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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 and Asaph Hall, 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</math> to .000000157, 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 the loss of the ability to get a simple result from the integration with an exponent of 2 would be regrettable, physicists would would have been willing to put up with that if it gave the right answer.  But it didn't.  As can be seen from the formula above, whatever value is chosen for <math>\delta/2</math>, it gives the same precession, per revolution, for all orbiting bodies.  The value chosen by Newcomb was "tweaked" for Mercury, but it got wrong values for the precessions of other planets, and, most notably, for the Moon.  The Newcomb-Hall hypothesis was soon discarded.  As can be seen from the table below, the measured values of the anomalous precessions of other planets agree well with the predictions of general relativity but poorly with those predicted by Newcomb and Hall.

: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 and Asaph Hall, 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</math> to .000000157, 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 the loss of the ability to get a simple result from the integration with an exponent of 2 would be regrettable, physicists would would have been willing to put up with that if it gave the right answer.  But it didn't.  As can be seen from the formula above, whatever value is chosen for <math>\delta\,</math>, it gives the same precession, per revolution, for all orbiting bodies.  The value chosen by Newcomb was "tweaked" for Mercury, but it got wrong values for the precessions of other planets, and, most notably, for the Moon.  The Newcomb-Hall hypothesis was soon discarded.  As can be seen from the table below, the measured values of the anomalous precessions of other planets agree well with the predictions of general relativity but poorly with those predicted by Newcomb and Hall.

:While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.

:While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.