Editing Potential energy (section)

=== Local approximation ===
The strength of a gravitational field varies with location. However, when the change of distance is small in relation to the distances from the center of the source of the gravitational field, this variation in field strength is negligible and we can assume that the force of gravity on a particular object is constant. Near the surface of the Earth, for example, we assume that the acceleration due to gravity is a constant {{math|1=''g'' = 9.8 m/s<sup>2</sup>}} ([[standard gravity]]). In this case, a simple expression for gravitational potential energy can be derived using the {{math|1=''W'' = ''Fd''}} equation for [[mechanical work|work]], and the equation
<math display="block">W_\text{F} = -\Delta U_\text{F}.</math>

The amount of gravitational potential energy held by an elevated object is equal to the work done against gravity in lifting it. The work done equals the force required to move it upward multiplied with the vertical distance it is moved (remember {{math|1=''W'' = ''Fd''}}). The upward force required while moving at a constant velocity is equal to the weight, {{math|''mg''}}, of an object, so the work done in lifting it through a height {{mvar|h}} is the product {{math|''mgh''}}. Thus, when accounting only for [[mass]], [[Gravitation|gravity]], and [[altitude]], the equation is:<ref>[https://feynmanlectures.caltech.edu/I_13.html The Feynman Lectures on Physics Vol. I Ch. 13: Work and Potential Energy (A)]</ref>
<math display="block">U = mgh</math>
where {{math|''U''}} is the potential energy of the object relative to its being on the Earth's surface, {{math|''m''}} is the mass of the object, {{math|''g''}} is the acceleration due to gravity, and ''h'' is the altitude of the object.<ref>{{cite web| url=http://hyperphysics.phy-astr.gsu.edu/Hbase/gpot.html| title=Hyperphysics – Gravitational Potential Energy}}</ref>

Hence, the potential difference is
<math display="block">\Delta U = mg \Delta h .</math>