I think the scenario that Brian describes is a description that might
attempt to explain the results of general relativity in somewhat
Newtonian terms. Sciama states that "Einstein's equations are so
constructed that to a first aproximation they coincide with Newton's
equation." According to his interpretation, the sun is the source of an
inverse-square field. However, this field possesses potential energy,
which, in turn, can act as a source of gravitation. The field, in the
case of a spherically symetric non-rotating mass, is given by the
Schwarzschild metric. Sciama claims that, because of the weakness of the
sun's gravitational field, the most one can hope observe is the
first-order non-linearity of Einstein's general relativity. Sciama asks,
"How will this non-linearity show up in the orbit of a planet?" He
answers, "The crucial point is that the source of the additional
gravitational field is distributed throughout space, and is not located
at a single point far from the planet." He goes on to say that the
deviation from a pure Newtonian field could not be inferred from a
planet in a circular orbit. An increase, for example, could be
attributed to an increase in the mass of the sun. However, a deviation
of sufficient magnitude could be detected with a planet in an elliptic
orbit -- one in which the distance from the sun varies."
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If memory serves, Newtonian physics does predict a precession of the
wrong value. Considering the perturbative influences of the other
planets and perhaps the mass quadrupole moment of the Sun serve to make
the gravitational field slightly different form inverse square; which is
how such a thing is possible. An earlier Goldstein problem (in the
central force section) has you calculate the precession that an inverse
cube term produces. IIRC
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Joel Rauber
Department of Physics - SDSU