Hi all,

Why is the Gravitational Constant so sloppy? Is it merely measureing error, or is there room to argue that the constant may fluctuate between the 2nd and 4th decimal?

Before posting these questions, I checked the Bautforum for previous posts, the most relevant one seems to be this query in aid of a seemingly dead-end contentious debate, which was of little help.

Following a reference link from Wikipidia's page on "Gravitational Constant", note this excerpt from the abstract:
"...G stands mysteriously alone, its history being that of a quantity which is extremely difficult to measure and which remains virtually isolated from the theoretical structure of the rest of physics. Several attempts aimed at changing this situation are now underway, but the most recent experimental results have once again produced conflicting values of G and, in spite of some progress and much interest, there remains to date no universally accepted way of predicting its absolute value..."

Reviewing a list of contemporary measurements, there seems little agreement to the third decimal:
Luther 1982 Torsion pendulum 6:6726 § 0:0005 75
Fitzgerald 1995 Torsion balance 6:6656 § 0:0006 90
Schwarz 1998 Free fall 6:6873 § 0:0094 1400
K¨undig 2002 Beam balance 6:67407 § 0:00022 200

The measurements seem surprisingly sketchy when considering that most Universal Constants can be measured to the 8th to 10th decimal.

Opinions, especially backed by sources, are appreciated.

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If a tree falls in the forest and no one is there to hear it, how do you know there's a forest?

My guess is, because gravity is so weak compared to other forces, it is going to be a big bear to measure it accurately. So no surprise it's sloppy to me. No surprise also they haven't been able to detect graviton or other predictions of gravity theory, at least not yet.

For example, suppose gravity were as strong as electromagnetism. Then the above methods would easily converge to at least 10 digits. But since gravity is orders of magnitude weaker, the precision should also be cut down by corresponding numbers of digits.

Take a typical freshmen text in physics. Look in the end cover, the list of constants. You'll see the only one that stands out like a sore thumb is G with only 4 significant digits.

I think it's mainly down to the weakness of gravity and experimental noise isolation issues. Here is a recent paper about an attempt to make measurements down to 10 ppm.

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Conscious reasoning is an attempt to justify the choice after it has been made.

It is interesting that modern efforts to measure it are giving such wildly varying values. Thanks.

Concerning why it is difficult to measure, gravity is a very weak force compared to the electrical forces that keep atoms together. If your experiment is very small, all sorts of strange effects need to be accurately accounted for. If it is very large, it will be expensive.

Imagine an experiment with a 1000 ton sphere made of Tungston, and polished to spherical to optical quality. This would be a sphere about 2.3 meters in radius, and the gravitational force it would supply to a one gram reference mass would be about 0.012 Dyne. With such an arrangement you could find G to a few more places, but at what price?

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Forming opinions as we speak

Good point. Results from such an expensive venture, narrowing the variable to a degree that denotes a stable constant, would merely confirm the expected. Armed with the advantage of hindsight, such a venture might seem a frivolous expenditure of resources.

However, would it not be exciting - and possibly worth the expenditure - if the results revealed a gravitational constant behaving like a cannon rolling around the proverbial deck?

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If a tree falls in the forest and no one is there to hear it, how do you know there's a forest?

antoniseb,

A quick heuristic follow-up...
It occurred to me - just for laughs - to place the Gravitational Constant measurements on the Solar Cycle, coinciding with the dates of the measurements:
Luther 1982 Torsion pendulum 6:6726 § 0:0005 75
Fitzgerald 1995 Torsion balance 6:6656 § 0:0006 90
Schwarz 1998 Free fall 6:6873 § 0:0094 1400
K¨undig 2002 Beam balance 6:67407 § 0:00022 200

Here is the result:


It is only meant as a tantalizing example of possibilities, moderators - please resist the urge to kick this thread into the new theory section! I fully realize this graph is bad astronomy! :-)

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If a tree falls in the forest and no one is there to hear it, how do you know there's a forest?

Which possiblity are you referring to? I see no statistical significance to your graph. The points aren't even placed in relation to magnitude, they're just arbitrarily put on a graph of sunspots.

Please read the last paragraph of my post:
It's an attempt at humor - honestly!
As to your question, the graph places the measurements according to the year they were published.

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If a tree falls in the forest and no one is there to hear it, how do you know there's a forest?

Was the position of Jupiter taken into account during those experiments?

As to why the Gravitational Constant is so sloppy, it may have to do with the creatures making the measurements. We humans just might be what appears sloppy as we explore things that are more fundamental. We and our math were not around when gravity froze out. If we were, the math to describe G would likely be much different than the math we use today. But it would be extremely simple to a species that was there when gravity made its first impressions. But our math along with us developed long after that happened. The more we try and describe more fundamental things in the universe, the more confusing and complex it should appear. That might be because it is us and our view of simplicity that is complex and confusing compared to what is fundamental in the universe.

Attached Images

g.png (1.5 KB, 5 views)

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Everyone is entitled to his own opinion, but not his own facts.

I think a big problem is simply that you have to know the mass of an object in order to measure gravity. But how do we know the mass of large objects? . . . Most commonly, I think it is by measuring how much gravity they exert! So it's somewhat difficult to get an accurate measurement of something very large whose mass can be known beforehand, without using gravity.

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As above, so below

This is a good point. I emailed JPL a few years back to ask what value they used for Horizons. I was told Horizons doesn't use G. Rather, it uses mu, which is G*M. It's easy to measure mu, but difficult to determine how much of mu is G and how much is M.

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www.gravitysimulator.com

Part of the reason is that the high-precision equation for calculating the graviational attraction between two masses includes more than half a dozen variables, not just their two respective masses.

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"Toward no crimes have men shown themselves so cold- bloodedly cruel as in punishing differences of belief." - James Russell Lowell

Good things take time. Its great to see the advancement of our technical ability. Strides forward are made yet we seek perfections we might never find. Gravity force is weak by comparison with momentum of mass and atomic scale forces and electro-magnetic energies. Jupiter, our sun and the moons tidal deference must wreck havoc with the forth decimal point measurement attempted.
Just to put some perspective to this... when astronomers talk of the distance to objects of interest. We do not get down to the forth decimal point do we.
The constant you seek is about... or nearly equal to... 6.6766., or nowhere near it... you can quote me... but I would not. why do you not just assign a value and call it Cmg. and just use it as it were pie... its never right.

Astromark, I'm just guessing, but it seems possible that the three body problem may rear its ugly head by the time one gets to the fourth decimal, thus making any meaningful measurement impossible. However, the second and third decimal might bear further monitoring. Could one argue that the Gravitational Constant is actually elastic, rather than a stable constant?
It would be interesting to see if there was a cyclical pattern between measurements over time.

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If a tree falls in the forest and no one is there to hear it, how do you know there's a forest?