5.2: Gravitational Field

The region around a gravitating body (by which I merely mean a mass, which will attract other masses in its vicinity) is a gravitational field. Although I have used the words “around” and “in its vicinity”, the field in fact extents to infinity. All massive bodies (and by “massive” I mean any body having the property of mass, however little) are surrounded by a gravitational field, and all of us are immersed in a gravitational field.

If a test particle of mass $m$ is placed in a gravitational field, it will experience a force (and, if released and subjected to no additional forces, it will accelerate). This enables us to define quantitatively what we mean by the strength of a gravitational field, which is merely the force experienced by unit mass placed in the field. I shall use the symbol $\textbf{g}$ for the gravitational field, so that the force $\textbf{F}$ on a mass $m$ situated in a gravitational field $\textbf{g}$ is

$$\textbf{F} = m \textbf{g}. \label{5.2.1} \tag{5.2.1}$$

It can be expressed in newtons per kilogram, $\text{N kg}^{-1}$. If you work out the dimensions of $g$, you will see that it has dimensions $\text{LT}^{−2}$, so that it can be expressed equivalently in $\text{m s}^{−2}$. Indeed, as pointed out in section 5.1, the mass $m$ (or indeed any other mass) will accelerate at a rate $g$ in the field, and the strength of a gravitational field is simply equal to the rate at which bodies placed in it will accelerate.

Very often, instead of using the expression “strength of the gravitational field” I shall use just “the gravitational field” or perhaps the “field strength” or even just the “field”. Strictly speaking, the “gravitational field” means the region of space surrounding a gravitating mass rather than the field strength, but I hope that, when I am not speaking strictly, the context will make it clear.