A satellite that goes around the earth once every 24 hours iscalled a geosynchronous satellite. If a geosynchronoussatellite is in an equatorial orbit, its position appearsstationary with respect to a ground station, and it is known as ageostationary satellite
Find the radius Rof the orbit of a geosynchronous satellite that circles the earth.(Note that Ris measured from the center of the earth, not the surface.)

R=4.22*10⁴km

Explanation:

The tangential speed of the geosynchronous satellite is given by:

Because is the circumference length (the distance traveled) and T is the period (the interval of time).

Now, we know that the centripetal force of an object undergoing uniform circular motion is given by:

If we substitute the expression for in this formula, we get:

Since the centripetal force is the gravitational force between the satellite and the Earth, we know that:

Where G is the gravitational constant () and M is the mass of the Earth (). Since the period of the geosynchronous satellite is 24 hours (equivalent to 86400 seconds), we finally can compute the radius of the satellite:

This means that the radius of the orbit of a geosynchronous satellite that circles the earth is 4.22*10⁴km.

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