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# 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).

A man-made satellite in orbit around the earth.