Losing gravitational potentional energy

[Tachyonie]

Ok, just a crazy idea of mine since I am bored, and arguing with itisali does not amuse me.

Imagine universe with nothing in it appart from a single planet, let's say something like earth. Now let's imagine that 100 km above the Earth you have a shoe. The shoe has some gravitational potential energy.
Now what would happen to that energy if I was to teleport that shoe another 1000 km further from the earth, without using any of the energy the shoe already has. Would it lose some of its gravitational potentional energy? And where would it go?

Tachyon.

 

[Doc Al]

The "shoe" doesn't have gravitational PE, the "shoe + planet" does.

 

[Mentz114]

I've seen this suggested somewhere. In the Lagrangian for the shoe/planet system, the potential energy of the shoe is negative

L = KE - PE

and some people object to this and prefer to write

L = KE + K - PE

where K is a large valued constant, representing a 'global pool' of energy. Changing the Lagrangian like this does not alter the equations of motion.

In this scenario, you could say that the 'lost' potential energy has gone back to K.

But this means that dK/dr is not zero and the EOMs have changed. I think this illustrates the difficulty in locating potential energy.

 

[ObsessiveMathsFreak]

If the shoe was suddenly teleported then it would gain potential energy, not lose it.

 

[Riogho]

Why would you bother using a shoe? I mean, isn't it much more fun to propose teleporting a kitten?

 

[Tachyonie]

Why would you bother using a shoe? I mean, isn't it much more fun to propose teleporting a kitten?

I am not a sadist who tests equipment which doesn't even exist yet on poor kittens and risking that the head will be teleported inside out. Thats why... murderer!

If the shoe was suddenly teleported then it would gain potential energy, not lose it.

Id love to know why!

Tachyon.