Planar Optimal Two-Impulse Transfers with Closed-Form Solutions of the Transverse Transfers

  • Thomas Carter
  • Mayer Humi


The problem of finding a planar two-impulse transfer orbit between two known elliptical orbits that minimizes the total characteristic velocity of the transfer arc is examined. Using a transformation of variables presented in previous work, necessary conditions for an optimal transfer are determined, followed by a proof that an optimal transfer exists. We then consider the problem of finding a minimizing planar two-impulse transfer over the set of two-impulse transverse transfers. A minimizing solution for this problem requires that either each of the boundary orbits has an apse that is the same distance from the center of attraction as the other, or else the boundary orbits are coaxial. The transfer orbits are tangent to the boundary orbits at apses. Minimizing solutions of the transverse transfer problem are found in closed form.


Minimizing transfers Orbit transfer Planar transfer 


  1. 1.
    Hohmann, W.: Die Erreichbarkeit der Himmelskorper. Oldenbourg, Munich (1925). The Attainability of Heavenly bodies, NASA Technical Translation F-44, (1960)Google Scholar
  2. 2.
    Lawden, D.S.: Impulsive transfer between elliptical orbits. In: Leitmann, G. (ed.) Optimization Techniques. AP, New York, Chapter 11, (1962)Google Scholar
  3. 3.
    Horner, J.M.: Optimum two-impulse transfer between arbitrary coplanar terminals. ARS J. 32, 95–96 (1962)CrossRefGoogle Scholar
  4. 4.
    Bender, D.F.: Optimum coplanar two-impulse transfers between elliptic orbits. Aerosp. Eng. 21, 44–52 (1962)Google Scholar
  5. 5.
    Altman, S.P., Pistiner, J.S.: Minimum velocity increment solution of the two-impulse coplanar orbital transfer. AIAA J. 1, 435–442 (1963)CrossRefMATHGoogle Scholar
  6. 6.
    Pontani, M.: Simple method to determine globally optimal orbital transfers. J. Guid. Control Dyn. 32, 899–915 (2009)CrossRefGoogle Scholar
  7. 7.
    Nevabi, M., Sanatifer, M.: Optimal impulsive orbital transfer between coplanar non-coaxial orbits, local and global solutions. In: Fifth International Conference on Recent Advances in Space Technology, pp. 9–11 (2011)Google Scholar
  8. 8.
    Zaborsky, S.: Analytical solution of two-impulse transfer between coplanar elliptical orbits. J. Guid. Control Dyn. 37, 996–1000 (2014)CrossRefGoogle Scholar
  9. 9.
    Carter, T., Humi, M.: Geometry of transformed variables in the impulsive transfer problem. In: AAS/AIAA Astrodynamics Specialist Conference, Hilton Head Island, SC, 11–15 Aug (2013)Google Scholar
  10. 10.
    Carter, T., Humi, M.: A new approach to impulsive rendezvous near circular orbit. J. Celest. Mech. Dyn. Astron. 112(4), 385–426 (2012)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics/Computer ScienceEastern Connecticut State UniversityWillimanticUSA
  2. 2.Department of Mathematical SciencesWPIWorcesterUSA

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