Do extended bodies move along geodesics of Riemannian space-time?

The motion of an extended self-gravitating body in the gravitational field of another distant body is studied in the post-Newtonian approximation of an arbitrary metric theory of gravitation. Comparison of the acceleration of the center of mass of the extended body with the acceleration of a point body moving in a Riemannian space-time whose metric is formally equivalent to the metric of two moving extended bodies shows that in any metric theory of gravitation possessing energy-momentum conservation laws for the matter and gravitational field taken together the center of mass of an extended body does not, in general, move along a geodesic of Riemannian space-time. Application of the obtained general formulas to the earth-sun system and the use of the lunar laser ranging data show that as the earth moves [n its orbit it executes oscillations with respect to a fiducial geodesic with a period of $\sim1$ h and an amplitude not less than $10^{-2}$ cm, which is a post-Newtonian quantity, so that the deviation of the earth's motion from a geodesic can be detected in a corresponding experiment with post-Newtonian accuracy. The difference between the accelerations of the center of mass of the earth and a test body in the post-Newtonian approximation is $10^{-7}$ of the earth's acceleration. The ratio of the earth's passive gravitational mass (defined as by Will) to its inertial mass is not unity but differs from it by an amount approximately equal to $10^{-8}$.