Analytical Effects of Gravitational Waves on the Motion of an Artificial Satellite

  • M. H. Youssef
  • M. K. Ahmed
Conference paper

Abstract

The motion of an artificial satellite in the Earth’s gravitational field is discussed in the post-Newtonian framework including the effect of weak gravitation waves using the perturbation technique of the canonical Lie-transformations. Two successive canonical transformations are used to derive analytical expressions for the short-period, long-period and secular perturbations of orbital elements. The solution is expressed in terms of the Delaunay variables.

Keywords

Gravitational Wave Gravitational Potential Orbital Element Canonical Transformation Order Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brouwer, D.: 1959, “Solution of the problem of artificial satellite theory without Drag”, Astron. J. 64, 378.MathSciNetADSCrossRefGoogle Scholar
  2. Deprit, A.: 1969, “Canonical transformations depending on a small parameter”, Celest. Mech. 1, 12.MathSciNetADSMATHCrossRefGoogle Scholar
  3. Heimberger J., Soffel, M., and Ruder, H.: 1990, “Relativistic effects in the motion of artificial satellites: The oblateness of the central body II”, Celest. Mech. 47, 205.MathSciNetADSMATHCrossRefGoogle Scholar
  4. Hori, G.: 1966, “Theory of general perturbations with unspecified canonical variables”, Publ. Astron. Soc. Jpn. 18, 287.ADSGoogle Scholar
  5. Hagihara, Y.: 1970, Dynamical Principles and Transformation Theory, Maple press, USA.MATHGoogle Scholar
  6. Soffel, M., Wirrer, R., Schastok, J., Ruder, H. and Schneider, M.: 1988, “Relativistic effects in the motion of artificial satellites: The oblateness of the central body. I”, Celest. Mech. 42, 81.MathSciNetADSGoogle Scholar
  7. Straumann, N.: 1984 General Relativity and Relativistic Astrophysics, Springer, Berlin.CrossRefGoogle Scholar
  8. Youssef, M.:1994, The effect of Gravitational Waves on the Motion of Artificial Satellites, Ph.D. thesis, Astronomy Dept., Cairo University, Egypt.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • M. H. Youssef
    • 1
  • M. K. Ahmed
    • 1
  1. 1.Faculty of ScienceAstronomy DepartmentCairoEgypt

Personalised recommendations