Big G and Maskelyne
Each of the really fundamental force laws of nature is very general, and needs to be linked to our own particular universe by measuring the value of a universal constant embedded in the law.
In the case of Newton it is G, the gravitational constant (as distinct from g which is merely the acceleration at the surface of the Earth and so of local interest only).
Once you know G here, you know it everywhere in the Universe.
Maskelyne measured it in Scotland, in fact, in 1776. A mountain pulls a pendulum sideways and the Earth pulls it downwards. Measuring the (very small) deflection allows the pull of the mountain alone to be deduced, and that gives G.
Twenty years later, the Duke of Devonshire, Henry Cavendish, attempted the measurement of the attraction between metal spheres suspended in his laboratory. (Cavendish was a brilliant physicist little known because of his extremely retiring nature.)
Whereas the mass of the mountain Schiehallion had to be estimated, the masses of the spheres could be accurately measured. This was a bold and pioneering experiment, especially for a man nearing 70.
It was remarkably successful (only 2% above the true value) but it was a century before the same method could start to be refined, thanks to the invention of quartz fibres by C.V. Boys.
Even so, G has remained the most difficult of the basic physical constants to measure accurately. It is for this reason that astronomers adopted the practice of relating their measurements to the AU, rather than directly to the metre (Why this is important is discussed in What does the AU mean?) and that discussion of the AU is inevitably paralled by discussion of G.
The measurements are very elegant, but they create an odd situation. The value of G is used mainly to understand astrophysics on the grand scale, from stellar structure to galaxy formation to cosmology. Yet its measurement comes from almost literally table top experiments; an extrapolation by at least a million million million times.
The danger is clear; why should gravity be exactly the same on the different scales? For instance, classical physics did not survive the relatively modest extrapolation in the opposite direction, down to atomic scales; it was replaced by quantum physics. In the last ten years or so there have been attempts to look for a departure from the inverse square law at distances of tens of metres.
Methods similar to those of Cavendish had to be further developed to test the equally important question of whether gravitational pull depends on the composition of a body ("Would a polystyrene Earth have the same AU?") or only on mass. It is essential to the truth of General Relativity that it should not be related to composition.