D.1.4—Gravitational field strength

Define the field

Gravitational field strength is force per unit test mass. For a point or spherical source of mass $M$, it depends on distance $r$ from the source centre. It is a vector directed toward the source, with unit $\mathrm{N\,kg^{-1}}$, numerically equivalent to $\mathrm{m\,s^{-2}}$.

Worked example — surface field

For $M=4.87\times10^{24}\,\mathrm{kg}$ and $r=6.05\times10^6\,\mathrm{m}$, $g=(6.67\times10^{-11})(4.87\times10^{24})/(6.05\times10^6)^2=8.87\,\mathrm{N\,kg^{-1}}$. The result is the force per kilogram at the surface, directed inward.

Read the scaling

At a fixed distance, $g$ is proportional to $M$. At a fixed source mass, doubling $r$ reduces $g$ to one quarter. The field direction is toward the source mass; the scalar expression gives the magnitude. Near a surface, the weight of a mass $m$ is $W=mg$.

Common trap

Do not use the object’s own mass in $g=GM/r^2$ as $M$, and do not use altitude alone for $r$: use distance from the source centre.