Skip to main content
SpringerLink
Log in

Perturbed Periodic Orbits as Landing Solutions with an Abort Option at Europa

  • Original Article
  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

Moons of the outer planets harbor great treasures of science, but landing on these bodies to study them up-close is a very difficult task. Two characteristics of an approach-trajectory that would help enable such a mission are: (1) the spacecraft can observe its target site prior to landing, and (2) the spacecraft can abort the landing in the event of a problem and easily come back later. Each of these requirements relies on repeatability in the multi-body problem, which is non-trivial to achieve. In the current work, stable and nearly-stable periodic orbits about Europa which offer solutions to the problem of repeatability for landing are studied. 17 total solutions are identified in a perturbed three-body problem which accounts for \(J_2\) and \(C_{22}\) of Europa.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Bury, L., McMahon, J.: Landing trajectories to moons from the unstable invariant manifolds of periodic libration point orbits. In: AIAA SciTech, Orlando, FL, pp. 1–12 (2020). https://doi.org/10.2514/6.2020-2181

  2. Beksinski, Jr., D.E.: Abort trajectories for manned lunar missions. Ph.D. thesis, University of Maryland (2007). https://hdl.handle.net/1903/4270

  3. Huang, W., Xi, X., Wang, W.: Characteristic analysis and design of near moon abort trajectory for manned lunar landing mission. Sci. China Technol. Sci. 53(11), 3129–3137 (2010). https://doi.org/10.1007/s11431-010-4118-x

    Article  MATH  Google Scholar 

  4. Senent, J.S.: Fast calculation of abort return trajectories for manned missions to the Moon. In: AIAA/AAS Astrodynamics Specialists Conference, AIAA 2010-8132 (2010). https://doi.org/10.2514/6.2010-8132

    Article  Google Scholar 

  5. Xi, X.N., Huang, W.D., Wang, W.: Review on abort trajectory for manned lunar landing mission. Sci. China Technol. Sci. 53(10), 2691–2698 (2010). https://doi.org/10.1007/s11431-010-4092-3

    Article  Google Scholar 

  6. Jesick, M.: Abort options for human missions to earth-moon halo orbits. In: AAS Astrodynamics Specialists Conference, pp. 1–21 (2011)

  7. Paskowitz, M.E., Scheeres, D.J.: Design of science orbits about planetary satellites: application to Europa. J. Guid. Control. Dyn. 29(5), 1147–1158 (2006). https://doi.org/10.2514/1.19464

    Article  Google Scholar 

  8. Lara, M., Russell, R., Villac, B.: Classification of the distant stability regions at Europa. J. Guid. Control. Dyn. 30(2), 409–418 (2007). https://doi.org/10.2514/1.22372

    Article  Google Scholar 

  9. Lara, M., Russell, R.: Computation of a science orbit about Europa. J. Guid. Control. Dyn. 30(1), 259–263 (2007). https://doi.org/10.2514/1.22493

    Article  Google Scholar 

  10. Lara, M.: Simplified equations for computing science orbits around planetary satellites. J. Guid. Control. Dyn. 31(1), 172–181 (2008). https://doi.org/10.2514/1.31107

    Article  Google Scholar 

  11. Bury, L., McMahon, J.: The effect of zonal harmonics on dynamical structures in the circular restricted three-body problem near the secondary body. Celest. Mech. Dyn. Astron. 132, 45 (2020). https://doi.org/10.1007/s10569-020-09983-3

  12. Burša, M.: Figure and dynamic parameters of synchronously orbiting satellites in the solar system. Bull. Astron. Inst. Czechoslov. 40(2), 125–130 (1989)

    Google Scholar 

  13. Roy, A.E.: Orbital Motion, 4th edn. Institute of Physics Publishing, Bristol (2005)

    MATH  Google Scholar 

  14. Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Dynamical Systems, the Three-Body Problem, and Space Mission Design. Marsden Books, Karori (2006)

    MATH  Google Scholar 

  15. Williams, D.R.: Jovian satellite fact sheet. In: NSSDCA, NASA Goddard Space Flight Center (2018). https://nssdc.gsfc.nasa.gov/planetary/factsheet/joviansatfact.html

  16. Russell, R.P., Lara, M.: Repeat ground track lunar orbits in the full-potential plus third-body problem. In: AIAA/AAS Astrodynamics Specialist Conference, Keystone, Colorado (2006). https://doi.org/10.2514/6.2006-6750

  17. Broucke, R.: Stability of periodic orbits in the elliptic, restricted three-body problem. AIAA J. 7(6), 1003–1009 (1969). https://doi.org/10.2514/3.5267

    Article  MATH  Google Scholar 

  18. Szebehely, V.: Theory of Orbits—The Restricted Problem of Three Bodies. Academic Press, New York (1967)

    MATH  Google Scholar 

  19. Restrepo, R.L.: Patched periodic orbits: a systematic strategy for low-energy trajectory and moon tour design. Ph.D. thesis (2018)

  20. Lo, M.: Low-energy interplanetary transfers using Lagrangian points: transport throughout the solar system using the invariant manifolds of unstable orbits generated by the Lagrange points. Filed New Technology Report NPO-20377. Tech. rep. (1999)

  21. Lo, M.W., Ross, S.D.: Low energy interplanetary transfers using invariant manifolds of L1, L2, and Halo orbits. In: NASA Tech Brief, vol. 23 (1999). https://doi.org/10.1038/517528a

  22. Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics. Chaos 10(2), 427–469 (2000). https://doi.org/10.1063/1.166509

    Article  MathSciNet  MATH  Google Scholar 

  23. Gómez, G., Koon, W.S., Lo, M.W., Marsden, J.E., Masdemont, J., Ross, S.D.: Connecting orbits and invariant manifolds in the spatial restricted three-body problem. Nonlinearity 17, 1571–1606 (2004). https://doi.org/10.1088/0951-7715/17/5/002

    Article  MathSciNet  MATH  Google Scholar 

  24. Parker, J.S.: Low-energy ballistic lunar transfers. Ph.D. thesis, University of Colorado Boulder (2007)

  25. Russell, R.P., Lam, T.: Designing ephemeris capture trajectories at Europa using unstable periodic orbits. J. Guid. Control. Dyn. 30(2), 11–13 (2007). https://doi.org/10.2514/1.22985

    Article  Google Scholar 

  26. Anderson, R.L., Lo, M.W.: Role of invariant manifolds in low-thrust trajectory design. J. Guid. Control. Dyn. 32(6), 1921–1930 (2009). https://doi.org/10.2514/1.37516

    Article  Google Scholar 

  27. Davis, K.E., Anderson, R.L., Scheeres, D.J., Born, G.H.: The use of invariant manifolds for transfers between unstable periodic orbits of different energies. Celest. Mech. Dyn. Astron. 107(4), 471–485 (2010). https://doi.org/10.1007/s10569-010-9285-3

    Article  MathSciNet  MATH  Google Scholar 

  28. Anderson, R.L., Parker, J.S.: Comparison of low-energy lunar transfer trajectories to invariant manifolds. Celest. Mech. Dyn. Astron. 115, 311–331 (2013). https://doi.org/10.1007/s10569-012-9466-3

    Article  MATH  Google Scholar 

  29. Parker, J.S., Anderson, R.L., Simon, M.K.: Low-Energy Lunar Trajectory Design, Deep Space Communications and Navigation Systems Center of Excellence. Jet Propulsion Laboratory, Pasadena (2013)

  30. Anderson, R.L., Lo, M.W.: Spatial approaches to moons from resonance relative to invariant manifolds. Acta Astronaut. 105(1), 355–372 (2014). https://doi.org/10.1016/j.actaastro.2014.09.015

    Article  Google Scholar 

  31. Anderson, R.L.: Approaching moons from resonance via invariant manifolds. J. Guid. Control Dyn. (2015). https://doi.org/10.2514/1.G000286

    Article  Google Scholar 

  32. Hernandez, S., Restrepo, R.L., Anderson, R.L.: Connecting resonant trajectories to a Europa capture through Lissajous staging orbits. In: AAS/AIAA Astrodynamics Specialists Conference, Maui, HI (2019)

  33. Sharma, R.K., Rao, P.V.S.: Collinear Equilibria and Their Characteristic Exponents in the Restricted Three-Body Problem When the Primaries are Oblate Spheroids. Applied Mathematics Division, Vikram Sarabhai Space Centre (1974)

  34. Bhatnagar, K.B., Hallan, P.P.: Effect of perturbed potentials on the stability of libration points in the restricted problem. Celest. Mech. 20, 95–103 (1979). https://doi.org/10.1007/BF01230231

    Article  MathSciNet  MATH  Google Scholar 

  35. Elshaboury, S.M.: The equilibrium solutions of restricted problem of three axisymmetric rigid bodies. Earth Moon Planet. 45, 205–211 (1989). https://doi.org/10.1007/BF00057743

    Article  MATH  Google Scholar 

  36. Arredondo, J.A., Guo, J., Stoica, C., Tamayo, C.: On the restricted three body problem with oblate primaries. Astrophys. Space Sci. 341(2), 315–322 (2012). https://doi.org/10.1007/s10509-012-1085-7

    Article  MATH  Google Scholar 

  37. Sharma, R.K.: Periodic orbits of collision in the restricted problem of three bodies, when the bigger primary is slowly rotating oblate spheroid. Indian Natl. Sci. Acad. 5(2) (1972)

  38. Sharma, R.K.: Periodic orbits of collision in the restricted problem of three bodies in a three-dimensional coordinate system, when the bigger primary is an oblate spheroid. Indian Natl. Sci. Acad. 5(2) (1972)

  39. Sharma, R.K.: Periodic orbits of collision in the restricted problem of three bodies, when the bigger primary is an oblate spheroid. Indian Natl. Sci. Acad. 4(4) (1972)

  40. Mittal, A., Ahmad, I., Bhatnagar, K.B.: Periodic orbits generated by Lagrangian solutions of the restricted three body problem when one of the primaries is an oblate body. Astrophys. Space Sci. 319(1), 63–73 (2009). https://doi.org/10.1007/s10509-008-9942-0

    Article  MATH  Google Scholar 

  41. Abouelmagd, E.I., Asiri, H.M., Sharaf, M.A.: The effect of oblateness in the perturbed restricted three-body problem. Meccanica 48(10), 2479–2490 (2013). https://doi.org/10.1007/s11012-013-9762-3

    Article  MathSciNet  MATH  Google Scholar 

  42. Abouelmagd, E.I., Alhothuali, M.S., Guirao, J.L., Malaikah, H.M.: Periodic and secular solutions in the restricted three-body problem under the effect of zonal harmonic parameters. Appl. Math. Inf. Sci. 9(4), 1659–1669 (2015)

    MathSciNet  Google Scholar 

  43. Salazar, F., Alkhaja, A., Fantino, E., Alessi, E.M.: Science orbits in the Saturn-Enceladus circular restricted three-body problem with oblate primaries. Acta Astronaut. 180, 398–416 (2021). https://doi.org/10.1016/j.actaastro.2020.12.045

    Article  Google Scholar 

  44. Markellos, V.V., Douskos, C.N., Dimitriadis, K.P., Perdios, E.A.: Lyapunov orbits and asymptotic connections in the hill problem with oblateness. In: Recent Advances in Mechanics and Related Fields, Volume in Honour of Prof. Constantine L. Goudas (2004)

  45. Bury, L., McMahon, J., Lo, M.: A study of periodic orbits near Europa. Celest. Mech. Dyn. Astron. 134, 27 (2022). https://doi.org/10.1007/s10569-022-100

  46. Restrepo, R.L., Russell, R.P.: A database of planar axisymmetric periodic orbits for the solar system. Celest. Mech. Dyn. Astron. 130(7), 1–24 (2018). https://doi.org/10.1007/s10569-018-9844-6

    Article  MathSciNet  MATH  Google Scholar 

  47. Bury, L., McMahon, J., Lo, M.: Low-energy boundaries on vertical motion near the secondary body. Submitted to J. Astronaut. Sci. (2021)

  48. Hénon, M.: Generating Families in the Restricted Three-Body Problem. Springer, Berlin (1997)

    MATH  Google Scholar 

  49. Howell, K.C.: Three-dimensional, periodic, ‘halo’ orbits. Celest. Mech. 32(1), 53–71 (1984). https://doi.org/10.1007/BF01358403

    Article  MathSciNet  MATH  Google Scholar 

  50. The Math Works Inc.: MATLAB R2021a (2021)

  51. Bury, L., McMahon, J., Lo, M.W.: Periodic orbits as viable landing solutions with an abort option at Europa. In: AAS Astrodynamics Specialists Conference, Big Sky, MT, pp. 1–18 (2021)

  52. Lara, M., San Juan, J.F.: Dynamic behavior of an orbiter around Europa. J. Guid. Control. Dyn. 28(2), 291–297 (2005). https://doi.org/10.2514/1.5686

    Article  Google Scholar 

Download references

Funding

Part of this research was carried out at the University of Colorado at Boulder under a NASA Space Technology Research Fellowship (80NSSC18K1183). Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NSSC18K1183).

Author information

Authors and Affiliations

  1. Colorado Center for Astrodynamics Research, University of Colorado Boulder, Aerospace Engineering Sciences Building, 3775 Discovery Dr, Boulder, CO, 80303, USA

    Luke Bury

  2. Colorado Center for Astrodynamics Research, University of Colorado Boulder, Office 461, Aerospace Engineering Sciences Building, 3775 Discovery Dr, Boulder, CO, 80303, USA

    Jay McMahon

  3. Jet Propulsion Laboratory, California Institute of Technology, M/S 301-121, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA

    Martin Lo

Authors
  1. Luke Bury
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jay McMahon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martin Lo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luke Bury.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bury, L., McMahon, J. & Lo, M. Perturbed Periodic Orbits as Landing Solutions with an Abort Option at Europa. J Astronaut Sci 69, 1493–1513 (2022). https://doi.org/10.1007/s40295-022-00359-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40295-022-00359-3

Keywords

Search

Navigation