Universal Gravitational Constant

In summary, the gravitational constant, also known as Newton's constant, is a fundamental physical constant that is used in the formula for gravitational force. It is determined by measuring the motions of planets and has a value of 6.683484 x 10-11 N(m/kg2). It has units of N m^2/kg^2, which means it is a conversion factor between units of mass and distance in the formula. While it is commonly denoted as G, it is also referred to as "Newton's constant" in honor of Sir Isaac Newton who first described the law of gravity.
  • #1
Allojubrious
61
0
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!
 
Physics news on Phys.org
  • #2
The only "gravitational constant" I know is the "G" in Newtons formula for gravitational force: [itex]F= -GmM/r^2[/itex] 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".
 
  • #3
HallsofIvy said:
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.
 
  • #4
HallsofIvy said:
it has the value 6.683484 x 10-11 N(m/kg2.

I don't think that's right either.
 
  • #5
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.
 
  • #6
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.
 
  • #7
But I'm just curious about what the N*m^2/kg^2 stand for. This is the only part that confuses me.
 
  • #8
Allojubrious said:
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.
 
  • #9
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!
 
  • #11
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.
 
  • #13
Allojubrious said:
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
[tex]F= \frac{GmM}{r^2}[/tex]
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 [itex]m^2[/itex] in the denominator, for [itex]r^2[/itex], leaving "N". To do that we need to multiply by a constant with units [itex]N m^2/kg^2= N(m/kg)^2[/itex].
 
  • #14
bcrowell said:
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
 
  • #15
mathfeel said:
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.
 
  • #16
HallsofIvy said:
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"?
 
  • #17
Allojubrious said:
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.
 
  • #18
So then, what is the general point of the "N*m^2/Kg^2" in the universal gravitational constant??
 
  • #19
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.
 
  • #20
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
 
  • #21
This is getting stranger and stranger. "mM" means that you multiply the two masses, not add them.
 
  • #22
Allojubrious said:
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 [itex]\frac{m1\times{m2}}{r^2}[/itex]. But this expression alone gives units [itex]kg^2/m^2[/itex] (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 [itex]kg^2/m^2[/itex] expression, and also include the unit N. In other words, we need [itex](units)\times{kg^2/m^2}=N[/itex]. This implies that [itex](units)=Nm^2/kg^2[/itex]. It has no other meaning than that.
 
  • #23
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!
 
  • #24
But just as a quick question, how do I find my mass?? Or the mass of anything for that matter??
 
  • #25
Allojubrious said:
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.
 
  • #26
Sorry I was just wondering!

But thanks for the help all!
 

1. What is the Universal Gravitational Constant?

The Universal Gravitational Constant, denoted as G, is a fundamental physical constant that represents the strength of the gravitational force between two objects with mass. It is a key component in Isaac Newton's Law of Universal Gravitation.

2. How is the Universal Gravitational Constant determined?

The Universal Gravitational Constant is determined through various experiments and measurements, such as the Cavendish experiment, which measures the gravitational force between two masses. The current accepted value of G is 6.67430(15) x 10^-11 m^3 kg^-1 s^-2.

3. Why is the Universal Gravitational Constant important?

The Universal Gravitational Constant is important because it helps us understand and predict the behavior of objects in the universe. It is a crucial component in many equations and theories, including the calculation of orbital motion and the gravitational potential between objects.

4. Does the Universal Gravitational Constant ever change?

There is no evidence to suggest that the Universal Gravitational Constant changes over time or in different locations in the universe. However, some theories, such as Einstein's General Theory of Relativity, propose that gravity is not a constant force, but rather a curvature of space-time caused by mass and energy.

5. How does the Universal Gravitational Constant relate to other physical constants?

The Universal Gravitational Constant is related to other physical constants, such as the speed of light and the Planck constant, through various equations, including Newton's Law of Universal Gravitation and Einstein's Field Equations. These constants are all fundamental in understanding the behavior of the universe at both the macro and micro levels.

Similar threads

Replies
4
Views
2K
Replies
19
Views
417
  • Other Physics Topics
Replies
5
Views
2K
Replies
3
Views
904
  • Other Physics Topics
Replies
8
Views
2K
  • Special and General Relativity
Replies
4
Views
1K
  • Other Physics Topics
Replies
4
Views
2K
  • Other Physics Topics
Replies
25
Views
3K
  • Introductory Physics Homework Help
Replies
10
Views
524
Replies
2
Views
857
Back
Top