As well as the force on a mass in a gravitational field, we can think about its energy. If you lift an object from the ground, you increase its gravitational potential energy (g.p.e.). The higher you lift it, the more work you do on it and so the greater its g.p.e. The object’s change in g.p.e. can be calculated as $mg\Delta h$, where $\Delta h$ is the change in its height (as we saw in Chapter 5).
This approach is satisfactory when we are considering objects close to the Earth’s surface. However, we need a more general approach to calculating gravitational energy, for two reasons:
- If we use $g.p.e = mg\Delta h$, we are assuming that an object’s g.p.e. is zero on the Earth’s surface. This is fine for many practical purposes but not, for example, if we are considering objects moving through space, far from Earth. For these, there is nothing special about the Earth’s surface.
- If we lift an object to a great height, g decreases and we would need to take this into account when calculating g.p.e.
For these reasons, we need to set up a different way of thinking about gravitational potential energy. We start by picturing a mass at infinity, that is, at an infinite distance from all other masses. We say that here the mass has zero potential energy. This is a more convenient way of defining the zero of g.p.e. than using the surface of the Earth.
Now we picture moving the mass to the point where we want to know its g.p.e. As with lifting an object from the ground, we determine the work done to move the mass to the point. The work done on it is equal to the energy transferred to it; that is, its g.p.e., and that is how we can determine the g.p.e. of a particular mass.