Potential energy in 2 gravity fields

[flm]

Hi everyone,

First, sorry if the question is stupid, I do not have any background
in Physics. Just very curious.

Potential energy due to gravity is:
m * g * h Joules

Now, suppose I lift a weight on Moon at a given height. I will have:
1.6 * m * h Joules

I maintain it at that height and go to Earth. There, I will have:
9.8 * m * h Joules

Where does the added energy come from ? I cannot see why it would
come from the Moon Earth travel itself, as only the mass matters during
the motion ...

Thanks for your time and answers !

Cheers,

Fabien.

 

[Orodruin]

First of all, the mgh formula is only a valid approximation as long as the gravitational field may be considered homogeneous. At scales as large as the distance from the gravitational center, this is no longer true.

I maintain it at that height and go to Earth.

You cannot do this. In order to transport it to Earth, it needs to change its height from both the lunar surface and the Earth's surface. This involves a change under which the gravitational field most certainly is not homogeneous. In addition, the zero-point of the different potentials are chosen differently. You are comparing apples and carrots.