From a fundamental approach, we can say that Newton's constant is the magnitude of the coupling which exists between "charges" appropriate to the field and force. That is, it is a scaling constant which is used to gauge the interactions of the gravitational fields. Being a conservative (inverse-square) law, this is what differentiates in between similar laws (e.g. Coulomb) which governs interactions of other fundamental fields. Why is it different than other similar constants? i.e. why is gravity such a weak coupling law? That's a very good question and a very fundamental one.
they often write G_{N} for the newtonian gravitational const instead of just plain G because G can mean so many other things you could look in a beginning physics text but PF has at least the advantage that you can get more than one definition. IMO one definition is never enough, that would make life too simple how to define it in the most basic terms? it relates the gravitational attractiveness of things to their inertia in the metric system, the kilogram is a measure of inertia---how sluggish something is, how resistant to acceleration--- how much force it takes to give the thing a unit of acceleration of a meter per second per second. it a world where gravity had been turned off things would still have inertia and they would still have masses that could be determined in kilograms well gravity has not been turned off and suppose you have two iron balls each with one kilogram of inertia and you place them one meter apart (center to center) how many newtons of gravitational pull is there between them? the answer is 6.6742 x 10^{-11} newtons if you had a very delicate force gauge you could even measure it. the way they determine G_{N} experimentally is not too different from that actually---Henry Cavendish invented a very delicate gauge of both force and inertia that does the trick. Does this number look familiar? 6.6742 x 10^{-11}
It is one of the profound question of physics - why the gravitational constant has the value it has - one hint comes from the units (Volumetric acceleration per unit mass). There was a topic not too long ago on PF where the author related the value of G to the expansion of the universe. While we do not have a perfect model for the universe and whether it is slowing or accelerating - you can get a number very close to G (plus or minus 50% of the measured value) by simply using the best estimate of the Hubble Constant and calculating the rate at which the cosmic volume is accelerating for a uniformly expanding Hubble sphere. Feynman once commented that gravity may be a pseudo force - it is always proportional to mass just as is inertia - if we were in a centrifuge we would not be aware of why we are forced against the wall of the container - but its really an inertial thing - an apparent or pseudo force that is always propertional to mass. Feynman concluded - perhaps gravity is due to the fact that we do not have a Newtonian reference frame.
The actual value of and error associated with Newton's gravitational constant is the source of some disagreement. Perhaps someone more knowledgeable about attempts to measure G would like to expound on this.
Quite right Loren - its one of the least accurately known parameters - would be nice to have a definitive formulation where the other factors in the equation are known with hi precision. My personal feeling is that it is a variable - but the method of measuring its variabilily always involves at least one mass (e.g., radar ranging of the orbits of the moons of Mars for example) which may not be known exactly, and which may be dependent upon the totality of the field energy which in turn depends upon the age of the universe.
if you want to get wider discussion you might have to start a thread with a topic like "difficulties and disagreements about measuring G" over the years I have seen a number of articles about this. G has been measured thousands of times and there has always been a lot of scatter in the results also there are off-the-beaten-track measurments an Australian scientist has been measuring it down a bore-hole and in a submerged laboratory---submarine I guess---to see if this makes any difference as far as I know all the measurements use some variant of the original Cavendish device (from around 1790 IIRC) I think the historical difficulties measuring G and the uncertainty about its constancy have been discussed in other PF threads I hope you succeed to start a discussion and that you can attract more knowledgeable people. Here is one small detail in a complicated story: the world standard for G is the "CODATA Recommended Value" which is what the NIST website posts and what handbooks copy. The 1986 recommended value was (mantissa only) 6.67259(85) relative uncertainty 128 ppm The 1998 recommended value was 6.673(10) relative uncertainty 1500 ppm The current, as of end 2002, recommended value is 6.6742(10) relative uncertainty about 150 ppm What you see here, if you look closely, is not supposed to happen. according to our idea of progress, the error bounds are supposed shrink, but in 1998 they leaped up a big amount, also the subsequent evolution of an experimental datum is supposed to be within the error bounds of the prior determination but in 2002 codata broke out of its 1986 error bounds (a precedent-breaking measurement was done in Seattle by a prestigious well-funded team and these are repercussions)
Thanks for all the information guys . It seems that a good summary of the original question is "no-one really knows".
Maybe these replies told you something different from the answer to your question. Physicists are perfectly clear what Newton's G is, but have trouble measuring its value.
At 50k', G is difficult to measure, as SelfAdjoint says. As marcus reports, there was a big revision ~1998 (why? previously unknown systematic errors in torsion balances). The Australian mines? Research to see determine deviations from pure inverse square, esp over 'short' distances (update: no detected deviations, even down to 10^{-6}m) Secular changes in G? None observed so far.