Universal Gravitational Constant

[Allojubrious]

I was wondering if somebody could please explain the gravitational constant to me and also if they could give me the correct equation for it and explain the equation, because I have been receiving many odd variations of the gravitational constant and I would really like a good clear explanation of it and it's equation.



Thanks so much!

 

[HallsofIvy]

The only "gravitational constant" I know is the "G" in Newtons formula for gravitational force: F= -GmM/r^2 where M and m are the masses of the two objects and r is the distance between their centers. There is no "formula" for G, it is, as the term "gravitational constant" says, a constant, a number.

It is determined by measurement of the motions of the planets and, when m and M are measured in kg and r in meters, and F in Newtons, it has the value 6.683484 x 10^-11 N(m/kg².

Of course, in Einstein's tensor formulation, there is no "gravitational constant".

 

[bcrowell]

Of course, in Einstein's tensor formulation, there is no "gravitational constant".

Wait, I don't think this is right. You may have been misled by the fact that in GR, people often work in units where G=1, so it can be omitted from equations.

 

[TurtleMeister]

it has the value 6.683484 x 10^-11 N(m/kg².

I don't think that's right either.

 

[Allojubrious]

I am aware of this common equation but my main wonder (with the equation) is the "N x
m/kg squared, if somebody could clarify that part, and especially what "Newton's constant" is exactly.

 

[atyy]

Let's say you have a car that goes 3 miles for every gallon of petrol.

More generally X miles requires L gallons.

X=GL where G=3 miles/gallon.

In this example, G is a constant in an equation that converts between miles and gallons. It has units of mile/gallon so that both sides of the equation have the same units.

Similarly the universal gravitational constant appears in the equation a=GM/r², where a is the acceleration of a particle at distance r from mass M.

So G is a constant in an equation that converts between acceleration and (mass/distance²). It has units of kg^-1 m³ s^-2 so that both sides of the equation have the same units.

 

[Allojubrious]

But I'm just curious about what the N*m^2/kg^2 stand for. This is the only part that confuses me.

 

[Mentz114]

But I'm just curious about what the N*m^2/kg^2 stand for. This is the only part that confuses me.

N is Newtons ( a unit of force), m is metres and Kg is Kilograms.

 

[Allojubrious]

Thank you very much, now my question is: metres for what? kilograms for what? and, what does Newtons constant equal??

So if somebody could answer these questions, it would be an extremely big help!

 

[pervect]

Try reading about the SI standard. The English version is published by the BIPM is at http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf, there are probably lots of other discussions.

 

[Allojubrious]

Thank you pervect, that link is actually very helpful! Extremely helpful! But I'd really rather a human being explain to me what the metres and kilograms are for in the universal gravitational constant equation, and also what exactly Newton's Constant equals!
So if somebody could just answer these questions it would be of immense gratitude.

 

[bcrowell]

I'm not a fan of Khan Academy, but they do have a lecture that covers this topic, including the units, in some detail: http://www.khanacademy.org/video/introduction-to-Newton-s-law-of-gravitation?playlist=Physics

 

[HallsofIvy]

Thank you very much, now my question is: metres for what? kilograms for what? and, what does Newtons constant equal??

So if somebody could answer these questions, it would be an extremely big help!

As I said, Newton's formula for gravitational force is
F= \frac{GmM}{r^2}
m and M are masses measured in kg (kilograms). r is a distance measured in m (meters). F is a force measured in N (Newtons). In order to get Newtons as the result, we have cancel the two "kg" s in the numerator, from "mM" and the m^2 in the denominator, for r^2, leaving "N". To do that we need to multiply by a constant with units N m^2/kg^2= N(m/kg)^2.

 

[mathfeel]

I'm not a fan of Khan Academy, but they do have a lecture that covers this topic, including the units, in some detail: http://www.khanacademy.org/video/introduction-to-Newton-s-law-of-gravitation?playlist=Physics

I have heard of Khan, but never actually saw one of its video until your link. I stopped after I hear him say that (paraphrasing):

I am not an expert on this, but I think G can change. It is not truly truly a constant. but for our purpose it's this number

I think he means that the numerical value of G can change in different unit system. Or did he meant that we might one day measures a different G? Does he have any idea what a physical constant is

 

[bcrowell]

I have heard of Khan, but never actually saw one of its video until your link. I stopped after I hear him say that (paraphrasing):
I think he means that the numerical value of G can change in different unit system. Or did he meant that we might one day measures a different G? Does he have any idea what a physical constant is

Yeah, that seemed like a goof to me, too, and it's one of the things that made a bad impression on me and makes me say that I'm not a fan of Khan Academy. He does, however, preface it modestly with a statement that he's not an expert and he could be wrong. What bothered me more about the video was that it was very plug-and-chug oriented. There was nothing about how we know Newton's law of gravity is true, for example.

 

[Allojubrious]

m and M are masses measured in kg (kilograms).

So do you add the two masses (in kilograms) to substitute for the "Kg^2" in this part:"N*m^2/Kg^2"?

 

[bcrowell]

So do you add the two masses (in kilograms) to substitute for the "Kg^2" in this part:"N*m^2/Kg^2"?

You don't add them, you multiply them. And they're not substituting for the kg symbols, they're canceling them.

 

[Allojubrious]

So then, what is the general point of the "N*m^2/Kg^2" in the universal gravitational constant??

 

[Dale]

Those are the units of G. It is no different than if you said your height was h=175 cm, or your mass were m=90 kg, or if the police said your speed was s=150 km/h.

 

[atyy]

It means that the force between two 1 kg masses placed 1 m apart is 6.67X10^-11 N.

F=Gm₁m₂/r²
=(6.67X10^-11 Nm²kg^-2)(1 kg)(1 kg)/(1 m)²
=6.67X10^-11 N

 

[HallsofIvy]

This is getting stranger and stranger. "mM" means that you multiply the two masses, not add them.

 

[inottoe]

So then, what is the general point of the "N*m^2/Kg^2" in the universal gravitational constant??

I'll have a go.

The force between two masses m1 and m2 separated by distance r is proportional to \frac{m1\times{m2}}{r^2}. But this expression alone gives units kg^2/m^2 (kg=kilograms, m=metres). But force is in units of N (Newtons), which means that whatever the proportionality constant, it's units must cancel out the kg^2/m^2 expression, and also include the unit N. In other words, we need (units)\times{kg^2/m^2}=N. This implies that (units)=Nm^2/kg^2. It has no other meaning than that.

 

[Allojubrious]

Oh okay now i finally understand the Universal Gravitational Constant!
Thank you so much all, this has been of enormous help, because this constant has bothered me quite a lot!

Thank you, thank you!

 

[Allojubrious]

But just as a quick question, how do I find my mass?? Or the mass of anything for that matter??

 

[russ_watters]

But just as a quick question, how do I find my mass?? Or the mass of anything for that matter??

With a scale...

I'm really starting to wonder if this is serious or not.

 

[Allojubrious]

Sorry I was just wondering!

But thanks for the help all!