= Solution
The <weak equivalence principle> says that freely falling test bodies with identical initial conditions follow the same trajectory independently of composition, when nongravitational forces and appreciable self-gravity are negligible. In Newtonian language it implies universal gravitational-to-inertial <mass> ratio. The <Einstein equivalence principle> additionally requires <local Lorentz invariance> and <local position invariance> of nongravitational experiments: a sufficiently small freely falling laboratory realizes <special relativity>. The <strong equivalence principle> extends universality to gravitational experiments and self-gravitating bodies.
A falling elevator makes the local content clear. Uniform gravitational acceleration can be removed along a freely falling <worldline> by a suitable frame, but <curvature> cannot generally be removed over an extended region. Nearby <geodesics> have relative acceleration
$$
\frac{D^2\xi^\mu}{D\tau^2}=-R^\mu{}_{\alpha\nu\beta}u^\alpha\xi^\nu u^\beta
$$
for the displayed Riemann-sign convention. <tidal forces> therefore remain detectable even in free fall. Equivalence motivates a metric description and gravitational clock shifts, but does not uniquely select Einstein's field equations.
Tests compare accelerations of different materials, <frequencies> of clocks at different gravitational potentials, or the response of self-gravitating bodies. <lunar laser ranging> times pulses reflected by lunar <retroreflectors> and fits Earth-Moon motion in the Sun's field; a differential free-fall violation would add a characteristic periodic range perturbation. The fit must also model tides, station and reflector geometry and propagation delays, with solar-radiation pressure and reflector thermal effects checked as possible mimics. Williams and collaborators' 2012 analysis is a concrete example of this method, published after this examination.<Lunar Laser Ranging Tests of the Equivalence Principle by James G. Williams and others>[§§2–4, pulse ranging, orbital fits and solar-radiation/thermal corrections]{ref}
\b[Equivalence is a local universality statement; tidal <curvature> and the detailed gravitational field equations are additional physics.]
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