On 10/03/2021 04.09, 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.

This question sent me on a search for error bars, starting with my
college physics text. The more I looked, the more varied values I found,
including 2010 CODATA and 2018 CODATA.

Then, I came across this page:
https://phys.org/news/2015-04-gravitational-constant-vary.html

TL;DR: Measured values of G seem to vary with a period of about 5.9
years.

I think that there's a Nobel out there for whoever explains this
phenomenon (assuming that it really exists).

--
Michael F. Stemper
You can lead a horse to water, but you can't make him talk like Mr. Ed
by rubbing peanut butter on his gums.

[Moderator's note: The month is April, but the date is not the first.
So the article seems to be meant seriously. My own chi-by-eye indicates
that the statistical significance of the period might not be high
enough, but I haven't investigated that in detail. The article mentions
"density variations [in the Earth], affecting G". They must mean
"affecting g". Later in the article, the difference between G and g is
pointed out, but they seem to have got it wrong here. Obviously, if g
varies, one could falsely ascribe it to a varying G, which seems to be
the main point of the article. By chance, I came across an interesting
paper today (see URL below) which asks the question what the probability
is that two measurements bracket the true value (assuming random
errors). Many or most might intuitively think that the probability is
rather high that the true value is between the two measurements, but
actually the probability is one half. (Note that the entire Physics
Today arXiv is, at least for a while, freely available for those who
register. https://physicstoday.scitation.org/d...1063/1.3057731
-P.H.]