# Satellite motion

The orbital speed ($$v_{\text{o}}$$) of a satellite is the speed at which a satellite moves around its primary on a circular orbit, for example the Moon around the Earth.

The escape speed ($$v_{\text{e}}$$) is the initial speed needed for a projectile to leave the gravitational field of another body. A projectile is an object without onboard propulsion. The equations are:

$$$ v_{\text{o}}=\sqrt{G\frac{M}{r_{\text{o}}}} \quad \quad v_e=\sqrt{2G\frac{M}{r_{\ell}}}$$$

If $$r_{\text{o}}=r_{\ell}$$, then $$v_{\text{e}}= v_{\text{o}} \sqrt{2} $$.

In any case, the mass of the satellite is irrelevant to its orbital or escape speed.

$$G=$$universal gravitational constant; $$M=$$mass of the primary (e.g the Earth); $$m=$$mass of the satellite (too small to significantly affect primary), $$r_{\text{o}}=$$orbital radius of a satellite; $$r_{\ell}=$$distance between centre of the Earth and launch position (launch radius).