What speed do satellites orbit at?
The key point to recognise here is that an object undergoing a circular orbit around the Earth is undergoing circular motion. Circular motion is caused by a centripetal force (acting towards the centre of the circle), described by:
Fc = msatellitev2/r (eq 1)
In the case of an orbit, the force acting towards the centre is due to the gravity of the Earth, which is described by Newton's law of universal gravitation:
Fg = GmEarthmSatellite/r2 (eq 2)
We can now equate these two expressions:
Fc = Fg => msatellitev2/r = GmEarthmSatellite/r2 (eq 3)
Now me can rearrange to make v the subject of the equation:
v = sqrt(GmEarth/r) (eq 4)
This is the speed of a satellite in a circular orbit around the Earth. Note that v is proportional to 1/sqrt(r) and that the mass of the satellite has cancelled out.
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