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"explain why the orbital radius and the speed of a satellite in circular orbit are not independent"

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In order to achieve stable circular gravitational and centrifugal force must be in balance.

(mv^2)/(r)=G(mM)/(r^2) \\ v^2=G(M)/(r)\\ v=\sqrt{G(M)/(r)
This relationship tells closer the closser your orbit is to the surface of the planet the faster you have to go. Which makes sense because the closer you are to the planet the stronger gravitational force gets.

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User Robert Sandiford
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