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# 5.4.1: Field of a Point Mass

[ "article:topic", "authorname:tatumj" ]

Equation 5.3.1, together with the definition of field strength as the force experienced by unit mass, means that the field at a distance $$r$$ from a point mass $$M$$ is

$g = \frac{GM}{r^2} \quad \text{N kg}^{-1} \text{ or m s}^{-2} \label{5.4.1} \tag{5.4.1}$

In vector form, this can be written as

$\textbf{g} = -\frac{GM}{r^2} \hat{\textbf{r}} \quad \text{N kg}^{-1} \text{ or m s}^{-2} \label{5.4.2} \tag{5.4.2}$

Here $$\hat{\textbf{r}}$$ is a dimensionless unit vector in the radial direction.

It can also be written as

$\textbf{g} = -\frac{GM}{r^3} \textbf{r} \quad \text{N kg}^{-1} \text{ or m s}^{-2} \label{5.4.3} \tag{5.4.3}$

Here $$\textbf{r}$$ is a vector of magnitude $$r$$ − hence the $$r^3$$ in the denominator.