# Gravitational Potential Energy

Hello,

I'm currently studying Gravitation and circular motion. I have a question on the reference point for gravitational potential energy:

In previous units, gravitational potential energy was usually measured from the surface of the Earth (the ground in most cases). Why when an object is in orbit around the earth is its gravitational potential energy measured with respect to the center of the Earth, and not the Earth's surface?

Thanks

## Answers and Replies

AlephZero
Science Advisor
Homework Helper
Newton showed that the gravitational attraction of a sphere, at any point outside of it, is the same as if all the mass of the sphere was at its center.

So assuming the earth is spherical, its the gravitational potential is a function of the distance from center and nothing else.

However if you are considering something moving a short distance relative to the size of the earth, near to the earth's surface, you can assume that a small part of the earth's surface is flat and gravity acts perpendicular to the flat surface. (Usually, you can also usually ignore the fact that the earth is rotating!)

Newton showed that the gravitational attraction of a sphere, at any point outside of it, is the same as if all the mass of the sphere was at its center. So assuming the earth is spherical, its the gravitational potential is a function of the distance from center and nothing else.
However if you are considering something moving a short distance relative to the size of the earth, near to the earth's surface, you can assume that a small part of the earth's surface is flat and gravity acts perpendicular to the flat surface. (Usually, you can also usually ignore the fact that the earth is rotating!)

Note that you can add a constant to the potential energy and all your equations will still work since changes in potential energy will be unaffected. You just can't use that definition of the potential energy as the work required to move an object to infinity. So you can think of the potential energy being zero at the surface of the Earth as being the potential energy zeroed at the center of the Earth plus a constant.