Proof of the equation of gravational potential energy

[jwu]

Homework Statement

All we know the gravitational potential energy is U=-GMm/r. But when I got confused when I was trying to understand the proof of this equation.

Homework Equations

Here's what they did:
W by grativity=GMm(1/r2-1/r1)
Therefore, since △Ugrav=-W by grav, we get
U2-U1=-GMm(1/r2-1/r1)
Let's choose out U=0 reference at infinity.that is , we decide to allow U2→0 as r2→infinity. Then this equation becomes U=-GMm/r

The Attempt at a Solution

Here's my question:
What does it mean by "Let's choose out U=0 reference at infinity.that is , we decide to allow U2→0 as r2→infinity. Then this equation becomes U=-GMm/r"?
Why the U2 would approach to 0 when r2 approached to infinity? And what ti U=0 reference?
Thank you!

 

[jack action]

We can't measure energy, only the difference between two states, just like velocity: Nobody can say "my velocity is 0". But you can say "my velocity is 0 with respect to ..."

So just like you assume something is at rest when measuring velocity (ex.: the ground, even though the Earth is moving w.r.t. the sun), you have to assume a point where energy is 0, no matter the one you choose. You just select the one that makes the equation "cleaner", which in this case is when r2 = infinity.

 

[Acut]

It's a matter of convention.
When you solve a few problems about gravitational potential energy, you will see this is a good convention to follow.
You could have set U=0 at Earth's surface, but it will give you some trouble when solving equations.

The same convention is used in electrostactics, get used to it!