# How well do we know the value of G?

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### Phillip Helbig (undress to reply)

Mar 10, 2021, 5:09:18 AMMar 10
to
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?

Just as an example, would a smaller value of G and correspondingly
higher masses be compatible with LIGO observations?

### Michael F. Stemper

Mar 10, 2021, 10:16:53 AMMar 10
to
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.

<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/doi/10.1063/1.3057731
-P.H.]

### Steven Carlip

Mar 11, 2021, 2:20:09 AMMar 11
to
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
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

Mar 11, 2021, 2:44:33 AMMar 11
to
In article <20210311041...@iron.bkis-orchard.net>, Steven Carlip
I suppose that there are relatively strong constraints on variation with
time; those were used to rule out theories like Dirac's and so on: the
temperature of the Sun would change, the structure of the Earth, and so
on, and as you note some weaker constraints on spatial variation.

More interesting is how well we know it and whether different
measurements are statistically compatible. (My guess is that they are
since the precision is not very good, compared to measurements of other
constants.)

My main point is that G is rarely measured, but rather GM, and one often
has no handle on M other than by assuming G. So perhaps it could vary
from place to place within, say, the Galaxy or the Local Group. I don't
have any reason to think that it does, but, as discussed in another
thread here recently, are there actually any useful constraints?
Obviously it doesn't vary by very much, as stellar populations in
different galaxies look broadly similar and so on.

Probably most difficult to rule out is something like MOND (which
actually has a lot of evidence in support of it, at least at the
phenomenological level) where the (effective) value of G varies. In
MOND, for small accelerations, the value is higher than the Newtonian
(or GR) value.

Suppose that in the case of very strong fields, the effective value is
less than the G we measure directly. To some extent, that could be
compensated for via larger masses (as often the product GM is relevant).
To take a concrete example, in the LIGO black-hole--merger events, could
one decrease G by, say, 1 per cent, and increase the masses accordingly,
and still fit the data?