Gravitational Potential Energy

[J. Richter]

Hi.

I am a little confused about this:

If I throw a stone straight upwards from the surface of the Earth, with the escape speed of 11,2 km/s, assuming that no air or other particles gets in the way, and waited for a very, very long time, the velocity of my stone (and the Earth in the opposite direction) would be almost 0, and the gravitational potential energy between my stone and the Earth would be almost 0 as well, according to the formula for gravitational potential energy.

However I used a lot of energy to throw that stone.
That energy I used to actually do some work, must be stored somehow, as it can’t disappear.

It is obvious, that the energy is stored in this “end” scenario itself.
If something far out there in space gave the stone a tiny little push towards the Earth, it would accelerate “backwards”, until it reaches 11,2 km/s, hit the surface of the Earth, and converts it’s kinetic energy to heat.

This kind of “stored” energy that the two masses have, when being far away from each other, to make it up for the loss of energy in my muscles after throwing the stone, appears to be different from the potential energy described in the formula for gravitational potential energy.

And that’s what confuses me.

If we can’t call this additional “stored” energy for potential energy between the masses, what can we call it then? And why does the formula for gravitational potential energy say that the resulting energy in this “throwing stone“ thought experiment is 0, when I actually did some work on the stone while throwing it?

That seems to be the same as saying, that the energy I used is lost forever.

 

[Doc Al]

This kind of “stored” energy that the two masses have, when being far away from each other, to make it up for the loss of energy in my muscles after throwing the stone, appears to be different from the potential energy described in the formula for gravitational potential energy.

Why do you think that? That "stored" energy is gravitational potential energy.

And that’s what confuses me.

If we can’t call this additional “stored” energy for potential energy between the masses, what can we call it then? And why does the formula for gravitational potential energy say that the resulting energy in this “throwing stone“ thought experiment is 0, when I actually did some work on the stone while throwing it?

You have to compare the final energy of 0 to what you started with. Gravitational PE between two objects is given by:

$$-\frac{Gm_1m_2}{r}$$

It is negative for finite distances. Thus the work you did on the stone increases the total energy to 0.

 

[astrokreng]

Hi there,

I can understand your confusion about the concept of gravitational potential energy. Allow me to clarify some points for you.

Firstly, the formula for gravitational potential energy (GPE) that you mentioned is only applicable in a system where the two masses are stationary and not in motion. In your thought experiment, the stone and the Earth are both in motion, and therefore the formula cannot accurately represent the energy of the system.

Secondly, the energy that you used to throw the stone is not lost forever. It is transformed into different forms of energy - kinetic energy of the stone, potential energy of the stone-Earth system, and heat energy due to friction. This transformation of energy is governed by the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

Now, coming to the additional "stored" energy that you mentioned - this is indeed potential energy between the two masses, but it is not gravitational potential energy as described by the formula. This energy is a combination of gravitational potential energy and kinetic energy of the system. In your thought experiment, the stone has both kinetic energy due to its motion and potential energy due to its position in the Earth's gravitational field.

In summary, the formula for gravitational potential energy is only applicable in specific conditions, and the energy you used to throw the stone is not lost forever but transformed into different forms. I hope this helps to clear up your confusion. Keep asking questions and exploring the wonders of science!