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# Summary of gravitation equations

Gravitational force: $F= GMm/r^2$

Gravitational field strength: $g=F/m=GM/ r^2$

Gravitational potential energy: $E_{\text{g}}=U=-GMm/r$

Change in gravitational PE (in uniform gravitational field): $\Delta E_{\text{g}}=\Delta U=W=m g \Delta h$

Gravitational potential: $\Phi=V=E_{\text{g}}/m=-GM/r$

The gravitational field strength is the negative of the gravitational potential gradient: $-\text{d}\Phi/\text{d}r=g=GM/r^2$

Orbital speed: $v_{\text{o}}=\sqrt{GM/r}$

Escape speed: $v_{\text{e}}=\sqrt{2GM/ r}$

Universal Gravitational Constant: $G=6.674\times 10^{-11} \text{ N M}^2 \text{ kg}^{-2}$

Gravitational field strength on Earth: $g = 9.81 \text{m s}^{-2}$

Radius of geostationary orbit: $r = 42 164 \text{ km}$

$M$ and $m$: mass, $r$: distance between two bodies; $\Delta h$: change in distance relative to the gravitational field (e.g. height).