Mgh & -gmM/R increase with distance from Earth

[ofeyrpf]

Hi,

I know potential = mgh where g can be considered constant close to the surface of the Earth. So as we move away from the Earth the h and P increase.
And taking P = 0 @ infinity then P = -GMm/r so P < 0 always and increases to 0 as you move away from the Earth.
So it seems there is no potential at infinity and even less as you get closer to the Earth! Is that correct?
What if for P = -Gmm/r, I put P = 0 at the surface of the Earth as it is for mgh?

 

[Dale]

Yes. Of course, only potential differences are physically significant so you can add any arbitrary constant to your potential and thereby set your zero somewhere else.

 

[rcgldr]

So it seems there is no potential at infinity and even less as you get closer to the Earth!

Better stated as potential = 0 at ∞, and about -62.53 mega-joules / kilogram at the surface of the earth. In either case, potential increases with distance from the Earth's surface. You could define P = 62.53 mega-joules / kilogram - GMm/r to get a potential of 0 at the Earth's surface and 62.53 mega-joules / kilogram at ∞, which would correspond to mgh at relatively low altitudes.

The constants that would correlate with ~ 62.53 mega-joules / kilogram and g = 9.80655 m / s² (standard value):

G = -6.674 x 10^-11 N (m/kg)²
mass of Earth = 5.974 x 10²⁴ kg
radius of Earth = 6376 x 10³ m

 

[ofeyrpf]

Hi,

Thanks for the reply. I understand now and see how P can be set to 0 anywhere but always "potential increases with distance from the Earth's surface."

It seems strange that although potential is caused because an object is in the Earth's gravitational field, it increases as you move away from the Earth, where i would think the Earth had less influence.

 

[rcgldr]

It seems strange that although potential is caused because an object is in the Earth's gravitational field, it increases as you move away from the Earth, where i would think the Earth had less influence.

That's because potential energy is defined as the negative of the work done by the force generating the field. If you consider the sum of the kinetic energy of an object in free fall (with no drag or other forces involved) in the gravitation field plus it's gravitational potential energy, the sum will be a constant as gravitational potential energy decreases and kinetic energy increases.

Gravitational potential is defined as the gravitational potential energy per unit mass, so it follows the same convention of increasing with distance from the source of the gravitational field.