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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).