The relativistic gravitational field of a spherically symmetric extended body

This paper investigates the Newtonian shell theorem within the framework of relativistic gravity using the Extended Relativity (ER) model. We derive the gravitational field metric of a spherically symmetric extended body by superposing the contributions from its mass elements. The resulting gravitational time dilation is identical to that of a point source, consistent with General Relativity. Although the shell theorem does not hold exactly in ER, it remains a good approximation in the far-field region. We also derive an explicit expression for the motion of a test particle in this field. Corrections due to the extended nature of the source are negligible for non-relativistic velocities, but become comparable to relativistic effects in the round-trip light travel time between Earth and the International Space Station.