In theoretical astrophysics, the Nordtvedt effect refers to the relative motion between the Earth and the Moon which would be observed if the gravitational self-energy of a body contributed differently to its gravitational mass and inertial mass. If observed, the Nordtvedt effect would violate the strong equivalence principle, which shows that an object's movement in a gravitational field does not depend on its mass or composition.
The effect is named after Dr. Kenneth L. Nordtvedt, from Montana State University, who first demonstrated that some theories of gravity suggest that massive bodies should fall at different rates, depending upon their gravitational self-energy.
Nordtvedt then observed that if gravity did in fact violate the strong equivalence principle, then the more-massive Earth should fall towards the Sun at a slightly different rate than the Moon, resulting in a polarization of the lunar orbit. To test for the existence (or absence) of the Nordtvedt effect, scientists have used the Lunar Laser Ranging Experiment, which is capable of measuring the distance between the Earth and the Moon with near-millimetre accuracy. Thus far, the results have failed to find any evidence of the Nordtvedt effect, demonstrating that if it exists, the effect is exceedingly weak. Subsequent measurements and analysis to even higher precision have improved constraints on the effect.
A wide range of scalar-tensor theories have been found to naturally lead to a tiny effect only, at present epoch. This is due to a generic attractive mechanism that takes place during the cosmic evolution of the universe. Other screening mechanisms  (chameleon, pressuron, Vainshtein etc.) could also be at play.
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Nordtvedt Jr., K (25 June 1968) "Testing Relativity with Laser Ranging to the Moon" Phys. Rev. 170, No. 5 (1186)
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