On 3/10/21 2:09 AM, Phillip Helbig (undress to reply) wrote:
How well do we know the value of G?

G is the constant (well, as far as we know) of nature whose value is
known with the least precision. How well do we know it? Presumably
only Cavendish-type experiments can measure it directly. Other
measurements of G, particularly astronomical ones, probably actually
measure GM, or GMm. In some cases, those quantities might be known to
more precision than G itself.

Suppose G were to vary with time, or place, or (thinking of something
like MOND here) with the acceleration in question. Could that be
detected, or would it be masked by wrong assumptions about the mass(es)
involved?

The idea that G may vary in time goes back to Dirac's "large
numbers hypothesis" in the 1930s. There's been a huge amount of
experimental and observational investigation. A classic review
article is Uzan, arXiv:hep-ph/0205340; a more recent version is
arXiv:1009.5514. There are quite strong constraints on time
variation, and some weaker constraints on spatial variation,
coming from everything from Lunar laser ranging to binary
pulsar timing to Big Bang Nucleosynthesis.

Steve Carlip