Alongside Planck's constant and the speed of light in a vacuum, the gravitational constant, G, is one of the most important and fundamental constants in our universe. However, since Isaac Newton introduced it in 1686, the value of G has been always been a little controversial. Despite centuries of physicists working on finding ever more accurate values (after the speed of light, the gravitational constant was the first to be measured scientifically), G is still the least accurately known physical constant. As an example, by the late 90s, Planck's constant was known to an accuracy 10000 times greater than G!
To make things worse, new experiments started to produce results wildly different from this "accepted" value, in some cases, up to 1% away from previous results. Some experiments showed G had a space and time variation of over 0.5% - this was fundamentally opposed to accepted theory. Was Newton wrong?
Not in this case; it's just that G is so hard determine. Compared to other forces, gravity is incredibly weak, meaning accurately measuring its effects is much harder than is the case with other forces.
Almost every experiment done to measure G, including the original one performed by Henry Cavendish, is based around a bar on the end of a thin fibre being placed near some objects of known mass. The attraction between the bar and the masses causes the fibre to twist, and by measuring that twist, it is possible to ascertain the forces involved, and hence G:
From the side:
| <--- fibre
+------+ | +------+
| | | | |
| MASS | +----------------+ | MASS |
| 1 | | BAR | | 2 |
| | +----------------+ | |
| | | |
From the top:
+------+ +----------------+ | MASS |
| MASS | | BAR | | 2 |
| 1 | +----------------+ +------+
There are a number of problems with this experiment that bring in serious systematic errors. One of these is that internal friction in the fibre can cause an unaccounted for inaccuracy when the amount of fibre twist is measured. Also, the dimensions and mass of the bar had to be known to an incredible accuracy that challenged engineering techniques to the limit.
In 2000, a team from the University of Washington successfully addressed these issues to produce a new value for G.
The first thing this team did (as other more recent attempts had) was to suspend the fibre from a rotating disc and instead of just measuring a single twisting displacement, the fibre was continually rotated between the masses, so that perturbations in the rotation can be measured and averaged over time.
Secondly, the bar, which was usually a thin shaft with dumbells on either end, was replaced by a thin rectangle of metal, hung from the side. It turns out that this completely removes the need to know the characteristics of the pendulum at all!
Also, to prevent the fibre from twisting at all, the speed of the rotationg disc was controlled by feedback from the pendulum, so that the rotating disc's speed was perturbed, not the pendulum's. As well as making the perturbation's easier to measure, the effects of internal fibre friction are completely eliminated.
The end result is that we have a figure for G which is now 1000 times less accurate than Planck's constant; a relative standard uncertainty of 1.5 x 10-4. Considering the accuracy had only been improving by about a factor of 10 per century, a ten fold improvement in a few years is quite extraordinary.