The inverse square law (ISL) of gravity has been meaningfully tested over length scales spanning 20 orders of magnitude, eliminating Yukawa-like couplings competitive with the strength of gravity from 10–4 to 1016 meter length scales. The deepest probe of the ISL is from LLR at a scale of 108 meters, where any new force must be weaker than gravity by more than ten orders-of-magnitude . Short-range tests of the ISL have recently been prompted by the energy scale of the cosmological acceleration, which suggest new-physics below 1 mm .
Modern tests of Newton’s inverse-square law of gravity often search for an additional Yukawa contribution to the gravitational potential::
Recent analysis of LLR data includes specifically fitting for Yukawa perturbation terms in the equations of motion leading to a measurement of at . While intriguing, this possible non-null result has yet to be thoroughly investigated .
Living Rev. Relativity 13, (2010), 7
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