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The field equations of general relativity are applied to pressure-free spherically symmetrical systems of particles. The equations of motion are determined without the use of approximations and are compared with the Newtonian equations. The total energy is found to be an important parameter, determining the geometry of 3-space and the ratio of effective gravitating to invariant mass. The Doppler shift is discussed and is found to contain both the velocity shift and the Einstein shift combined in a rather complex expression.
Hermann Bondi (Mon,) studied this question.