Advertisement

Astrophysics and Space Science

, 363:253 | Cite as

A review of low-energy transfers

  • Pooja DuttEmail author
Review Article
  • 104 Downloads

Abstract

Low-energy transfers (LET) for lunar and interplanetary missions has received immense attention of the scientific community during the last few decades as its importance was understood by the success of JAXA’s Hiten, ESA’s SMART-1, NASA’s GRAIL and ARTHEMIS missions, and several proposals, like the BepiColombo, Multi-Moon Orbiter and Europa Orbiter. In this paper the developments in the area of LET and low-thrust trajectories are reviewed. Starting with the basics of the restricted three-body problem and its use in finding invariant manifolds in phase space, the design of LET trajectories and optimisation methods used to find optimal LET and low-thrust transfers is discussed.

Keywords

Weak stability boundary Ballistic capture Low thrust Invariant manifolds Optimisation methods Phase space Restricted three-body problem 

Notes

Acknowledgements

The author is working in Vikram Sarabhai Space Centre (VSSC) and registered for Ph.D. at Indian Institute of Space Science and Technology (IIST). She would like to acknowledge the support provided by VSSC and IIST in carrying out this research work. The author also acknowledges the support and motivation given by Dr. A.K. Anilkumar, Head APMD, VSSC, Shri Abhay Kumar, Group Director AFDG, VSSC, Shri S. Pandian, Deputy Director AERO Entity, VSSC and Dr. Raju K. George, Dean (R&D), IIST. The author is thankful to the reviewers for constructive review comments and the editor for his support, which has helped in bringing this paper to the present form.

References

  1. Alessi, E.M., Gómez, G., Marsdemont, J.J.: Leaving the Moon by means of invariant manifolds of libration-point orbits. Commun. Nonlinear Sci. Numer. Simul. 14, 4153–4167 (2009a) ADSMathSciNetzbMATHGoogle Scholar
  2. Alessi, E.M., Gómez, G., Marsdemont, J.J.: Transfer orbits in the Earth–Moon system and refinement to JPL ephemerides. In: 21st International Symposium on Space Flight Dynamics, Toulouse, France (2009b) Google Scholar
  3. Alessi, E.M., Gómez, G., Marsdemont, J.J.: Two-manoeuvres transfers between LEOs and Lissajous orbits in the Earth–Moon system. Adv. Space Res. 45, 1276–1291 (2010) ADSGoogle Scholar
  4. Anderson, R.L., Lo, M.W.: The role of invariant manifolds in low thrust trajectory design (Part II). AIAA Paper 2004-5305 (2004) Google Scholar
  5. Anderson, R.L., Lo, M.W.: Role of invariant manifolds in low thrust trajectory design. J. Guid. Control Dyn. 32(6), 1921–1930 (2009) ADSGoogle Scholar
  6. Anderson, R.L., Parker, J.S.: Comparison of low-energy lunar transfer trajectories to invariant manifolds. In: AAS/AIAA Astrodynamics Specialist Conference, Girdwood, AK, 31 July–4 Aug. (2011). AAS Paper 11-423 Google Scholar
  7. Assadian, N., Pourtakdoust, S.H.: Multiobjective genetic optimization of Earth–Moon trajectories in the restricted four-body problem. Adv. Space Res. 45, 398–409 (2010) ADSGoogle Scholar
  8. Belbruno, E.A.: Lunar capture orbits, a method of constructing Earth–Moon trajectories and the Lunar GAS mission. In: Proceedings of AIAA/DGLR/JSASS, Inter Propl. Conf. (1987). AIAA Paper No. 87-1054 Google Scholar
  9. Belbruno, E.: Examples of nonlinear dynamics of ballistic capture and escape in the Earth–Moon system. In: Proc. Annual Astrodyn. Conf. (1990). AIAA Paper No. 90-2896 Google Scholar
  10. Belbruno, E.A.: Capture Dynamics and Chaotic Dynamics in Celestial Mechanics. Princeton University Press, Princeton (2004) zbMATHGoogle Scholar
  11. Belbruno, E.A.: A low energy lunar transportation system using chaotic dynamics. AAS 05-382 (2005) Google Scholar
  12. Belbruno, E.A.: Fly Me to the Moon: An Insider’s Guide to the New Science of Space Travel, pp. 55–63. Princeton University Press, Princeton (2007). Chap. 9 zbMATHGoogle Scholar
  13. Belbruno, E.A., Carrico, J.P.: Calculation of weak stability boundary ballistic lunar transfer trajectories. In: AIAA/AAS Astrodynamics Specalist Conference (2000). AIAA 2000-4142 Google Scholar
  14. Belbruno, E.A., Marsden, B.: Resonance hopping in comets. Astron. J. 113, 1433–1444 (1997) ADSGoogle Scholar
  15. Belbruno, E.A., Miller, J.K.: Sun perturbed Earth-to-Moon transfers with ballistic capture. J. Guid. Control Dyn. 16(4), 770–775 (1993) ADSGoogle Scholar
  16. Belbruno, E.A., Humble, R., Coil, J.: Ballistic capture lunar transfer determination for the U.S. Air Force Acadamy Blue Moon mission. AAS 97-171 (1997) Google Scholar
  17. Belbruno, E.A., Topputo, F., Gidea, M.: Resonance transitions associated to weak capture in the restricted three-body problem. Adv. Space Res. 42, 1330–1351 (2008) ADSGoogle Scholar
  18. Biesbroek, R., Ancarola, B.P.: Study of genetic algorithms settings for trajectory optimization. IAC-03-A.P.30, Oct. 2003 Google Scholar
  19. Biesbroek, R., Janin, G.: Ways to the Moon? ESA Bull. 103, 92–99 (2000) Google Scholar
  20. Biesbroek, R., Ockels, W., Janin, G.: Optimization of weak stability boundary orbits from GTO to the Moon using genetic algorithms. IAF-99-A.6.10, Amsterdam (1999) Google Scholar
  21. Bollt, E.M., Meiss, J.D.: Controlling chaotic transport through recurrence. Physica D 81(3), 280–294 (1995) ADSzbMATHGoogle Scholar
  22. Brunini, A.: On the satellite capture problem Capture and stability regions for planeatry satellites. Celest. Mech. Dyn. Astron. 64, 79–92 (1996) ADSzbMATHGoogle Scholar
  23. Cabette, R.E.S., Prado, A.F.B.A.: Transfer orbits to/from the Lagrangian points in the restricted four-body problem. Acta Astronaut. 63(11–12), 1221–1232 (2008) ADSGoogle Scholar
  24. Campagnola, S., Lo, M.: BepiColombo gravitational capture and the elliptic restricted three-body problem. PAMM 7, 1030905–1030906 (2007) Google Scholar
  25. Canalias, E., Masdemont, J.J.: Computing natural transfers between Sun–Earth and Earth–Moon Lissajous libration point orbits. Acta Astron. 63, 238–248 (2008) Google Scholar
  26. Capuzzo-Dolcetta, R., Giancotti, M.: A study of low-energy transfer orbits to the Moon: towards an operational optimization technique. Celest. Mech. Dyn. Astron. 115(3), 215–232 (2013) ADSMathSciNetzbMATHGoogle Scholar
  27. Castellà, E., Jorba, Á.: On the vertical families of two-dimensional Tori near the triangular points of the bicircular problem. Celest. Mech. Dyn. Astron. 76, 35–54 (2000) ADSMathSciNetzbMATHGoogle Scholar
  28. Castillo, A., Bello, M., Gonzalez, J.A., Janin, G., Graziani, F., Teofilatto, P., Circi, C.: Use of weak stability boundary trajectories for planetary capture, IAF-03-A.P.31. In: 54th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law, 29 Sep–3 Oct 2003, Bremen, Germany (2003) Google Scholar
  29. Chung, M.J., Hatch, S.J., Kangas, J.A., Long, S.M., Roncoli, R.B., Sweetser, T.H.: Trans-lunar cruise trajectory design of GRAIL (Gravity Recovery and Interior Laboratory) mission. In: Proc. AIAA Guidance, Navigation and Control Conference, Toronto, Ontario, Canada, 2–5 Aug. (2010). AIAA 2010-8384 Google Scholar
  30. Circi, C., Teofilatto, P.: On the dynamics of weak stability boundary lunar transfers. Celest. Mech. Dyn. Astron. 79, 41–72 (2001) ADSzbMATHGoogle Scholar
  31. Circi, C., Teofilatto, P.: Weak Stability boundary trajectories for the deployment of lunar spacecraft constellations. Celest. Mech. Dyn. Astron. 95, 371–390 (2006) ADSMathSciNetzbMATHGoogle Scholar
  32. Coffee, T.M., Anderson, R.L., Lo, M.W.: Multiobjective optimization of low-energy trajectories using optimal control on dynamical channels (Part-1). AAS 11-129 (2011) Google Scholar
  33. Conley, C.: Low energy transit orbits in the restricted three body problem. SIAM J. Appl. Math. 16(4), 732–746 (1968) MathSciNetzbMATHGoogle Scholar
  34. Dachwald, B.: Low Thrust Trajectory Optimization and Interplanetary Mission Analysis Using Evolutionary Neurocontrol. Deutscher Luft- und Raumfahrtkongress, Dresden (2004) Google Scholar
  35. Demeyer, J., Gurfil, P.: Transfer to distant retrograde orbits using manifold theory. J. Guid. Control Dyn. 30(5), 1261–1267 (2007) ADSGoogle Scholar
  36. Dutt, P., Anilkumar, A.K., George, R.K.: Dynamics of weak stability boundary transfer trajectories to the Moon. Astrophys. Space Sci. 361(11), 1–12 (2016) MathSciNetGoogle Scholar
  37. Dutt, P., Anilkumar, A.K., George, R.K.: Design and analysis of weak stability boundary trajectories to the Moon. Astrophys. Space Sci. 363, 161 (2018a) ADSMathSciNetGoogle Scholar
  38. Dutt, P., Anilkumar, A.K., George, R.K.: Analysis of weak stability boundary transfers from Earth to Mars. J. Spacecr. Rockets (2018b, accepted).  https://doi.org/10.2514/1.A34193
  39. Egorov, V.A.: Certain problems of moon flight dynamics. In: The Russian Literature of Satellites, Part 1. International Physical Index, New York (1958) Google Scholar
  40. Fantino, E., Gómez, G., Masdemont, J.J., Ren, Y.: A note on libration point orbits, temporary capture and low-energy transfers. Acta Astronaut. 67, 1038–1052 (2010) ADSGoogle Scholar
  41. Farquhar, R.W.: The control and use of libration-point satellites. Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, California (1968) Google Scholar
  42. Folta, D., Woodard, M., Sweetser, T., Broschart, S.B., Cosgrove, D.: Design and implementation of the ARTEMIS lunar transfer using multi-body dynamics. AAS 11-511 (2011) Google Scholar
  43. García, F., Gómez, G.: A note on weak stability boundaries. Celest. Mech. Dyn. Astron. 97, 87–100 (2007) ADSMathSciNetzbMATHGoogle Scholar
  44. Gómez, G., Masdemont, J.: Some zero cost transfers between libration point orbits. In: AAS/AIAA Space Flight Mechanics Meeting, Clearwater, Florida (2000). Paper No. AAS 00-177 Google Scholar
  45. Gómez, G., Jorba, A., Masdemont, J., Simo, C.: Study of the transfer from the Earth to a Halo orbit around the equilibrium point \(L_{1}\). Celest. Mech. Dyn. Astron. 56(4), 541–562 (1992) ADSzbMATHGoogle Scholar
  46. 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) ADSMathSciNetzbMATHGoogle Scholar
  47. Graziani, F., Teofilatto, P., Circi, C., Porfilio, M., Mora, M.B., Hechler, M.: A strategy to find weak stability boundary lunar transfers. In: AIAA (2000) Google Scholar
  48. Griesemer, P.R., Ocampo, C., Cooley, D.S.: Targeting ballistic lunar capture trajectories using periodic orbits. J. Guid. Control Dyn. 34(3), 893–902 (2011) ADSGoogle Scholar
  49. Grover, P., Andersson, C.: Optimized three-body gravity assists and manifold transfers in end-to-end lunar mission design. AAS 12-184 (2012) Google Scholar
  50. Gurfil, P., Kasdin, N.J.: Characterization and design of out-of-ecliptic trajectories using deterministic crowding genetic algorithms. Comput. Methods Appl. Mech. Eng. 191, 2141–2158 (2002) MathSciNetzbMATHGoogle Scholar
  51. Hatch, S.J., Roncoli, R.B., Sweetser, T.H.: GRAIL trajectory design: lunar orbit insertion through science. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference, Aug 2–5, 2010, Toronto, Ontario (2010). Paper AIAA 2010-8385 Google Scholar
  52. Heaton, A.F., Strange, N.J., Longuski, J.M., Bonfiglio, E.P.: Automated design of the Europa Orbiter Tour. J. Spacecr. Rockets 39(1), 17–22 (2002) ADSGoogle Scholar
  53. Heppenheimer, T.A.: Colonies in Space: Take an Expedition to Dream Cities in the Stars. Warner, Los Angeles (1978a) Google Scholar
  54. Heppenheimer, T.A.: A mass-catcher for large-scale lunar material transport. J. Spacecr. Rockets 15, 242–249 (1978b) ADSGoogle Scholar
  55. Howell, K.C.: Three-dimensional, periodic, ‘halo orbits’. Celest. Mech. 32, 53 (1984) ADSMathSciNetzbMATHGoogle Scholar
  56. Howell, K.C., Mains, D.L., Barden, B.T.: Transfer trajectories from Earth parking orbits to Sun Earth halo orbits. In: AAS/AIAA Space Flight Mechanics Meeting, Cocoa Beach, Florida (1994). Paper No. AAS 94-160 Google Scholar
  57. Howell, K.C., Barden, B., Lo, M.: Application of dynamical systems theory to trajectory design for a libration point mission. J. Astronaut. Sci. 45(2), 161–178 (1997) MathSciNetGoogle Scholar
  58. Huang, T.-Y., Innanen, K.A.: The gravitational escape/capture of planetary satellites. Astron. J. 88, 1537–1548 (1983) ADSGoogle Scholar
  59. Hunter: Motions of satellites and asteroids under the influence of Jupiter and the Sun: I. Stable and unstable satellite orbits. Mon. Not. R. Astron. Soc. 136(3), 245–265 (1967) ADSGoogle Scholar
  60. Ivashkin, V.V.: On trajectories of the Earth–Moon flight of a particle with its temporary capture by the Moon. Dokl. Phys. 47(11), 825–827 (2002) ADSMathSciNetGoogle Scholar
  61. Ivashkin, V.V.: On particle’s trajectories of Moon-to-Earth space flights with the Gravitational escape from the lunar attraction. Dokl. Phys. 49(9), 539–542 (2004) ADSGoogle Scholar
  62. Jehn, R., Campagnola, S., Garcia, D., Kemble, S.: Low thrust approach and gravitational capture at mercury. In: 18th International Symposium on Space Flights Dynamics, Munich, Germany, 11–15 Oct. (2004) Google Scholar
  63. Jehn, R., Companys, V., Corral, C., Yarnoz, D.G., Sanchez, N.: Navigating BepiColombo during the weak stability capture at Mercury. Adv. Space Res. 42, 1364–1369 (2008) ADSGoogle Scholar
  64. Johannesen, J.R., D’Amario, L.A.: Europa Orbiter mission trajectory design. AAS Paper 99-360 (1999) Google Scholar
  65. Jorba, Á.: A numerical study on the existence of stable motions near the triangular points of the real Earth–Moon system. Astron. Astrophys. 364(1), 327–338 (2000) ADSMathSciNetGoogle Scholar
  66. Kawaguchi, J., Yamakawa, H., Uesugi, T., Matsuo, H.: On making use of lunar and solar gravity assists in LUNAR-A, PLANET-B missions. Acta Astronaut. 35(9–11), 633–642 (1995) ADSGoogle Scholar
  67. Kluever, C.A.: Optimal Earth–Moon trajectories using combined chemical–electric propulsion. J. Guid. Control Dyn. 20(2), 253–258 (1997) ADSzbMATHGoogle Scholar
  68. Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Dynamical Systems, the Three-Body Problem and Space Mission. Mission Design Book Online (2006) zbMATHGoogle Scholar
  69. Krish, V.: An investigation into critical aspects of a new form of low energy lunar transfer, the Belbruno–Miller trajectories. M.Sc. Thesis, Massachusetts Institute of Technology (1991) Google Scholar
  70. Kulkarni, T.R., Mortari, D.: Low energy interplanetary transfers using halo orbit hopping method with STK/Astrogator. AAS 05-111 (2005) Google Scholar
  71. Lantoine, G., Russell, R.P., Campagnola, S.: Optimization of low-energy resonant hopping transfers between planetary moons. IAC-09.C1.1.1 (2009) Google Scholar
  72. Lee, K.H.: Lunar orbiter trade study and conceptual design of onboard propulsion systems. J. Spacecr. Rockets 48(2), 346–354 (2011) ADSGoogle Scholar
  73. Li, M., Zheng, J.: Indirect transfer to the Earth–Moon L1 libration point. Celest. Mech. Dyn. Astron. 108, 203–213 (2010) ADSMathSciNetzbMATHGoogle Scholar
  74. Liang, Y., Xu, M., Xu, S.: The classification of cislunar trajectories and its applications in Earth–Moon system. Astrophys. Space Sci. 361, 5 (2016) ADSMathSciNetGoogle Scholar
  75. Liang, Y., Xu, M., Xu, S.: The cislunar polygonal-like periodic orbit: construction, transition and its application. Acta Astronaut. 133, 282–301 (2017) ADSGoogle Scholar
  76. Lin, M., Xu, M., Fu, X.: GPU-accelerated computing for Lagrangian coherent structures of multi-body gravitational regimes. Astrophys. Space Sci. 362(4), 66 (2017) ADSMathSciNetGoogle Scholar
  77. Liu, C.B., Hou, X.Y., Liu, L.: Transfer from the Earth to a Lissajous orbit around the collinear libration point by Lunar swing-by. Adv. Space Res. 40, 76–82 (2007) ADSGoogle Scholar
  78. Lizia, P.D., Radice, G., Izzo, D., Vasile, M.: On the solution of interplanetary trajectory design problems by global optimisation methods. In: Proceedings of GO, pp. 1–7 (2005) Google Scholar
  79. Llibre, J., Martinez, R., Simo, C.: Transversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near L2 in the restricted three-body problem. J. Differ. Equ. 58, 104–156 (1985) ADSzbMATHGoogle Scholar
  80. Lo, M.W., Chung, M.K.: Lunar Sample return via the interplanetary superhighway. In: AIAA/AAS Astrodynamics Specialist Meeting, Monterey, CA (2002). Paper No. AIAA 2002-4718 Google Scholar
  81. Lo, M.W., Parker, J.S.: Chaining simple periodic three body orbits. AAS 05-380 (2005) Google Scholar
  82. Lo, M.W., Anderson, R.L., Whiffen, G., Romans, L.: The role of invariant manifolds in low thrust trajectory design (Part I). AAS Paper 04-288 (2004) Google Scholar
  83. Luo, Y.Z., Tang, G.J., Li, H.Y.: Optimization of multiple-impulse minimum-time rendezvous with impulse constraints using a hybrid genetic algorithm. Aerosp. Sci. Technol. 10(6), 534–540 (2006) zbMATHGoogle Scholar
  84. Luo, Y.Z., Lei, Y.J., Tang, G.J.: Optimal multi-objective nonlinear impulsive rendezvous. J. Guid. Control Dyn. 30(4), 994–1002 (2007) ADSGoogle Scholar
  85. Markellos, V.V.: Numerical investigation of the planar restricted three body problem. Celest. Mech. Dyn. Astron. 10(1), 87–134 (1974) zbMATHGoogle Scholar
  86. McGehee, R.: Some homoclinic orbits for the restricted three-body problem. Ph.D. thesis, University of Wisconsin, Madison (1969) Google Scholar
  87. Melo, C.F., Macau, E.E.N., Winter, O.C., Neto, E.V.: Numerical study about natural escape and capture routes by the Moon via Lagrangian points L1 and L2. Adv. Space Res. 40, 83–95 (2007) ADSGoogle Scholar
  88. Miller, J.K.: Lunar transfer trajectory design and the four body problem. ASS 03-144 (2003) Google Scholar
  89. Miller, J.K., Belbruno, E.A.: A method for the construction of a lunar transfer trajectory using ballistic capture. In: AAS/AIAA Spacecraft Mechanics Meeting (1991). AAS 91-100 Google Scholar
  90. Mingotti, G., Topputo, F.: Ways to the Moon: a survey. In: 21st AAS/AIAA Space Flight Mechanics Meeting, New Orleans, LA, United States, 13–17 Feb. 2011. Advances in the Astronautical Sciences Series, vol. 140, pp. 2531–2547 (2011) Google Scholar
  91. Mingotti, G., Topputo, F., Bernelli-Zazzera, F.: Hybrid propulsion transfers to the Moon. IAA-AAS-DyCoSS1-03-01 (2003) Google Scholar
  92. Mingotti, G., Topputo, F., Bernelli-Zazzera, F.: Combined optimal low-thrust and stable-manifold trajectories to the Earth–Moon halo orbits. New. Trends Astrodyn. Appl. 3(886), 100–112 (2007) ADSMathSciNetzbMATHGoogle Scholar
  93. Mingotti, G., Topputo, F., Bernelli-Zazzera, F.: Low-energy, low-thrust transfers to the Moon. Celest. Mech. Dyn. Astron. 105, 61–74 (2009) ADSMathSciNetzbMATHGoogle Scholar
  94. Mingotti, G., Topputo, F., Bernelli-Zazzera, F.: Transfers to distant periodic orbits around the Moon via their invariant manifolds. Acta Astronaut. 79, 20–32 (2012) ADSzbMATHGoogle Scholar
  95. Moore, A.: Two approaches utilising invariant manifolds to design trajectories for DMOC optimization (2009) Google Scholar
  96. Mora, M.B., Graziani, F., Teofilatto, P., Circi, C., Porfilio, M., Hechler, M.: A systematic analysis on weak stability boundary transfers to the Moon. IAF-00-A.6.03 (2003) Google Scholar
  97. Murison, M.A.: The fractal dynamics of satellite capture in the circular restricted three-body problem. Astron. J. 98(6), 2346–2359 (1989) ADSGoogle Scholar
  98. Nakamiya, M., Yamakawa, H., Scheeres, D.J., Yoshikawa, M.: Analysis of capture trajectories into periodic orbits about libration points. J. Guid. Control Dyn. 31(5), 1344–1351 (2008) ADSGoogle Scholar
  99. Nakamiya, M., Yamakawa, H., Scheeres, D.J., Yoshikawa, M.: Interplanetary transfers between halo orbits: connectivity between escape and capture trajectories. J. Guid. Control Dyn. 33(3), 803–813 (2010) ADSGoogle Scholar
  100. Neto, E.V., Prado, A.F.B.A.: Time-of-flight analyses for the gravitational capture manoeuvre. J. Guid. Control Dyn. 21(1), 122–126 (1998) ADSzbMATHGoogle Scholar
  101. Ockels, W.J., Biesbroek, R.: Genetic algorithms used to determine WSB trajectories for LunarSat mission. In: Proceedings of Fifth International Symposium on Artificial Intelligence, Robotics and Automation in Space, 1–3 June (1999) Google Scholar
  102. Oshima, K., Campagnola, S., Yanao, T.: Global search for low-thrust transfers to the Moon in the planar circular restricted three-body problem. Celest. Mech. Dyn. Astron. 128(2–3), 303–322 (2017).  https://doi.org/10.1007/s10569-016-9748-2 ADSMathSciNetCrossRefGoogle Scholar
  103. Parker, J.S.: Monthly variations of low energy ballistic transfers to lunar halo orbits. In: AIAA/AAS Astrodynamics Specialist Conference, Canada, 2–5 Aug. (2010) Google Scholar
  104. Parker, J.S., Anderson, R.L.: Surveying ballistic transfers to low lunar orbit. J. Guid. Control Dyn. 36(5), 1501–1511 (2013) ADSGoogle Scholar
  105. Parker, T.S., Chua, L.O.: Practical Numerical Algorithms for Chaotic Systems. Springer, New York (1989) zbMATHGoogle Scholar
  106. Peng, L., Wang, Y., Dai, G., Chang, Y., Chen, F.: Optimization of the Earth–Moon low energy transfer with differential evolution based on uniform design. In: IEEE Congress on Evolutionary Computation (CEC), 18–23 July (2010) Google Scholar
  107. Peng, L., Dai, G., Wang, M., Hu, H., Chang, Y., Chen, F.: Self-adaptive uniform differential evolution for optimizing the initial integral point of the Earth–Moon low-energy transfer. J. Aerosp. Eng. 225(11), 1263–1276 (2011) Google Scholar
  108. Pérez-Palau, D., Epenoy, R.: Indirect optimization of low-thrust Earth–Moon transfers in the Sun–Earth–Moon system. In: 68th International Astronautical Congress 25–29 September 2017, Adelaide, Australia (2017). Paper IAC-17.C1.6.2 Google Scholar
  109. Pérez-Palau, D., Epenoy, R.: Fuel optimization for low-thrust Earth–Moon transfer via indirect optimal control. Celest. Mech. Dyn. Astron. 130, 21 (2018).  https://doi.org/10.1007/s10569-017-9808-2 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  110. Prado, A.F.B.: Numerical and analytical study of the gravitational capture in the bicircular problem. Adv. Space Res. 36, 578–584 (2005) ADSGoogle Scholar
  111. Qu, Q., Xu, M., Peng, K.: The cislunar low-thrust trajectories via the libration point. Astrophys. Space Sci. 362(5), 96 (2017) ADSMathSciNetGoogle Scholar
  112. Radice, G., Olmo, G.: Ant colony algorithms for two-impulse interplanetary trajectory optimization. J. Guid. Control Dyn. 29(6), 1440–1444 (2006) ADSGoogle Scholar
  113. Romagnoli, D., Circi, C.: Earth–Moon weak stability boundaries in the restricted three and four body problem. Celest. Mech. Dyn. Astron. 103, 79–103 (2009) ADSMathSciNetzbMATHGoogle Scholar
  114. Roncoli, R.B., Fujii, K.K.: Mission design overview for Gravity Recovery and Interior Laboratory (GRAIL) mission. In: Proceedings of AIAA/AAS Astrodynamics Specialist Conference, Toronto, Ontario, August 2–5, 2010 (2010). Paper AIAA 2010-8383 Google Scholar
  115. Ross, S.D., Koon, W.S., Lo, M.W., Marsden, J.E.: Design of a Multi-Moon Orbiter. In: 13th AAS/AIAA Space Flight Mechanics Meeting, Puerto Rico (2003) Google Scholar
  116. Ross, S.D., Koon, W.S., Lo, M.W., Marsden, J.E.: Application of dynamical systems theory to a very low energy transfer. AAS 04-289 (2004) Google Scholar
  117. Schoenmaekers, J., Horas, D., Pulido, J.A.: SMART-1: with solar electric propulsion to the Moon. In: 16th Intl. Symp. Space Flight Dyn., Pasadena, CA, 3–7 Dec. (2001) Google Scholar
  118. Schroer, C.G., Ott, E.: Targeting in Hamiltonian systems that have mixed regular/chaotic phase spaces. Chaos 7, 512–519 (1997) ADSMathSciNetzbMATHGoogle Scholar
  119. Senent, J., Ocampo, C., Capella, A.: Low-thrust variable-specific-impulse transfers and guidance to unstable periodic orbits. J. Guid. Control Dyn. 28(2), 280–290 (2005) ADSGoogle Scholar
  120. Sousa Silva, P.A., Terra, M.O.: Applicability and dynamical characterisation of associated sets of the algorithmic weak stability boundary in the lunar sphere of influence. Celest. Mech. Dyn. Astron. 113(2), 141–168 (2012a) ADSGoogle Scholar
  121. Sousa Silva, P.A., Terra, M.O.: Diversity and validity of stable-unstable transitions in the algorithmic weak stability boundary. Celest. Mech. Dyn. Astron. 113(4), 453–478 (2012b) ADSMathSciNetGoogle Scholar
  122. Starchville, T., Melton, R.: Optimal low-thrust trajectories to Earth–Moon L2 halo orbits (circular problem). In: AAS/AIAA Astrodynamics Specialist Conference, Advances in the Astronautical Sciences, vol. 97(1), pp. 1741–1757. Univelt, San Diego (1997). Paper No. 97-714 Google Scholar
  123. Starchville, T., Melton, R.: Optimal low-thrust transfers to halo orbits about the L2 libration point in the Earth–Moon system (elliptical problem). In: AAS/AIAA Astrodynamics Specialist Conference, Advances in the Astronautical Sciences, vol. 99(1), pp. 1489–1506 (1998). Paper No. 98-205 Google Scholar
  124. Strizzi, J.D., Kutrieb, J.M., Damphousse, P.E., Carrico, J.P.: Sun-Mars libration points and Mars mission simulations. AAS 01-159 (2001) Google Scholar
  125. Sukhanov, A., Eismont, N.: Low thrust transfer to Sun–Earth L1 and L2 points with a constraint on the thrust direction. In: Proceedings of the Libration Point Orbits and Applications Conference, pp. 439–454. World Scientific, London (2003) Google Scholar
  126. Sweetser, T.: An estimate of the global minimum \(\Delta \mbox{v}\) needed for Earth–Moon transfer. Adv. Astronaut. Sci. Ser. 75, 111–120 (1991) Google Scholar
  127. Sweetser, T., Maddock, R., Johannesen, J., Bell, J., Penzo, P., Wolf, A., Williams, S., Matousek, S., Weinstein, S.: Trajectory design for a Europa Orbiter mission: a plethora of astrodynamic challenges. In: AAS/A IAA Space Flight Mechanics Meeting, Huntsville, Alabama, p. 174 (1997). Paper No. AAS97 Google Scholar
  128. Sweetser, T.H., Broschart, S.B., Angelopoulos, V., Whiffen, G.J., Folta, D.C., Chung, M.-K., Hatch, S.J., Woodard, M.A.: ARTEMIS mission design Space Sci. Rev. 165(1), 27–57 (2011).  https://doi.org/10.1007/s11214-012-9869-1 ADSCrossRefGoogle Scholar
  129. Taheri, E., Abdelkhalik, O.: Fast initial trajectory design for low-thrust restricted three-body problems. J. Guid. Control Dyn. 38(11), 2146–2160 (2015).  https://doi.org/10.2514/1.G000878 ADSCrossRefGoogle Scholar
  130. Topputo, F.: On optimal two-impulse Earth Moon transfers in a four-body model. Celest. Mech. Dyn. Astron. 117, 279–313 (2013) ADSMathSciNetGoogle Scholar
  131. Topputo: Fast numerical approximation of invariant manifolds in the circular restricted three-body problem. Commun. Nonlinear Sci. Numer. Simul. 32, 89–98 (2016) ADSMathSciNetGoogle Scholar
  132. Topputo, F., Belbruno, E.: Computation of weak stability boundaries: Sun–Jupiter system. Celest. Mech. Dyn. Astron. 105, 3 (2009) ADSMathSciNetzbMATHGoogle Scholar
  133. Topputo, F., Belbruno, E.: Earth–Mars transfers with ballistic capture. Celest. Mech. Dyn. Astron. 121, 329–346 (2015) ADSMathSciNetGoogle Scholar
  134. Topputo, F., Vasile, M., Finzi, A.E.: An approach to the design of low energy interplanetary transfers exploiting invariant manifolds of the restricted three-body problem. AAS 04-245 (2004) Google Scholar
  135. Topputo, F., Vasile, M., Bernelli-Zazzera, F.: Earth-to-Moon low energy transfers targeting L1 hyperbolic transit orbits. Ann. N.Y. Acad. Sci. 1065, 55–76 (2005) ADSGoogle Scholar
  136. Topputo, F., Belbruno, E., Gidea, M.: Resonant motion, ballistic escape, and their applications in astrodynamics. Adv. Space Res. 42, 1318–1329 (2008) ADSGoogle Scholar
  137. Uesugi, K.: Results of the Muses-A “Hiten” mission. Adv. Space Res. 18(11), 69–72 (1996) ADSGoogle Scholar
  138. Villac, B.F., Scheeres, D.J.: A simple algorithm to compute hyperbolic invariant manifolds near L1 and L2. AAS 04-243 (2004) Google Scholar
  139. Wiggins, S.: Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Springer, New York (1994) zbMATHGoogle Scholar
  140. Xu, M., Xu, S.: Exploration of distant retrograde orbits around Moon. Acta Astronaut. 65(5–6), 853–860 (2009) Google Scholar
  141. Xu, M., Tan, T., Xu, S.: Research on the transfers to halo orbits from the view of invariant manifolds. Sci. China, Phys. Mech. Astron. 55(4), 671–683 (2012) ADSGoogle Scholar
  142. Xu, M., Wei, Y., Xu, S.: On the construction of low-energy cislunar and translunar transfers based on the libration points. Astrophys. Space Sci. 348(1), 65–88 (2013) ADSGoogle Scholar
  143. Xu, M., Liang, Y., Ren, K.: Survey on advances in orbital dynamics and control for libration point orbits. Prog. Aerosp. Sci. 82, 24–35 (2016) Google Scholar
  144. Yagasaki, K.: Computation of low energy Earth-to-Moon transfers with moderate flight time. Physica D 197, 313–331 (2004a) ADSMathSciNetzbMATHGoogle Scholar
  145. Yagasaki, K.: Sun-perturbed Earth-to-Moon transfers with low energy and moderate flight time. Celest. Mech. Dyn. Astron. 90(3–4), 197–212 (2004b) ADSMathSciNetzbMATHGoogle Scholar
  146. Yam, C.H., Biscani, F., Izzo, D.: Global optimization of low-thrust trajectories via impulsive Delta-V transcription, 2009-d-03. In: 27th International Symposium on Space Technology and Science (2009) Google Scholar
  147. Yamakawa, H.: On Earth–Moon transfer trajectory with gravitational capture. Ph.D. thesis, University of Tokyo (1992) Google Scholar
  148. Yamakawa, H., Kawaguchi, J., Ishii, N., Matsuo, H.: A numerical study of gravitational capture orbit in the Earth–Moon system. AAS 92-186 (1992) Google Scholar
  149. Yamakawa, H., Kawaguchi, J., Ishii, N., Matsuo, H.: On Earth–Moon transfer trajectory with gravitational capture. AAS 93-633 (1993) Google Scholar
  150. Yokoyama, N., Suzuki, S.: Modified genetic algorithm for constrained trajectory optimization. J. Guid. Control Dyn. 28(1), 139–144 (2005) ADSGoogle Scholar
  151. Zhang, C., Topputo, F., Bernelli-Zazzera, F., Zhao, Y.S.: Low-thrust minimum-fuel optimization in the circular restricted three-body problem. J. Guid. Control Dyn. 38, 1501–1510 (2014).  https://doi.org/10.2514/1.G001080 ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Applied Mathematics DivisionVikram Sarabhai Space CentreThiruvananthapuramIndia

Personalised recommendations