (2013)Google Scholar
  19. 19.
    Tsirogiannis, G.A., Markellos, V.: A greedy global search algorithm for connecting unstable periodic orbits with low energy cost.: Application to the Earth-Moon system. Cel. Mech. Dyn. Astron 117, 2 (2013)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Broschart, S.B., Lantoine, G., Grebow, D.J.: Characteristics of Quasi-Terminator Orbits Near Primitive Bodies. In: Tanygin, S., Park, R.S., Thomas J., Starchville, J., Newman, L.K. (eds.) Spaceflight Mechanics: Proceedings of the AAS/AIAA Spaceflight Mechanics Conference August held February 10-14, 2013 in Kauai, Hawaii. Vol. 148 of Advances in the Astronautical Sciences, San Diego, California, American Astronautical Society, Univelt Inc., 2013, pp. 953–968Google Scholar
  21. 21.
    Lantoine, G., Broschart, S.B., Grebow, D.J., Design of Quasi-Terminator Orbits Near Primitive Bodies, AAS/AAIA Astrodynamics Specialist Conference, No. AAS 13-815. Hilton Head Island, South Carolina (2013)Google Scholar
  22. 22.
    Mondelo, J.M., Barrabés, E., Gómez, G., Ollé, M.: Numerical parametrization of libration point trajectories and their invariant manifolds. Adv. Astronaut. Sci. 129, 1153–1168 (2008)Google Scholar
  23. 23.
    Olikara, Z., Howell, K.: Computation of Quasi-Periodic Orbit Invariant Tori in the Restricted Three-Body Problem, AAS Spaceflight Mechanics Meeting, No. AAS 10-120. West Lafayette, Indiana (2010)Google Scholar
  24. 24.
    Kolemen, E., Kasdin, N.J., Gurfil, P.: Multiple Poincaré sections method for finding the quasiperiodic orbits of the restricted three body problem. Cel. Mech. Dyn. Astron. 112 (2012)Google Scholar
  25. 25.
    Villac, B.F.: Using FLI maps for preliminary spacecraft trajectory design in Multi-Body environments. Celest. Mech. Dyn. Astron. 102(1-3), 29–48 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Anderson, R.L., Lo, M.W.: Flyby Design using Heteroclinic and Homoclinic Connections of Unstable Resonant Orbits. In: Jah, M.K., Guo, Y., Bowes, A.L., Lai, P.C. (eds.) Spaceflight Mechanics: Proceedings of the 21st AAS/AIAA Space Flight Mechanics Meeting held February 13-17, 2011, New Orleans, Louisiana. Vol. 140 of Advances in the Astronautical Sciences, San Diego, California, American Astronautical Society, Univelt Inc., 2011, pp. 321–340Google Scholar
  27. 27.
    Anderson, R.L.: Approaching Moons from Resonance via Invariant Manifolds. 22nd AAS/AIAA Space Flight Mechanics Meeting, No. AAS 12-136, Charleston, South Carolina (2012)Google Scholar
  28. 28.
    Schlei, W.R., Howell, K.C., Tricoche, X.M., Garth, C.: Enhanced Visualization and Autonomous Extraction of Poincaré Map Topology. AAS/AIAA Astrodynamics Specialist Conference, No. AAS 13-903, Hilton Head Island, South Carolina (2013)Google Scholar
  29. 29.
    Nakhjiri, N., Villac, B.: Automated Stable Region Detection. AAS Spaceflight Mechanics Meeting, No. AAS 13-904, Irvine, California (2013)Google Scholar
  30. 30.
    Trumbauer, E.: Autonomous Trajectory Redesign for Phobos Orbital Operations. 24th AAS/AIAA Space Flight Mechanics Meeting, No. AAS 14-270, Santa Fe, New Mexico (2014)Google Scholar
  31. 31.
    Anderson, R.L., Parker, J.S.: Survey of ballistic transfers to the lunar surface. J. Guid. Control Dyn. 35, 1256–1267 (2012)CrossRefGoogle Scholar
  32. 32.
    Anderson, R.L., Parker, J.S.: Comparison of Low-Energy lunar transfer trajectories to invariant manifolds. Celest. Mech. Dyn. Astron. 115, 311–331 (2013)CrossRefGoogle Scholar
  33. 33.
    Parker, J.S., Anderson, R.L.: Targeting low-energy transfers to low lunar orbit. Acta Astronautica 84, 1-14 (2013)CrossRefGoogle Scholar
  34. 34.
    Parker, J.S., Anderson, R.L., Peterson, A.: Surveying ballistic transfers to low lunar orbit. J. Guid. Control. Dyn. 36(5), 1501–1511 (2013)CrossRefGoogle Scholar
  35. 35.
    Parker, J.S., Anderson, R.L.: Low-Energy Lunar Trajectory Design, Vol. 12 of JPL Deep Space Communications and Navigation Series, 1st edn. Wiley, Hoboken, New Jersey (2014)Google Scholar
  36. 36.
    Strange, N., Landau, D., McElrath, T., Lantoine, G., Lam, T., McGuire, M., Burke, L., Martini, M., Dankanish, J.: Overview of Mission Design for NASA Asteroid Redirect Robotic Mission Concept. 33rd International Electric Propulsion Conference, No. IPEC-2013-321, Washington, DC (2013)Google Scholar
  37. 37.
    Reeves, D.M., Naasz, B.J., Wright, C.A., Pini, A.J.: Proximity operations for the robotic boulder capture option for the asteroid redirect mission. AIAA SPACE 2014 Conference and Exposition, No. AIAA 2014-4433, San Diego, California (2014)Google Scholar
  38. 38.
    Brophy, J.R., Friedman, L., Strange, N.J., Prince, T.A., Landau, D., Jones, T., Schweickart, R., Lewicki, C., Elvis, M., Manzella, D.: Synergies of Robotic Asteroid Redirection Technologies and Human Space Exploration. 65th International Astronautical Congress, No. IAC-14.A5.3-B3.6.7,x26388, Toronto, Canada (2014)Google Scholar
  39. 39.
    Scheeres, D.J., Gaskell, R., Abe, S., Barnouin-Jha, O., Hashimoto, T., Kawaguchi, J., Kubota, T., Saito, J., Yoshikawa, M., Hirata, N., Mukai, T., Ishiguro, M., Kominato, T., Shirakawa, K., Uo, M.: The Actual Dynamical Environment About Itokawa. AIAA/AAS Astrodynamics Specialist Conference and Exhibit, No. AIAA 2006-6661, Keystone, Colorado (2006)Google Scholar
  40. 40.
    Busch, M.W., Ostro, S.J., Benner, L.A.M., Brozovic, M., Giorgini, J.D., Jao, J.S., Scheeres, D.J., Magri, C., Nolan, M.C., Howell, E.S., Taylor, P.A., Margot, J. -L., Brisken, W.: Radar observations and the shape of Near-Earth asteroid 2008 EV5. Icarus 212, 649–660 (2011)CrossRefGoogle Scholar
  41. 41.
    Llanos, P.J., Miller, J.K., Hintz, G.R.: Orbital Evolution and Environmental Analysis Around Asteroid 2008 EV5, No. AAS 14-360 (2014)Google Scholar
  42. 42.
    Markellos, V.V., Roy, A.E., Velgakis, M.J., Kanavos, S.S.: A photogravitational Hill problem and radiation effects on hill stability of orbits. Astrophys. Space Sci. 271, 293–301 (2000)CrossRefzbMATHGoogle Scholar
  43. 43.
    Werner, R.A., Scheeres, D.J.: Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Cel. Mech. Dyn. Astron. 65, 313–344 (1996/1997)Google Scholar
  44. 44.
    Colombi, A., Hirani, A., Villac, B.: Adaptive gravitational force representation for fast trajectory propagation near small bodies. J. Guid. Control. Dyn. 31(4), 1041–1051 (2008)CrossRefGoogle Scholar
  45. 45.
    Vallado, D.A.: Fundamentals of astrodynamics and applications microcosm press (2007)Google Scholar
  46. 46.
    Sternberg, S.: Dynamical systems Dover publications (2010)Google Scholar
  47. 47.
    Doedel, E.: AUTO software for continuation and bifurcation problems in ordinary differential equations, ”http://indy.cs.concordia.ca/auto/
  48. 48.
    Markellos, V.V., Black, W., Moran, P.E.: A grid search for families of periodic orbits in the restricted problem of three bodies. Cel. Mech. 9, 507–512 (1974)CrossRefzbMATHGoogle Scholar
  49. 49.
    Roy, A.E., Ovenden, M.W.: On the occurrence of commensurable mean motions in the solar system. The mirror theorem. Mon. Not. R. Astron. Soc. 115(3), 296–309 (1955)CrossRefzbMATHGoogle Scholar
  50. 50.
    Miele, A.: Theorem of image trajectories in the Earth-Moon space. Astronaut. Acta 6(51), 225–232 (1960)zbMATHGoogle Scholar
  51. 51.
    Howell, K.C., Breakwell, J.V.: Three-Dimensional, Periodic, ‘Halo’ orbits. Celest. Mech. 32, 53–71 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Marchand, B.G., Howell, K.C., Wilson, R.S.: Improved Corrections Process for Constrained Trajectory Design in the n-Body Problem. J. Spacecr. Rocket. 44, 884-894 (2007)CrossRefGoogle Scholar
  53. 53.
    Nakhjiri, N., Villac, B.: Automated stable region generation, detection, and representation for applications to mission design, Celestial Mechanics and Dynamical Astronomy, Published online 25 June 2015Google Scholar
  54. 54.
    Nilsson, N., Intelligence, Artificial: A new synthesis san francisco: Morgan kaufmann (1998)Google Scholar
  55. 55.
    Bürk, I.: Spectral Clustering. Bachelor thesis, Universität Stuttgart (2012). Available online on Matlab central (file ID File ID: #34412)Google Scholar
  56. 56.
    Smith, P.H., Rizk, B., Kinney-Spano, E., Fellows, C., D’Aubigny, C., Merrill, C.: The OSIRIS-REx Camera Suite (OCAMS). 44th Lunar and Planetary Science Conference, The Woodlands, TX (2013)Google Scholar
  57. 57.
    Scheeres, D.J.: Close Proximity Operations for Implementing Mitigation Strategies. 2004 Planetary Defense Conference: Protecting Earth from Asteroids, No. AIAA-2004-1445, Orange County, CA (2004)Google Scholar
  58. 58.
    Pini, A.J.: Investigation of the Effect of Repeat Orbits on GRACE Gravity Recovery. Master’s thesis, The University of Texas at Austin (2012)Google Scholar
  59. 59.
    Gunter, B.: Computational Methods and Processing Strategies for Estimating Earth’s Gravity Field. PhD thesis, The University of Texas at Austin (2004)Google Scholar
  60. 60.
    Gaskell, R.W., Barnouin-Jha, O.S., Scheeres, D.J., Konopliv, A.S., Mukai, T., Abe, S., Saito, J., Ishiguro, M., Kubota, T., Hashimoto, T., Kawaguchi, J., Yoshikawa, M., Shirakawa, K., Kominato, T., Hirata, N., Demura, H.: Characterizing and navigating small bodies with imaging data. Meteorics Planet. Sci. 43, 1049–1061 (July 2008)Google Scholar

Copyright information

© American Astronautical Society 2016

Authors and Affiliations

  • Benjamin F. Villac
    • 1
  • Rodney L. Anderson
    • 2
  • Alex J. Pini
    • 3
  1. 1.Pr. Systems Engineer, a.i.solutions, Inc.LanhamUSA
  2. 2.Technologist, Jet Propulsion Laboratory, California Institute of TechnologyPasadenaUSA
  3. 3.Systems Engineer, a.i.solutions, Inc.GreenbeltUSA

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