Nature 320, 39 - 41 (06 March 1986); doi:10.1038/320039a0

The real value of Mercury's perihelion advance

Anna M. Nobili^*† & Clifford M. Will^‡

^*School of Mathematical Sciences, Theoretical Astronomy Unit, Queen Mary College, London E1 4NS, UK
^‡McDonnell Center for the Space Sciences, Department of Physics, Washington University, St Louis, Missouri 63130, USA
^†Permanent address: Dipartimento di Matematica, Universita di Pisa, I-56100 Pisa, Italy.

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.

References

1.	Clemence, G. M. Rev. mod. Phys. 19, 361−364 (1947). | Article | ISI |
2.	Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Freeman, San Francisco, 1973).
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).
6.	Weinberg, S. Gravitation and Cosmology (Wiley, New York, 1972).
7.	Adler, R., Bazin, M. & Schiffer, M. Introduction to General Relativity 2nd edn (McGraw-Hill, New York, 1975).
8.	McVittie, G. C. General Relativity and Cosmology (University of Illinois, Urbana, 1965).
9.	Ohanian, H. C. Gravitation and Spacetime (Norton, New York, 1976).
10.	Robertson, H. P. & Noonan, T. W. Relativity and Cosmology (Saunders, Philadelphia, 1968).
11.	Stephani, H. General Relativity (Cambridge University Press, 1982).
12.	Synge, J. L. Relativity: The General Theory (North-Holland. Amsterdam, 1964).
13.	Richard, J.-P. in General Relativity and Gravitation (eds Shaviv, G. & Rosen, J.) 169−188 (Wiley, New York, 1975).
14.	Will, C. M. in General Relativity: An Einstein Centenary Survey (eds Hawking, S. W. & Israel, W.) 24−89 (Cambridge University Press, 1979).
15.	Will, C. M. Theory and Experiment in Gravitational Physics (Cambridge University Press, 1981).
16.	Will, C. M. Phys. Rep. 113, 345−422 (1984). | Article | ISI |
17.	Anderson, J. D., Keesey, M. S. W., Lau, E. L., Standish, E. M.Jr & Newhall, X. X. Acta astr. 5, 43−61 (1978). | Article | ISI |
18.	Hellings, R. W. in General Relativity and Gravitation (eds Bertotti, B., de Felice, F. & Pascolini, A.) 365−385 (Reidel, Dordrecht, 1984).
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). | ISI |
21.	Hill, H. A., Bos, R. J. & Goode, P. R. Phys. Rev. Lett. 49, 1794−1797 (1982). | Article | ISI |
22.	Tangherlini, F. R. Nuovo Cim. Suppl. 20, 1−86 (1961).
23.	Bertotti, B., Brill, D. R. & Krotkov, R. in Gravitation: An Introduction to Current Research (ed. Witten, L.) 1−48 (Wiley, New York, 1962).
24.	Born, M. Einstein's Theory of Relativity (Dover, New York, 1962).
25.	Pathria, R. K. The Theory of Relativity (Hindustan Publishing Corp., Delhi, 1963).
26.	Dicke, R. H. The Theoretical Significance of Experimental Relativity (Gordon & Breach, New York, 1964).
27.	Dicke, R. H. & Peebles, P. J. Space Sci. Rev. 4, 419−460 (1965). | Article | ISI |
28.	Dicke, R. H. Phys. Today 20, No. 1 55−70 (1967). | ISI |
29.	Rees, M., Ruffini, R. & Wheeler, J. A. Black Holes, Gravitational Waves and Cosmology: An Introduction to Current Research (Gordon & Breach, New York, 1974).
30.	Ginzburg, V. L. Sov. Phys. Usp. 22, 514−527 (1979).
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).
32.	Brumberg, V. A. Relyativistskaya Nebesnaya Mekhanika (Izdatelstvo Nauka, Moskva, 1972).
33.	Will, C. M. Ann. N.Y. Acad. Sci. 336, 307−321 (1980).
34.	Straumann, N. General Relativity and Relativistic Astrophysics (Springer, Berlin, 1984).
35.	The American Ephemeris and Nautical Almanac (US Government Printing Office, Washington, DC, 1947; 1960).