Question

Let G be the universal gravitational constant and mp be the mass of the planet a satellite is orbiting

Answer 1

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  

$F = \frac{Gm_{p}m }{r^{2} }$ 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'

$F^{'} = \frac{mv^{2}}{r}$ where m = mass of satellite, v = speed of satellite and r = radius of geostationary orbit.

Since both forces are equal,

F = F'

$\frac{Gm_{p}m }{r^{2} } = \frac{mv^{2} }{r}$

$v^{2} = \frac{Gm_{p} }{r} \\v = \sqrt{\frac{Gm_{p} }{r} }$

So, the speed of the satellite is v = √(Gmp/r)

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