Newtonian constant of gravitation

Newton wrote the inverse-square law in 1687 but never knew G; Cavendish finally weighed it in 1798 with a torsion balance of lead spheres, an experiment he described as "weighing the world". Two and a quarter centuries later G is still known to only about 22 parts per million — a relative uncertainty ten thousand times worse than the electron mass — because gravity cannot be screened, cannot be amplified, and is swamped by every seismic tremor and thermal gradient in the laboratory.

Worse, high-quality experiments disagree with each other by far more than their quoted error bars, which is why CODATA inflates the uncertainty rather than believing any one result. Note also what is not uncertain: the product GM for the Earth and the Sun is known to nine or ten digits from spacecraft tracking, so orbital mechanics is unaffected. It is the masses of the Earth, the Sun and every star that inherit G's 22 ppm — we know the Sun's gravitational pull superbly and its kilograms poorly.