The gravitational constant was the first constant whose constancy was questioned . From a theoretical point of view, theories with a varying gravitational constant can be designed to satisfy the equivalence principle in its weak form but not in its strong form  (see also Section 5). Most theories of gravity that violate the strong equivalence principle predict that the locally measured gravitational constant may vary with time.
The value of the gravitational constant is = 6.674 28(67) × 10–11 m3 kg–1 s–2 so that its relative standard uncertainty fixed by the CODATA11 in 2006 is 0.01%. Interestingly, the disparity between different experiments led, in 1998, to a temporary increase of this uncertainty to 0.15% , which demonstrates the difficulty in measuring the value of this constant. This explains partly why the constraints on the time variation are less stringent than for the other constants.
A variation of the gravitational constant, being a pure gravitational phenomenon, does not affect the local physics, such as, e.g., the atomic transitions or the nuclear physics. In particular, it is equivalent at stating that the masses of all particles are varying in the same way to that their ratios remain constant. Similarly all absorption lines will be shifted in the same way. It follows that most constraints are obtained from systems in which gravity is non-negligible, such as the motion of the bodies of the Solar system, astrophysical and cosmological systems. They are mostly related in the comparison of a gravitational time scale, e.g., period of orbits, to a non-gravitational time scale. It follows that in general the constraints assume that the values of the other constants are fixed. Taking their variation into account would add degeneracies and make the constraints cited below less stringent.
We refer to Section IV of FVC  for earlier constraints based, e.g., on the determination of the Earth surface temperature, which roughly scales as and gives a constraint of the order of , or on the estimation of the Earth radius at different geological epochs. We also emphasize that constraints on the variation of are meant to be constraints on the dimensionless parameter .
Living Rev. Relativity 14, (2011), 2
This work is licensed under a Creative Commons License.