If the fundamental constants of nature have a cosmic spatial variation , there will in general be extra forces with a preferred direction in space which violate the equivalence principle .
We show that the millimeter-precision Apache Point Observatory Lunar Laser-ranging Operation provides a very sensitive probe of such variation that has the capability of detecting a cosmic gradient of the ratio between the quark masses and the strong interaction scale at the level \mathbf { \nabla } \ln ( m _ { quark } / \Lambda _ { QCD } ) \sim 2.6 \times 10 ^ { -6 } ~ { } { Glyr% } ^ { -1 } , which is comparable to the cosmic gradients suggested by the recently reported measurements of Webb et al .
We also point out the capability of presently planned improved equivalence principle tests , at the \Delta g / g \lesssim 10 ^ { -17 } level , to probe similar cosmic gradients .