Third-Order Solution of an Artificial-Satellite Theory

  • Hiroshi Kinoshita
Part of the Astrophysics and Space Science Library book series (ASSL, volume 72)


A third-order solution is developed for the motions of artificial satellites moving in the gravitational field of the Earth, whose potential includes the second-, third-, and fourth-order zonal harmonics. Third-order periodic perturbations with fourth-order secular perturbations are derived by Hori’s perturbations method. All quantities are expanded into power series of the eccentricity, but the solution is obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a close-earth satellite with a small eccentricity with an accuracy of better than 1 cm over 1 month.


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Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1978

Authors and Affiliations

  • Hiroshi Kinoshita
    • 1
  1. 1.Center for AstrophysicsHarvard College Observatory and Smithsonian Astrophysical ObservatoryCambridgeUSA

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