Subject: What is the method for measuring gravitational potential?

I recently read an article in your archives (something like "What 
is gravity")in which the author states that as a body decreases 
its distance from another object its gravitational potential 
energy decreases because there is less curvature in space-time.  
In school I learned that as you increase your height above the 
earth your potential energy increases (which makes sense because 
the higher up you are the more kinetic energy you will have by 
the time you come down).  Does the latter method of measuring 
gravitational potential energy only deal with everyday life on 
earth and the former method for larger systems dealing with 
galaxies and solar systems?  Which is more accurate?  It doesn't 
seem right that as you get five meters above the ground you have 
more potential than at twenty meters (as with the former method). 
  As you get farther away from a planet and the curvature 
decreases, an object's acceleration might initially be slower 
since the force is decreased, but by the time it eventually falls 
back down towards the planet it will have much kinetic energy 
which means it must have started with much potential.  Please 
explain.

Re: What is the method for measuring gravitational potential?