Absolute potential enegy

Potential energy is given by 'mgh' where the 'g' is acceleration due to the Earth's gravity. As soon as you escape the Earth's gravitational field, it stops affecting you. So the value of PE at infinity doesn't really come up.

 

Ya I realized that. Do I feel silly!

 

As others have pointed out, typically the potential energy is conventionally defined as U = 0 when the distance is infinity, r = ∞. Following this convention, U is negative for values of r < ∞. In other words, most of the time U is negative when an object is near Earth.

This is merely a convention though. You can define U = 0 at any distance you wish, but it's usually chosen to be zero at r = ∞. There is no such thing as "absolute" potential energy.

Although this is not part of your original question, if you wanted to you can find the rest of the formula by evaluating the work done by slowly lifting a mass from the surface of the Earth R, up to infinity.
[tex] W = \int_R^{\infty} \vec F \cdot \vec {dr} [/tex]
or more generally at an arbitrary radius r (such that r is greater than the radius of the Earth, of course),
[tex] W = \int_r^{\infty} \vec F \cdot \vec {dr'} [/tex]


Then use the work-energy theorem to express that work in terms of potential energy.

I gather you know what the gravitational force, [itex] \vec F [/itex] is, as a function of [itex] r [/itex]?