Some general remarks

The gravitational fields of the Earth and the Sun constitute our natural environment and it is in these fields that the laws of gravity have been investigated and summed up by equations. Both fields are to good approximation spherically symmetric and, as a result, suitable objects to test the Einstein theory as represented in the Schwarzschild metric.

The Einstein theory contains the Newtonian theory of gravitation as a first approximation and in this sense is of course also confirmed by Kepler's laws. What chiefly interests us here, however, are the – mostly very small – corrections to the predictions of the Newtonian theory. In very exact experiments one must distinguish carefully between the following sources of deviation from the Newtonian spherically symmetric field:

1. (a) Relativistic corrections to the spherically symmetric field,

2. (b) Newtonian corrections, due to deviations from spherical symmetry (flattening of the Earth or Sun, taking into account the gravitational fields of other planets),

3. (c) Relativistic corrections due to deviations from spherical symmetry and staticity.

The Newtonian corrections (b) are often larger than the relativistic effects (a) which are of interest to us here, and can be separated from them only with difficulty. Except for the influence of the rotation of the Earth (Lense–Thirring effect, see Section 27.5), one can almost always ignore the relativistic corrections of category (c).