Journal of Geodesy

, Volume 70, Issue 9, pp 554–561 | Cite as

Compatibility of first-order circular orbit perturbations theories; consequences for cross-track inclination functions

  • G. Balmino
  • E. Schrama
  • N. Sneeuw


First-order circular orbit perturbation techniques have found their application in geodesy since the early beginning of modern spaceflight. Two representatives of such techniques, the first one Kaula's linear perturbation theory based on Lagrange's planetary equations, the other one a perturbation theory based on the Hill equations, have been compared. Direct attention is paid to the perturbations in a local Cartesian frame, especially to the cross-track orbit error representations. The equality of both theories is proven analytically and numerically. Furthermore, the comparison reveals two interesting properties, connecting inclination functions with their derivatives and the so-called cross-track inclination functions.


Perturbation Theory Interesting Property Circular Orbit Perturbation Technique Error Representation 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • G. Balmino
    • 1
  • E. Schrama
    • 2
  • N. Sneeuw
    • 3
  1. 1.CNES/GRGSToulouse CedexFrance
  2. 2.TUD/FMRDelftThe Netherlands
  3. 3.TUM/IAPGMünchenGermany

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