A satellite that goes around the earth once every 24 hours (86,400 s) is called

Question

A satellite that goes around the earth once every 24 hours (86,400 s) is called a geosynchronous satellite. If a geosynchronous satellite is in an equatorial orbit, its position appears stationary with respect to a ground station, and it is known as a geostationary satellite.

Find the radius (as measured from the center of the Earth) of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants:

The universal gravitational constant G is 6.667*10^-11 N*m*2/kg^2.
The mass of the earth is 5.98*10^24 kg.

Explanation / Answer

Let v be the speed of the satellite.

Hence => 2r = v*86400 ....1

Also
mv2/r = GMm/r2

=>(2r/86400)2 /r = GM/r2

r = 42.24*106 m

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