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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.  While other orbits do not have a similar precession, Mercury experiences a gravitational pull far higher than any other planet in the solar system due to its proximity the Sun.  Mathematicians falsely claimed that the exponent must be precisely 2 in order to make the integrals work properly, and Newcomb's 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.  There may have been another effect working against Newcomb's theory.  There is sometimes "intellectual inertia", a reluctance to accept new theories.  This would have been particularly evident in the case of Newtonian gravitation, because the Newtonian formula, with its exponent of exactly 2, can be integrated exactly, in closed form.  In fact, the invention of calculus, and mathematical physics in general, was largely founded on Newton's exact closed-form solution for an inverse square force field, and the demonstration that it exactly matched Kepler's laws.  Mathematical physics would have had a very rocky start if this weren't the case.  Giving up the exact Newtonian formulation, with its exponent of exactly 2, did not come easily.

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 may be some controversy over whether general relativity's results are really accurate in terms of modern observations.

 

 

[[Image:Cassini-science-289.jpg|right|thumb|The Shapiro effect: A spacecraft signal dipping into a gravity well around the [[Sun]] is delayed slightly.]]

[[Image:Cassini-science-289.jpg|right|thumb|The Shapiro effect: A spacecraft signal dipping into a gravity well around the [[Sun]] is delayed slightly.]]