• back

One series of tests of general relativity involves the behavior of orbiting bodies. The paths are slightly different than predicted by Newtonian gravitation. An important feature involves elliptical orbits. In an elliptical orbit, the distance of the orbiting body from the body exerting the force is changing. The orbiting body is therefore passing through regions of different space-time curvature. (See Fig. 8.7, which may help in visualizing this.) The effect of the changing curvature is to cause the orbit not to close. After each orbit, the position of perihelion (closest approach) has moved around slightly.

The effect will be greatest for orbits of highest eccentricity, since the widest range of curvatures will be covered. Also, the smaller the semi-major axis, the greater the effect. This is because the gravitational field changes faster with distance when you are closer to the object exerting the force. In the Solar System, both of these points make the effect most pronounced for Mercury..

It is closest to the Sun, and, except for Pluto, has the most eccentric orbit.

The perihelion of Mercury's orbit advances by some 5600 arc seconds per century. However, of this, all but 43 arc seconds per century can be accounted for by Newtonian effects and the perturbations due to motions of other planets. The Newtonian effects could be calculated accurately and subtracted off. Einstein was able to explain the 43 arc seconds per century exactly in his general relativity calculations. This was considered to be an interesting result for general relativity, but not a crucial test, since Einstein explained something that had been observed. A crucial test involves predicting things that haven't been observed yet.

In recent years a controversy has grown out of this test of general relativity. A group at Princeton in the 1960s measured the shape of the Sun and found a slight flattening. A flattened Sun would also have an effect on the orbit of Mercury, reducing the general relativistic effects by enough to say that Einstein's calculation is wrong. Further measurements have indicated that the original experiment on the Sun's shape was in error, but some experiments suggest that there is some flattening. While some of this research is continuing, at this point it appears that there is not enough solar flattening to challenge Einstein's results.