Celestial Mechanics and Dynamical Astronomy

, Volume 110, Issue 3, pp 239–256 | Cite as

Asymptotic solution for the two-body problem with constant tangential thrust acceleration

Original Article

Abstract

An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space with negligible error.

Keywords

Two body problem Tangential thrust Asymptotic expansion Orbit transfer 

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References

  1. Battin R.: An introduction to the mathematics and methods of astrodynamics. AIAA Education Series. American Institute of Aeronautics and Astronautics Inc., New York (1999)Google Scholar
  2. Benney D.: Escape from a circular orbit using tangential thrust. Jet Propul. 28(3), 167–169 (1958)Google Scholar
  3. Boltz F.: Orbital motion under continuous tangential thrust. J. Guid. Control Dyn. 15, 1503–1507 (1992)ADSCrossRefGoogle Scholar
  4. Gao Y., Kluever C.: Analytic orbital averaging technique for computing tangential-thrust trajectories. J. Guid. Control Dyn. 28(6), 1320–1323 (2005)CrossRefGoogle Scholar
  5. Kechichian J.: Orbit raising with low-thrust tangential acceleration in presence of Earth shadow. J. Spacecr. Rockets 35(4), 516–525 (1998)ADSCrossRefGoogle Scholar
  6. Kemble S.: Interplanetary mission analysis and design. Springer, Berlin (2006)Google Scholar
  7. Kevorkian J., Cole J., John F.: Perturbation Methods in Applied Mathematics, vol. 34. Springer, New York (1981)Google Scholar
  8. Peláez J., Hedo J., de Andrés P.R.: A special perturbation method in orbital dynamics. Celest. Mech. Dyn. Astron. 97(2), 131–150 (2007)ADSMATHCrossRefGoogle Scholar
  9. Waldvogel J.: Quaternions for regularizing celestial mechanics: the right way. Celest. Mech. Dyn. Astron. 102(1), 149–162 (2008)ADSMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Claudio Bombardelli
    • 1
  • Giulio Baù
    • 2
  • Jesus Peláez
    • 1
  1. 1.ETSI AeronauticosMadridSpain
  2. 2.CISASPadovaItaly

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