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The real value of Mercury's perihelion advance


The perihelion advance of the orbit of Mercury has long been one of the observational cornerstones of general relativity. After the effects of the gravitational perturbations of the other planets have been accounted for, the remaining advance fits accurately to predictions according to the theory of general relativity, that is, 43 arc s per 100 yr. In fact, radar determinations of Mercury's motion since the mid-1960s have produced agreement with general relativity at the level of 0.5%, or to ±0.2arcs per 100 yr. We have recently been puzzled by an apparent uncertainty in the value of the theoretical prediction for the advance within general relativity, as cited in various sources. The origin of this discrepancy is a 1947 article by Clemence1, who used unconventional values for the astronomical unit (A) and the speed of light (c) in his calculation of the predicted advance. Since that time, virtually everyone has followed suit. Although the current value of the prediction, using the best accepted values for the astronomical constants and for the orbital elements of Mercury, is 42.98 arc s per 100 yr, there is a preponderance of citations over the past 25 years of Clemence's value 43.03 arc s per 100 yr. Here we derive the accurate value and uncover the source of Clemence's value.

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  1. Clemence, G. M. Rev. mod. Phys. 19, 361–364 (1947).

    ADS  Article  Google Scholar 

  2. Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Freeman, San Francisco, 1973).

    Google Scholar 

  3. The Astronomical Almanac for the year 1984 (US Government Printing Office, Washington, DC, 1983).

  4. Supplement to the Astronomical Almanac 1968 (US Government Printing Office, Washington, DC, 1966).

  5. Dorsey, N. E. Trans. Am. phil. Soc. 34, 1–106 (1944).

    Article  Google Scholar 

  6. Weinberg, S. Gravitation and Cosmology (Wiley, New York, 1972).

    Google Scholar 

  7. Adler, R., Bazin, M. & Schiffer, M. Introduction to General Relativity 2nd edn (McGraw-Hill, New York, 1975).

    MATH  Google Scholar 

  8. McVittie, G. C. General Relativity and Cosmology (University of Illinois, Urbana, 1965).

    Google Scholar 

  9. Ohanian, H. C. Gravitation and Spacetime (Norton, New York, 1976).

    MATH  Google Scholar 

  10. Robertson, H. P. & Noonan, T. W. Relativity and Cosmology (Saunders, Philadelphia, 1968).

    MATH  Google Scholar 

  11. Stephani, H. General Relativity (Cambridge University Press, 1982).

    MATH  Google Scholar 

  12. Synge, J. L. Relativity: The General Theory (North-Holland. Amsterdam, 1964).

    MATH  Google Scholar 

  13. Richard, J.-P. in General Relativity and Gravitation (eds Shaviv, G. & Rosen, J.) 169–188 (Wiley, New York, 1975).

    Google Scholar 

  14. Will, C. M. in General Relativity: An Einstein Centenary Survey (eds Hawking, S. W. & Israel, W.) 24–89 (Cambridge University Press, 1979).

    Google Scholar 

  15. Will, C. M. Theory and Experiment in Gravitational Physics (Cambridge University Press, 1981).

    Google Scholar 

  16. Will, C. M. Phys. Rep. 113, 345–422 (1984).

    ADS  MathSciNet  Article  Google Scholar 

  17. Anderson, J. D., Keesey, M. S. W., Lau, E. L., Standish, E. M. Jr & Newhall, X. X. Acta astr. 5, 43–61 (1978).

    ADS  Article  Google Scholar 

  18. Hellings, R. W. in General Relativity and Gravitation (eds Bertotti, B., de Felice, F. & Pascolini, A.) 365–385 (Reidel, Dordrecht, 1984).

    Book  Google Scholar 

  19. Ashby, N., Bender, P. L. & Wahr, J. M. Proc. 10th int. Conf. General Relativity and Gravitation. 947 (Conf. Pap., Padua, 1983).

  20. Dicke, R. H., Kuhn, J. R. & Libbrecht, K. G. Nature 316, 687–690 (1985).

    ADS  Article  Google Scholar 

  21. Hill, H. A., Bos, R. J. & Goode, P. R. Phys. Rev. Lett. 49, 1794–1797 (1982).

    ADS  Article  Google Scholar 

  22. Tangherlini, F. R. Nuovo Cim. Suppl. 20, 1–86 (1961).

    ADS  MathSciNet  Google Scholar 

  23. Bertotti, B., Brill, D. R. & Krotkov, R. in Gravitation: An Introduction to Current Research (ed. Witten, L.) 1–48 (Wiley, New York, 1962).

    Google Scholar 

  24. Born, M. Einstein's Theory of Relativity (Dover, New York, 1962).

    Google Scholar 

  25. Pathria, R. K. The Theory of Relativity (Hindustan Publishing Corp., Delhi, 1963).

    MATH  Google Scholar 

  26. Dicke, R. H. The Theoretical Significance of Experimental Relativity (Gordon & Breach, New York, 1964).

    MATH  Google Scholar 

  27. Dicke, R. H. & Peebles, P. J. Space Sci. Rev. 4, 419–460 (1965).

    ADS  Article  Google Scholar 

  28. Dicke, R. H. Phys. Today 20, No. 1 55–70 (1967).

    ADS  Article  Google Scholar 

  29. Rees, M., Ruffini, R. & Wheeler, J. A. Black Holes, Gravitational Waves and Cosmology: An Introduction to Current Research (Gordon & Breach, New York, 1974).

    Google Scholar 

  30. Ginzburg, V. L. Sov. Phys. Usp. 22, 514–527 (1979).

    ADS  Article  Google Scholar 

  31. Cowsik, R. in Gravitation, Quanta and the Universe (eds Prasanna, A. R., Narlikar, J. V. & Vishveshwara, C. V.) 18–40 (Wiley, New York, 1980).

    Google Scholar 

  32. Brumberg, V. A. Relyativistskaya Nebesnaya Mekhanika (Izdatelstvo Nauka, Moskva, 1972).

    MATH  Google Scholar 

  33. Will, C. M. Ann. N.Y. Acad. Sci. 336, 307–321 (1980).

    ADS  Article  Google Scholar 

  34. Straumann, N. General Relativity and Relativistic Astrophysics (Springer, Berlin, 1984).

    Book  Google Scholar 

  35. The American Ephemeris and Nautical Almanac (US Government Printing Office, Washington, DC, 1947; 1960).

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Nobili, A., Will, C. The real value of Mercury's perihelion advance. Nature 320, 39–41 (1986).

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