Skip to main content
SpringerLink
Log in

Capture orbits around asteroids by hitting zero-velocity curves

  • Original Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

The problem of capturing a spacecraft from a heliocentric orbit into a high parking orbit around binary asteroids is investigated in the current study. To reduce the braking \(\Delta V\), a new capture strategy takes advantage of the three-body gravity of the binary asteroid to lower the inertial energy before applying the \(\Delta V\). The framework of the circular restricted three-body problem (CR3BP) is employed for the binary asteroid system. The proposed capture strategy is based on the mechanism by which inertial energy can be decreased sharply near zero-velocity curves (ZVCs). The strategy has two steps, namely, hitting the target ZVC and raising the periapsis by a small \(\Delta V\) at the apoapsis. By hitting the target ZVC, the positive inertial energy decreases and becomes negative. Using a small \(\Delta V\), the spacecraft inserts into a bounded orbit around the asteroid. In addition, a rotating mass dipole model is employed for elongated asteroids, which leads to dynamics similar to that of the CR3BP. With this approach, the proposed capture strategy can be applied to elongated asteroids. Numerical simulations validate that the proposed capture strategy is applicable for the binary asteroid 90 Antiope and the elongated asteroid 216 Kleopatra.

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
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

Notes

  1. https://en.wikipedia.org/wiki/90_Antiope [retrieved on 2017/3/11].

References

  • Bao, C., Yang, H., Barsbold, B., Baoyin, H.: Capturing near-Earth asteroids into bounded Earth orbits using gravity assist. Astrophys. Space Sci. 360(2), 61 (2015)

    Article  ADS  Google Scholar 

  • Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics. AIAA Education Series. AIAA, New York (1999)

    Book  MATH  Google Scholar 

  • Campagnola, S., Russell, R.P.: Endgame problem part 1: V-infinity-leveraging technique and the leveraging graph. J. Guid. Control Dyn. 33(2), 463–475 (2010a)

    Article  ADS  Google Scholar 

  • Campagnola, S., Russell, R.P.: Endgame problem part 2: multibody technique and the Tisserand-Poincare graph. J. Guid. Control Dyn. 33(2), 476–486 (2010b)

    Article  ADS  Google Scholar 

  • Campagnola, S., Skerritt, P., Russell, R.P.: Flybys in the planar, circular, restricted, three-body problem. Celest. Mech. Dyn. Astron. 113, 343–368 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Campagnola, S., Boutonnet, A., Schoenmaekers, J., Grebow, D.J., Petropoulos, A.E., Russell, R.P.: Tisserand-leveraging transfers. J. Guid. Control Dyn. 37(4), 1202–1210 (2014)

    Article  ADS  Google Scholar 

  • Casalino, L., Colasurdo, G., Pastrone, D.: Optimization of ? V Earth-gravity-assist trajectories. J. Guid. Control Dyn. 21(6), 991–995 (1998)

    Article  ADS  MATH  Google Scholar 

  • Casalino, L., Colasurdo, G., Pastrone, D.: Optimal low-thrust escape trajectories using gravity assist. J. Guid. Control Dyn. 22(5), 637–642 (1999a)

    Article  ADS  Google Scholar 

  • Casalino, L., Colasurdo, G., Pastrone, D.: Simple strategy for powered swingby. J. Guid. Control Dyn. 22(1), 156–159 (1999b)

    Article  ADS  Google Scholar 

  • Çelik, O., Sánchez, J.P.: Opportunities for ballistic soft landing in binary asteroids. J. Guid. Control Dyn. 40(6), 1390–1402 (2017)

    Article  ADS  Google Scholar 

  • Chen, Y., Baoyin, H., Li, J.: Accessibility of main-belt asteroids via gravity assists. J. Guid. Control Dyn. 37(2), 623–632 (2014)

    Article  ADS  Google Scholar 

  • Cheng, A.F., Atchison, J., Kantsiper, B., Rivkin, A.S., Stickle, A., Reed, C., Galvez, A., Carnelli, I., Michel, P., Ulamec, S.: Asteroid impact and deflection assessment mission. Acta Astronaut. 115, 262–269 (2015)

    Article  Google Scholar 

  • Diehl, R., Kaplan, D., Penzo, P.: Satellite tour design for the Galileo mission. In: 21st Aerospace Sciences Meeting, Reno, Nevada (1983)

    Google Scholar 

  • Jiang, F., Baoyin, H., Li, J.: Practical techniques for low-thrust trajectory optimization with homotopic approach. J. Guid. Control Dyn. 35(1), 245–258 (2012)

    Article  ADS  Google Scholar 

  • Kohlhase, C.E., Penzo, P.A.: Voyager mission description. Space Sci. Rev. 21(2), 77–101 (1977)

    Article  ADS  Google Scholar 

  • Lantoine, G., Russell, R.P., Campagnola, S.: Optimization of low-energy resonant hopping transfers between planetary moons. Acta Astronaut. 68(7), 1361–1378 (2011)

    Article  ADS  Google Scholar 

  • Lauretta, D.S., Team, O.R.: An overview of the OSIRIS-REx asteroid sample return mission. In: 43rd Lunar and Planetary Institute Science Conference, vol. 43, p. 2491 (2012)

    Google Scholar 

  • Longuski, J.M., Williams, S.N.: Automated design of gravity-assist trajectories to Mars and the outer planets. Celest. Mech. Dyn. Astron. 52(3), 207–220 (1991)

    Article  ADS  Google Scholar 

  • McAdams, J.V., Dunham, D.W., Farquhar, R.W., Taylor, A.H., Williams, B.G.: Trajectory design and maneuver strategy for the MESSENGER mission to Mercury. J. Spacecr. Rockets 43(5), 1054–1064 (2006)

    Article  ADS  Google Scholar 

  • McConaghy, T.T., Debban, T.J., Petropoulos, A.E., Longuski, J.M.: Design and optimization of low-thrust trajectories with gravity assists. J. Spacecr. Rockets 40(3), 380–387 (2003)

    Article  ADS  Google Scholar 

  • Michałowski, T., Bartczak, P., Velichko, F.P., Kryszczyńska, A., Kwiatkowski, T., Breiter, S., Colas, F., Fauvaud, S., Marciniak, A., Michalowshi, J., Hirsch, R., Behrend, R., Bernasconi, L., Rinner, C., Charbonnel, S.: Eclipsing binary asteroid 90 Antiope. Astron. Astrophys. 423(3), 1159–1168 (2004)

    Article  ADS  Google Scholar 

  • Penzo, P.A., Mayer, H.L.: Tethers and asteroids for artificial gravity assist in the solar system. J. Spacecr. Rockets 23(1), 79–82 (1986)

    Article  ADS  Google Scholar 

  • Petropoulos, A.E., Longuski, J.M.: Shape-based algorithm for the automated design of low-thrust, gravity assist trajectories. J. Spacecr. Rockets 41(5), 787–796 (2004)

    Article  ADS  Google Scholar 

  • Qiao, D., Cui, H., Cui, P.: Evaluating accessibility of near-Earth asteroids via Earth gravity assists. J. Guid. Control Dyn. 29(2), 502–505 (2006)

    Article  ADS  Google Scholar 

  • Ross, S.D., Scheeres, D.J.: Multiple gravity assists, capture, and escape in the restricted three-body problem. SIAM J. Appl. Dyn. Syst. 6(3), 576–596 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Scheeres, D.J., Ostro, S.J., Hudson, R.S., Werner, R.A.: Orbits close to asteroid 4769 Castalia. Icarus 121(1), 67–87 (1996)

    Article  ADS  Google Scholar 

  • Shen, H.X., Casalino, L.: Indirect optimization of three-dimensional multiple-impulse Moon-to-Earth transfers. J. Astronaut. Sci. 61(3), 255–274 (2014)

    Article  Google Scholar 

  • Sims, J.A., Longuski, J.M., Staugler, A.J.: V8 leveraging for interplanetary missions: multiple-revolution orbit techniques. J. Guid. Control Dyn. 20(3), 409–415 (1997)

    Article  ADS  MATH  Google Scholar 

  • Strange, N.J., Longuski, J.M.: Graphical method for gravity-assist trajectory design. J. Spacecr. Rockets 39(1), 9–16 (2002)

    Article  ADS  Google Scholar 

  • Strange, N., Landau, D., McElrath, T., Lantoine, G., Lam, T., McGuire, M., Burke, L., Martini, M., Dankanich, J.: Overview of mission design for NASA asteroid redirect robotic mission concept. In: 33rd International Electric Propulsin Conference. The George Washington University, Washington (2013)

    Google Scholar 

  • Tsuda, Y., Yoshikawa, M., Abe, M., Minamino, H., Nakazawa, S.: System design of the Hayabusa 2—asteroid sample return mission to 1999 JU3. Acta Astronaut. 91, 356–362 (2013)

    Article  ADS  Google Scholar 

  • Wang, X.Y., Gong, S.P., Li, J.F.: A method for classifying orbits near asteroids. Acta Mech. Sin. 30(3), 316–325 (2014)

    Article  ADS  MATH  Google Scholar 

  • Yang, H., Li, J., Baoyin, H.: Low-cost transfer between asteroids with distant orbits using multiple gravity assists. Adv. Space Res. 56(5), 837–847 (2015a)

    Article  ADS  Google Scholar 

  • Yang, H.W., Zeng, X.Y., Baoyin, H.: Feasible region and stability analysis for hovering around elongated asteroids with low thrust. Res. Astron. Astrophys. 15(9), 1571–1586 (2015b)

    Article  ADS  Google Scholar 

  • Yang, H., Jiang, Y., Baoyin, H.: Fuel efficient control strategy for constellation orbital deployment. Aircr. Eng. Aerosp. Technol. 88(1), 159–167 (2016)

    Article  Google Scholar 

  • Yang, H., Baoyin, H., Bai, X., Li, J.: Bounded trajectories near collinear-like equilibrium points of elongated asteroids using linear control. Astrophys. Space Sci. 362(2), 27 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  • Yu, Y., Baoyin, H.: Resonant orbits in the vicinity of asteroid 216 Kleopatra. Astrophys. Space Sci. 343(1), 75–82 (2013)

    Article  ADS  Google Scholar 

  • Zeng, X., Alfriend, K.T.: Periodic orbits in the Chermnykh problem. Astrodynamics 1(1), 41–55 (2017)

    Article  Google Scholar 

  • Zeng, X., Jiang, F., Li, J., Baoyin, H.: Study on the connection between the rotating mass dipole and natural elongated bodies. Astrophys. Space Sci. 356(1), 29–42 (2015)

    Article  ADS  Google Scholar 

  • Zeng, X., Fang, B., Li, J., Yu, Y.: Generalized flyby trajectories around elongated minor celestial bodies as a rotating mass dipole. Acta Mech. Sin. 32(3), 535–545 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by Shanghai Key Laboratory of Deep Space Exploration Technology (Grant No. 13dz2260100), National Basic Research Program of China (Grant No. 2014CB744200), Innovation Funded Project of Shanghai Aerospace Science and Technology (Grant No. SAST2017-032) and Scientific Research Foundation for New Staffs of Nanjing University of Aeronautics and Astronautics (Grant No. 1011-YAH17071). The authors would like to thank Xianyu Wang, from Tsinghua University, for the many discussions on the inertial energy of three-body systems.

Author information

Authors and Affiliations

  1. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, China

    Wei Wang & Guangfu Ma

  2. Shanghai Institute of Satellite Engineering, Shanghai, 201109, China

    Wei Wang & Wei Zhang

  3. College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Hongwei Yang

  4. Laboratory of Space New Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Hongwei Yang

Authors
  1. Wei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongwei Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guangfu Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Wei Wang or Hongwei Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, W., Yang, H., Zhang, W. et al. Capture orbits around asteroids by hitting zero-velocity curves. Astrophys Space Sci 362, 229 (2017). https://doi.org/10.1007/s10509-017-3206-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10509-017-3206-9

Keywords

Search

Navigation