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
10^{16} meter length scales. The deepest probe of the ISL is from LLR at a scale of 10^{8} meters, where
any new force must be weaker than gravity by more than ten orders-of-magnitude [38]. 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 [1].

Modern tests of Newton’s inverse-square law of gravity often search for an additional Yukawa contribution to the gravitational potential:

where is the dimensionless strength and is the length scale. Such a potential would generate a precession of the Moon’s perigee with frequency [1]: where is the mean radius of the Moon’s orbit. The agreement of geodetic precession with GR described below leads to a limit on an anomalous precession of . This translates into a limit on the strength of a new Yukawa potential of at where the lunar test is most sensitive.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 [38].

Living Rev. Relativity 13, (2010), 7
http://www.livingreviews.org/lrr-2010-7 |
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