# Gravitational Constant (Big G I think)

#### p1l0t

G = (6.674215 ± 0.000092) x 10-11 m3/kg/s2 or there abouts is the constant that we multiply to the mass of m1 to m2 divided by the distance squared. This gives us the attractive force between bodies. In the equation F = G(m1m2/r2) it is obvious that the attractive force depends on the mass of each object and exponentially more the distance between them (inversely). This "Big G" though.. what is it? I get that it is the gravitational constant but where does it come from and what is its significance. Why do we need this very tiny number to accurately determine the attractive force of massive bodies? Also how does it represent the strength of gravity as a force? Is it because it is an independent variable?

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#### pervect

Staff Emeritus
Science Advisor
We have a FAQ on why "c" has the value it does https://www.physicsforums.com/showthread.php?t=511385 [Broken], but not one for G.

The rationale is pretty similar though.

I'll mark-up the answer there for G. You might try some of the references there as well.

Because [STRIKE]xxcxx[/STRIKE] G has units, its value is what it is only because of our choice of units, and there is no meaningful way to test whether it changes. These questions [STRIKE]are[/STRIKE] would be more meaningful [STRIKE]when[/STRIKE] if posed in terms of the unitless [STRIKE]fine structure constant.[/STRIKE] gravitational coupling constant http://en.wikipedia.org/wiki/Gravitational_coupling_constant.

Except that unlike the case for the fine structure constant, I don't think we have any direct experimental data on the Gravitational coupling constant.

Basically the numerical value of c, or G, has every bit as much physical significance as saying there are 2.54 centimeters per inch.

I would particularly recommend http://math.ucr.edu/home/baez/constants.html in the references section of the FAQ.

You might at first think that the speed of light, Planck's constant and Newton's gravitational constant are great examples of fundamental physical constants.

But in fundamental physics, these constants are so important that lots of people use units where they all equal 1! The point is that we can choose units of length, time and mass however we want. That's three independent choices, so with a little luck we can use them to get our favorite three constants to equal 1. Planck was the first to notice this, so these units are called "Planck units".
...

Thus, by a proper choice of units, one can (and often does) make G equal to 1 by using geometric units. These are similar to the plack units Baez discusses, except that we don't bother making planck's constant equal to 1.

General relativity and pure quantum mechanics have no dimensionless constants, because the speed of light, the gravitational constant, and Planck's constant merely suffice to set units of mass, length and time. Thus, all the dimensionless constants come in from our wonderful, baroque theory of all the forces other than gravity: the Standard Model.

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#### p1l0t

We have a FAQ on why "c" has the value it does https://www.physicsforums.com/showthread.php?t=511385 [Broken], but not one for G.

The rationale is pretty similar though.

I'll mark-up the answer there for G. You might try some of the references there as well.

Because [STRIKE]xxcxx[/STRIKE] G has units, its value is what it is only because of our choice of units, and there is no meaningful way to test whether it changes. These questions [STRIKE]are[/STRIKE] would be more meaningful [STRIKE]when[/STRIKE] if posed in terms of the unitless [STRIKE]fine structure constant.[/STRIKE] gravitational coupling constant http://en.wikipedia.org/wiki/Gravitational_coupling_constant.

Except that unlike the case for the fine structure constant, I don't think we have any direct experimental data on the Gravitational coupling constant.

Basically the numerical value of c, or G, has every bit as much physical significance as saying there are 2.54 centimeters per inch.

I would particularly recommend http://math.ucr.edu/home/baez/constants.html in the references section of the FAQ.

...

Thus, by a proper choice of units, one can (and often does) make G equal to 1 by using geometric units. These are similar to the plack units Baez discusses, except that we don't bother making planck's constant equal to 1.
I understand the number depends on the units you measure it in, that wasn't really what I meant with my questions though. I'll try to think of a better way to restate them I guess.

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#### p1l0t

It is just dawning on me that multiplying by a really tiny number really reduces the overall value. In some respects I guess that makes it quite meaningful. It is that constant which makes it such a weak force.

#### Nugatory

Mentor
It is just dawning on me that multiplying by a really tiny number really reduces the overall value. In some respects I guess that makes it quite meaningful. It is that constant which makes it such a weak force.
Or you could say that it is the weakness of the force that makes the constant so small. Physics is about using math to describe the world around us, so the world tells us what the math must be and not the other way around.

#### p1l0t

Or you could say that it is the weakness of the force that makes the constant so small. Physics is about using math to describe the world around us, so the world tells us what the math must be and not the other way around.
Good point.

#### pervect

Staff Emeritus
Science Advisor
I understand the number depends on the units you measure it in, that wasn't really what I meant with my questions though. I'll try to think of a better way to restate them I guess.
Really good questions / comparisons probably won't involve constants with units. For instance you could take the ratio of the fine structure constant to the gravitational coupling constant. That would be more or less comparing the electrical repulsion between two electrons to their gravitational attraction.

#### p1l0t

Really good questions / comparisons probably won't involve constants with units. For instance you could take the ratio of the fine structure constant to the gravitational coupling constant. That would be more or less comparing the electrical repulsion between two electrons to their gravitational attraction.
Having something to compare it too is probably a good start. I wasn't aware gravity was even noticeable at the molecular level.

#### WannabeNewton

Science Advisor
It's definitely hard to notice; for two protons the ratio will yield about 36 orders of magnitude in favor of the electrostatic force (i.e. $F_{E}/F_{G}\approx 10^{36}$ for the aforementioned system).

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