# Is Gravitational Potential Energy real?

1. Jun 1, 2010

### Mattowander

Exactly what the title says. I wonder if gravitational potential energy close to the Earth is something intrinsic in the object that can be measured or is it completely dependent upon where we consider our 0 level to be. For example if we lifted an object a distance h above the ground and set it on a table, would we be able to measure the potential energy without pushing that object off the table? Obviously if we did that we could measure the final velocity of that object assuming we could apply the conservation of mechanical energy but is there any way we can directly measure the gravitational potential energy of an object? I ask this question because unless I am mistaken, in this type of situation we are free to choose where we set y = 0 and therefore we could give an object a desired potential energy simply by changing what we consider to be ground level.

Am I over-thinking this problem or over thinking it?

2. Jun 1, 2010

### Andrew Mason

It depends on what you mean by "real".

AM

3. Jun 1, 2010

### Mattowander

I know I phrased that badly. But I keep thinking of the following situation : Close to Earth,thinking in 2-D, an object has gravitational potential energy equal to mgh where h is the height above the point y = 0. Since we can set y = 0 at an arbitrary position and therefore give the object pretty much any potential energy we desire, I'm wondering if an object can have an intrinsic potential energy like it has an intrinsic kinetic energy relative to the Earth.

I hope that even though I might have made a mistake in my writing that you can still get the gist of what I'm trying to say.

4. Jun 1, 2010

### dulrich

Two points. First kinetic energy is not as intrinsic as you may think -- it depends on the observer's reference frame. An observer moving with constant velocity will measure a different kinetic energy.

Second, the potential energy is coming from the interaction between the earth and the object. Truly, the potential energy involves the distances between the two centers (of the earth and the object). But for the very small distances involved on the surface of the earth, the interaction is practically constant ($F = GMm/r^2$). This is why the zero point of the potential energy is arbitrary.

5. Jun 1, 2010

### stewartcs

Remember that Thermodynamics (i.e. the study of energy) does not deal with quantities of energy, but rather changes in energy. Therefore an arbitrary reference point is required to describe the change in potential energy of an object from one elevation to another.

CS

6. Jun 3, 2010

### Andrew Mason

As several posters have mentioned, gravitational potential energy is relative. A skier half way up a mountain has positive potential energy with respect to the bottom but negative potential energy with respect to the top. If the skier goes down the hill, that potential energy is converted into kinetic energy, which would seem pretty real to the skier. If the skier goes up the hill, he has to do work against gravity, which is also pretty real to the skier.

When we talk about gravitational potential energy being -GMm/r it is relative to the potential at $r = \infty$.

AM