# The height in the potential gravitational energy

Is the height in the formula the vertical distance from the bottom to the center of gravity of object, or is it just the vertical distance from the bottom to the very top of the object.

I mean..
If there is a sphere with mass m and radius r and placed at height h, what is its potential gravitational energy ?
Is it just mgh or mg(h-r) ?

Doc Al
Mentor
If there is a sphere with mass m and radius r and placed at height h
Height "h" measured from what point? Also, is that the height of the center of the sphere or the bottom?

Realize that the reference point for measuring the gravitational PE is arbitrary. What really matters is the change in PE.

• terryds
Height "h" measured from what point? Also, is that the height of the center of the sphere or the bottom?

Realize that the reference point for measuring the gravitational PE is arbitrary. What really matters is the change in PE.

So, it is the vertical distance from Earth surface to the very bottom of an object, right ?
I think when I refer the height to the center of gravity or anything that is above the very bottom of an object, when it reaches the Earth surface, it'll still have the height (measured to the center of gravity or radius in a sphere). But, the fact is that it has no potential gravitational energy since it has reached the Earth surface.
Am i right?

Last edited:
Doc Al
Mentor
So, it is the vertical distance from Earth surface to the very bottom of an object, right ?
As I said before, the GPE = 0 point is arbitrary.

I think when I refer the height to the center of gravity or anything that is above the very bottom of an object, when it reaches the Earth surface, it'll still have the height (measured to the center of gravity or radius in a sphere). But, the fact is that it has no potential gravitational energy since it has reached the Earth surface.
Am i right?
If you want to measure the GPE from some reference level (using the earth's surface is fine) one usually measures the height of the center of mass with respect to that reference. But for a sphere, it doesn't matter, since it is symmetric.

Again, what matters is the change in GPE when the object moves from one point to another.

• terryds