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The second "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury.  There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun.  These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century.  This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

The second "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury.  There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun.  These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century.  This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

This created quite a problem&mdash;physicists by then were accustomed to having their theories check out very accurately.  One proposal that was made, by Simon Newcomb, was that the exponent of the radius in the gravitational formula wasn't exactly 2.  He showed that, by choosing an exponent of <math>2+\delta</math>, the precession, as a fraction of a full orbit per planet's year, is <math>\delta/2</math>.  By setting <math>\delta = .000000157</math>, that is, an exponent of 2.000000157, Newcomb was able to get a precession of .000000078 revolutions per Mercury year, or 43 arcseconds per Earth year.  Unfortunately, mathematicians opposed this theory and falsely insisted that the exponent must be precisely 2 in order to make the integrals work, and this approach was abandoned.

This created quite a problem&mdash;physicists by then were accustomed to having their theories check out very accurately.  One proposal that was made, by Simon Newcomb, was that the exponent of the radius in the gravitational formula wasn't exactly 2.  He showed that, by choosing an exponent of <math>2+\delta</math>, the precession, as a fraction of a full orbit per planet's year, is <math>\delta/2</math>.  By setting <math>\delta = .000000157</math>, that is, an exponent of 2.000000157, Newcomb was able to get a precession of .000000078 revolutions per Mercury year, or 43 arcseconds per Earth year.  Unfortunately, any such fudging of the exponent gives the same precession, per planetary year, for ''any'' orbiting object.  This would have given the Moon a very noticeable precession, which was not observed.  Also, some people may have objected because it ruined the very elegant integral that is obtained when the exponent is exactly 2.  Newcomb's approach was abandoned.

General relativity predicts this extra precession, in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.  There is some controversy over whether general relativity's results are really accurate in terms of modern observations.

General relativity predicts this extra precession, in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.  There is some controversy over whether general relativity's results are really accurate in terms of modern observations.