Gravitational Potential (problems with definition)

[Cozy_Powell]

I tried to get the potential from the potential energy and I get a positive sign for potential...! I cannot find what I did wrong.
- Gravitational force is conservative so its work W is symmetrical to the change in potential energy U.
- Potential is the work done by gravitational force, per unit mass, to bring a mass from infinity to a certain point P.

Initial position of mass: ∞
Final position of mass: point P

W = - ΔU
W = - (U_p - U_∞)
W = - (-GMm/r_p - (-GMm/r_∞))
W = - (-GMm/r + 0)
W = GMm/r
W/m = GM/r

Potential = φ = W/m = GM/r

It should be negative...

Thank you.

 

[jbriggs444]

The definition you used has the wrong sign convention. Potential energy is the work that must be done by you to bring a mass from infinity to a certain point P. It is the negative of the work done by gravity during that same process.

Equivalently, potential energy can be taken as the work that would be done by gravity as a mass moves from point P to infinity.