Illustrating the covariances of general relativity by perihelion precession


We calculate the perihelion precession of a test particle in the Edditington-Robertson parameterized metric via the rate of change of the Runge-Lenz vector. It is shown that the calculation results are the same as in the standard, isotropic and harmonic coordinates. These results provide concrete illustrations of the covariances of general relativity. In addition, we find some typos in the derivation of the perihelion precession via the Runge-Lenz vector in Weinberg's classic general relativity textbook, and this finding might also be useful for the beginners who are reading the textbook.

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  1. 1

    A. Einstein, Erklirung der Perihelbewegung des Merkurs aus der allgemeinen Relativitiitstheorie, Sitzungsberichte der preussischen Akademie der Wissenschaften, 831 (1915)

  2. 2

    C.M. Will, Theory and experiment in gravitational physics, revised edition (Cambridge University Press, 1993)

  3. 3

    U.J.J. Le Verrier, R. Acad. Sci. Paris 59, 379 (1859)

    Google Scholar 

  4. 4

    S. Weinberg, Gravitation and cosmology: principles and applications of the general theory of relativity (John Wiely & Sons, NY 1972) pp. 176--185, 230--233

  5. 5

    G.M. Clemence, Astron. Papers Am. Ephemeris 11, 1 (1943)

    Google Scholar 

  6. 6

    G.M. Clemence, Rev. Mod. Phys. 19, 361 (1947)

    ADS  Article  Google Scholar 

  7. 7

    S. Newcomb, Astron. Papers Am. Ephemeris 1, 472 (1882)

    Google Scholar 

  8. 8

    J. Bodenner, C. Will, Am. J. Phys. 71, 770 (2003)

    ADS  Article  Google Scholar 

  9. 9

    C.E. Aguiar, M.F. Banoso, Am. J. Phys. 64, 1042 (1996)

    ADS  Article  Google Scholar 

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Correspondence to W. Lin.

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Jiang, C., Lin, W. Illustrating the covariances of general relativity by perihelion precession. Eur. Phys. J. Plus 129, 47 (2014).

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  • General Relativity
  • Test Particle
  • Geodesic Equation
  • Harmonic Form
  • Isotropic Form