Re: What is the method for measuring gravitational potential?

You have gone in a couple of different directions in describing your 
question.  I don't think it is necessary for me to get into general 
relativity and curved space-time to adequately answer the question, 
however.  There are two ways in which people generally look at 
gravitational potential energy.  The first is used to solve dynamics and 
kinematics problems here on earth.  The second is used in more general 
problems involving interactions between any two bodies, particularly 
celestial bodies.

The first method is the one you allude to when you say that potential 
energy increases when you go up in altitude.  This makes intuitive sense 
since it takes work to raise an object to any height above the earth.  This 
energy can then be used by releasing the object from that height and 
allowing it to free fall.  The key to using this technique is the idea that 
only changes in potential energy matter when solving problems.  Since only 
the difference between the potential energy of a system in two different 
configurations matters, the student or engineer is free to choose any 
height as the height at which the potential energy is zero.  In fact, as 
long as the bookkeeping is done consistently, you can choose a different 
point for every object in the system.  In this scheme, we are always 
treating the earth as a fixed object and "assigning" the potential energy 
to the second object.  In reality, of course, the potential energy is a 
property of the system of two objects.

The second, more general approach shares the property that an arbitrary 
zero can be chose, but there is a different intuitive approach.  If there 
were only two objects in the universe and they were infinitely far apart, 
the gravitational attraction between them would be zero.  With no force 
acting, gravity has no potential to do work, so it makes sense to assign 
this configuration the zero point of potential energy.  If one object is 
nudged a little bit toward the other the gravitational force will take over 
and the objects will accelerate toward one another.  The gravitational 
force does work to increase the kinetic energy.  Now, since there was zero 
total energy at the beginning and kinetic energy is increasing, the 
gravitational potential energy must become more and more negative as the 
kinetic energy becomes more and more positive.  So, the closer two objects 
are to one another, the more negative their potential energy becomes.  Look 
in your textbook for the general equation for gravitational potential 
energy and you will find a minus sign.  This minus sign expresses the ideas 
I have been writing about and is consistent with the idea of an attractive 
force between two objects.

Ray Nelson