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Computerized series solution of relativistic equations of motion


A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.

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  1. Anderson, J.: 1969,JPL Space Programs Summary, Vol. 37-50-3, p. 39.

  2. Brans, C. and Dicke, R. H.: 1961,Phys. Rev. 124, 925.

  3. Broucke, R.: 1969,Celes. Mech. 1, 110

  4. Broucke, R.: 1970,Astron. Astrophys. 6, 173.

  5. Broucke, R. and Garthwaite, K.: 1969,Celes. Mech. 1, 271.

  6. Brouwer, D. and Clemence, G. M.: 1961, inThe Solar System, University of Chicago Press, Chicago, p. 31–94.

  7. Clemence, G. M.: 1962,Astron. J. 67, 379.

  8. Estabrook, F. E.: 1969,Astrophys. J. 158, 81.

  9. Marsden, B. C. and Wright, P.: 1966, SAO Special Report 236, p. 101.

  10. Moyer, T.: 1965,Relativistic Equations of Motion, Master of Science Dissertation, UCLA.

  11. Muhleman, D. O. and Reichley, P.: 1965,JPL Space Programs Summary, Vol. 37-31-4, p. 342.

  12. O'Connell, R. F.: 1968,Am. J. Phys. 36, 757.

  13. Richard, J. P.: 1965,Compt. Rend. Acad. Paris. 260, 2139.

  14. Ross, D. K. and Schiff, L. I.: 1966,Phys. Rev. 141, 1215.

  15. Shapiro, I. I.: 1964,Phys. Rev. Letters 13, 789.

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Broucke, R. Computerized series solution of relativistic equations of motion. Astrophys Space Sci 12, 366–377 (1971).

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  • Fourier
  • Mercury
  • Harmonic Analysis
  • Fourier Series
  • Relativistic Equation