Potential Energy and gravitation

[shounakbhatta]

Hello,

Can someone please explain me:

F=G m1xm2/R^2

In potential energy U=mgh

Generally it is also written that:

U=-Gxm1xM2/r+K. How -G comes into play?

Also Newton's above law of Gravitation in vector form is written as:

F_12=-Gm1m2/r12^2 r12

Here also how -G comes into play?

Coming to Gravitation acceleration:
If one of the masses is larger than the other, gravitational field is defines as:

g=-GM/r^2xr_hat

How again -G comes into play?

If somebody can explain in a step by step method....


Thanks,

-- Shounak

 

[russ_watters]

Upper-case G is the universal gravitational constant. It is basically just a conversion factor. It is negative by convention.

 

[shounakbhatta]

Hello,

What is the conversion factor?

Does that mean the equation for G and -G are the same?

-- Shounak

 

[tiny-tim]

Hello Shounak!

This thread is similar to your other thread, https://www.physicsforums.com/showthread.php?t=662573

Is there anything here that has not yet been answered there?

 

[PJC01]

Hello Shounak,

Firstly, the equation F=G m1xm2/R^2 represents Newton's law of gravitation. This equation shows the force of attraction between two objects with masses m1 and m2 at a distance R apart. G is the gravitational constant, which is a constant value that helps determine the strength of the gravitational force between two objects. It is a fundamental constant of nature and is approximately equal to 6.67 x 10^-11 Nm^2/kg^2.

Next, the equation U=mgh represents the potential energy of an object at a height h above the ground. This is known as gravitational potential energy, and it is derived from the work-energy theorem. The negative sign in front of G in the equation U=-Gxm1xM2/r+K represents the attractive nature of the gravitational force. This means that the potential energy decreases as the objects get closer together, and it increases as they move further apart.

In the vector form of Newton's law of gravitation, F_12 represents the force exerted on object 1 by object 2, and it is equal to -Gm1m2/r12^2 r12. The negative sign in front of G represents the attractive nature of the force, and r12 is the vector from object 2 to object 1. This equation is used to calculate the direction and magnitude of the gravitational force between two objects.

Finally, the equation g=-GM/r^2xr_hat represents the gravitational field, which is a measure of the gravitational force per unit mass at a given point in space. The negative sign in front of G here also represents the attractive nature of the gravitational force, and r^2 is the distance from the center of the larger mass (M) to the point where the gravitational field is being measured. The unit vector r_hat indicates the direction of the gravitational field.

In summary, the negative sign in front of G in these equations represents the attractive nature of the gravitational force, and it is a fundamental constant that helps determine the strength of this force. I hope this explanation helps clarify your understanding of potential energy and gravitation. Let me know if you have any further questions.

Best,