Gravitational Potential Energy Definition

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I have a technical question regarding the definition of gravitational potential energy: How correct is it to discuss/define the gravitational potential energy of object A without regard for the other bodies that are exerting a gravitational force on object A?

I find this kind of thing in science books all the time: "The gravitational potential energy of the vase is 20 J..."

How well does this compare with: "The gravitational potential energy of the vase-Earth system is 20 J..."?

I personally think the second version is better, but I have enough doubts and interest to ask.

Ultimately, how should gravitational potential energy be defined?
 

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I have a technical question regarding the definition of gravitational potential energy: How correct is it to discuss/define the gravitational potential energy of object A without regard for the other bodies that are exerting a gravitational force on object A?
It's not correct at all.

I find this kind of thing in science books all the time: "The gravitational potential energy of the vase is 20 J..."
Little by little, such sloppy usage is going away.

How well does this compare with: "The gravitational potential energy of the vase-Earth system is 20 J..."?
That's the more correct version, found in the better textbooks.

I personally think the second version is better, but I have enough doubts and interest to ask.
Good for you. :smile:

Ultimately, how should gravitational potential energy be defined?
As a joint property of the two objects and their gravitational field.
 

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