Define gravitational field

Gravitational field

The gravitational field $\vec{g}$ at a point in space is defined as the gravitational force $\vec{F_g}$ exerted on a small test mass $m$ (with units kg) divided by that test mass.

Step 1: Formula
$\vec{g} = \frac{\vec{F_g}}{m}$

Step 2: Units
Gravitational field has units of newtons per kilogram $\left( \frac{N}{kg} \right)$, equivalent to meters per second squared $\left( m/s^2 \right)$.

Step 3: For a point mass $M$
At a distance $r$ (units m) from point mass $M$ (units kg),
$\vec{g} = -G \frac{M}{r^2} \hat{r}$
where $G = 6.67430 \times 10^{-11} \, \frac{m^3}{kg \cdot s^2}$ is the gravitational constant (units $\frac{m^3}{kg \cdot s^2}$) and $\hat{r}$ is the unit vector.

\vec{g = \frac{\vec{F_g}}{m}
(units: N/kg or m/s²)}