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Hello everyone, I'd like to share a doubt I am currently struggling with.

So we know that ΔU=−W, where ΔU is the difference of potential energy and Wthe work done by the force to move the body from point A to point B.

When analyzing this for the gravitational force, since we have U=−GmM/R, with the minus due to the fact that we're dealing with an attractive force, if we pick U(∞)=0, we have that ΔU<0 when a particle is moved from infinity to another point.

That makes sense to me because the work done by the gravitational force is positive, and that means that the kinetic energy is increasing ( ΔK=W); since the total energy must be conserved, when starting at infinity with a null total energy, if K is increasing then U

must decreasing accordingly.

On the other hand, if we move a body from a point A to a point B "outwards", the work done by gravity is negative and that means that gravity will "slow down" the body (aka, the kinetic energy will decrease and the potential one will increase).

Supposing that what I've said so far is actually correct, what confuses me is the definition that some books give when dealing with the potential energy.

More precisely, a possible definition is that "the potential energy of a system is the work done by an external agent against the force to create such a configuration, with the particles of the system starting from a picked reference point".

I'm having a hard time understanding the correct interpretation of the work done by the "external agent", especially in this specific case: here this external agent would do negative work to bring the particles from infinity to a certain configuration. What does someone having to do negative work mean?

That such a configuration would happen even without them doing anything, since the force will do the job in their stead? I think I can sort of tell that's because gravity would pull these particles close to each other without me having to work against it to build the desired configuration, and on the other hand if I start with n particles close to each other and I want to move them apart I have to do work against gravity hindering me, but I cannot say I'm totally comfortable with this explanation.

How should I interpret it?

So we know that ΔU=−W, where ΔU is the difference of potential energy and Wthe work done by the force to move the body from point A to point B.

When analyzing this for the gravitational force, since we have U=−GmM/R, with the minus due to the fact that we're dealing with an attractive force, if we pick U(∞)=0, we have that ΔU<0 when a particle is moved from infinity to another point.

That makes sense to me because the work done by the gravitational force is positive, and that means that the kinetic energy is increasing ( ΔK=W); since the total energy must be conserved, when starting at infinity with a null total energy, if K is increasing then U

must decreasing accordingly.

On the other hand, if we move a body from a point A to a point B "outwards", the work done by gravity is negative and that means that gravity will "slow down" the body (aka, the kinetic energy will decrease and the potential one will increase).

Supposing that what I've said so far is actually correct, what confuses me is the definition that some books give when dealing with the potential energy.

More precisely, a possible definition is that "the potential energy of a system is the work done by an external agent against the force to create such a configuration, with the particles of the system starting from a picked reference point".

I'm having a hard time understanding the correct interpretation of the work done by the "external agent", especially in this specific case: here this external agent would do negative work to bring the particles from infinity to a certain configuration. What does someone having to do negative work mean?

That such a configuration would happen even without them doing anything, since the force will do the job in their stead? I think I can sort of tell that's because gravity would pull these particles close to each other without me having to work against it to build the desired configuration, and on the other hand if I start with n particles close to each other and I want to move them apart I have to do work against gravity hindering me, but I cannot say I'm totally comfortable with this explanation.

How should I interpret it?

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