Hi people. G constant is a complicated subject ,that's right, but at the moment no experiment has ever shown that General Relativity (Newtonian Gravity if we are talking about ordinary objects) is wrong. How do you explain Cavendish and a lot of experiments that clearly show that massive bodies generate an attractive force (or pseudo-force in GR, phenomenologically speaking they are the same)? Are you telling me that every gravitational physicist is part of the conspiracy? I'm doing research on theoretical GR, so I will be soon part of this big conspiracy.. that's sounds good..
G is very difficult to measure due to the weakness of gravitational interaction between ordinary objects. Perhaps it is not exactly a constant (that is an interesting discussion regarding the possibility of non-linear coupling in Newtonian approximation, or even a fifth force , and could be related to quantum gravity theories and brane cosmology) but we don't have enough evidence to believe in that, and every experiment we have performed so far has found G within that 1% of Cavendish. Actually, nowadays we can say (not everybody agree with this, but I do) that we have measurements of G to 0.15%. Could be much more accurate if we found systematic errors in some measurements (some scientists believe in measurements to 0.01%). And I think that's quite well for such a complicated issue. Just tell me how come something that doesn't exist has been measured in a lot of different experiments whose uncertainties are less than 1% (the worst possible) (...idiotic refutation...)
Neverterless, we believe in gravity mainly because GM product (M gravitational mass) can be accurately measured (much more than G itself) for many celestial objects. The inverse square law (and its relativistic corrections) allows us to understand the motion of almost everything we can see in the sky... And not only that, I just don't have enough free time to write everything down (think about black holes, pulsars, red-shift, cosmic microwave background, gravitational lens, stellar structure and so on…). Ok, many data has been collected by NASA. But it is not only NASA.. Perhaps you are suggesting that every observatory around the world is part of the conspiracy...
Could be GR wrong? Yes, it could be wrong. For example if we don't measure gravitational waves would mean that we need another theory. Would that mean gravity doesn't work as a concept to understand reality? Of course not, it has helped us to understand many things. But I'm open-minded, so if someone formulates a theory explaining all this stuff without gravity (a rigorous and mathematical theory, not just a bunch of assumptions) I would listen to them and consider they may are right.....
Of course existence of gravity alone doesn't directly imply RE. But... Anyway, I wrote this just to clarify some misconceptions that I found in this forum ...
Sorry for my English once again..
Cheers