Strong equivalence principle (SEP)

The strong equivalence principle extends universality of free fall to bodies with appreciable gravitational self-energy and requires local experiments, including gravitational ones, in a freely falling laboratory to be independent of the laboratory's location and velocity. This statement neglects external tidal variation across the laboratory; it does not remove Riemann curvature tensor. In general relativity, universal metric coupling, fixed local gravitational coupling and the absence of extra preferred-frame gravitational fields implement this principle.

A violation of the strong equivalence principle can make the gravitational-to-inertial mass ratio depend on a body's negative gravitational self-energy $E_G$. Bodies with different self-binding fractions would then fall differently in the same external field, even after composition-dependent weak-equivalence effects are removed. For the Earth and Moon this produces a polarization of the lunar orbit toward the Sun, measurable by lunar laser ranging. General relativity predicts ${\eta }_N=0$.