In practice, it is more useful to talk about the gravitational potential at a point. This tells us the g.p.e. per unit mass at the point (just as field strength g tells us the force per unit mass at a point in a field). The symbol used for potential is $\phi $ (Greek letter phi), and unit mass means one kilogram. Gravitational potential at a point is defined as the work done per unit mass bringing a unit mass from infinity to the point.
For a point mass M, we can write an equation for $\phi $ at a distance r from M:

$\phi  =  - \frac{{GM}}{r}$

where G is the gravitational constant as before. Notice the minus sign; gravitational potential is always negative. This is because, as a mass is brought towards another mass, its g.p.e. decreases. Since g.p.e. is zero at infinity, it follows that, anywhere else, g.p.e. and potential are less than zero; that is, they are negative.

Imagine a spacecraft coming from a distant star to visit the Solar System. The variation of the gravitational potential along its path is shown in Figure 17.8. We will concentrate on three parts of its journey: 
As the spacecraft approaches the Earth, it is attracted towards it. The closer it gets to Earth, the lower its g.p.e. becomes and so the lower its potential.
As the spacecraft moves away from the Earth, it has to work against the pull of the Earth’s gravity. Its g.p.e. increases and so we can say that the potential increases. The Earth’s gravitational field creates a giant ‘potential well’ in space. We live at the bottom of that well.
As the spacecraft approaches the Sun, it is attracted into a much deeper well. The Sun’s mass is much greater than the Earth’s and so its pull is much stronger and the potential at its surface is more negative than on the Earth’s surface.

Gravitational potential difference

Very often, we consider problems where it is useful to know how much energy is needed to lift a satellite from the surface of a planet or moon to a height where the satellite can be put into orbit. The equation for the change in potential, $\phi  = \frac{{GM}}{r}$, can be used twice, once to find the potential at the surface and once to find the potential at the orbital height. However, it is much easier to combine the two operations and use the equation:

$\Delta \phi  = GM(\frac{1}{{{r_1}}} - \frac{1}{{{r_2}}})$

Fields: terminology

The words used to describe gravitational (and other) fields can be confusing. Remember:
- Field strength tells us about the force on unit mass at a point;
- Potential tells us about potential energy of unit mass at a point.
You will meet the idea of electric field strength in Chapter 21, where it is the force on unit charge.
Similarly, when we talk about the potential difference between two points in electricity, we are talking about the difference in electrical potential energy per unit charge. In that chapter, you will meet repulsive fields as well as attractive fields and this should develop your understanding as to why the choice of infinity for the zero of potential is the only sensible choice.