The speed of the satellite is v = √(Gmp/r)
At the geostationary orbit, the gravitational force of attraction of the planet on the satellite equals the centripetal force on the satellite.
Let F = gravitational force
[tex]F = \frac{Gm_{p}m }{r^{2} }[/tex] where G = universal gravitational constant, mp = mass of the planet, m = mass of satellite and r = radius of geostationary orbit.
Also, the centripetal force F'
[tex]F^{'} = \frac{mv^{2}}{r}[/tex] where m = mass of satellite, v = speed of satellite and r = radius of geostationary orbit.
Since both forces are equal,
F = F'
[tex]\frac{Gm_{p}m }{r^{2} } = \frac{mv^{2} }{r}[/tex]
[tex]v^{2} = \frac{Gm_{p} }{r} \\v = \sqrt{\frac{Gm_{p} }{r} }[/tex]
So, the speed of the satellite is v = √(Gmp/r)
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