How Do You Calculate the Height and Speed of a Geosynchronous Satellite?

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To calculate the height and speed of a geosynchronous satellite, one must first determine the radius "r" using the satellite's orbital period, which matches the Earth's rotation period of 24 hours. The gravitational force acting on the satellite can be equated to the centripetal force to derive the necessary equations. The velocity can be calculated using the formula v = 2πr/T, where T is the orbital period. After finding the radius, the Earth's radius should be subtracted to obtain the satellite's height above the Earth's surface. This approach ensures accurate calculations for both the height and speed of the satellite.
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Homework Statement


A geosynchronous satellite is used for communication and stays at the same place above the equator all the time. Calculate the a)Height of the satellite
b)Speed at which it travels.


Homework Equations



v=2πr\t
a=v2/r
F=Gm1m2\r2

The Attempt at a Solution



I'm not sure how to start this,but i started with velocity but didn't know what radius to use. Is it double the radius of the earth?
 
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I can't stay long but here's a hint: You're solving for the radius "r". What is the period of the Earth's rotation, in other words, how long does it take for the Earth to make one complete revolution? You know by application of Newton's 2nd law that the gravitational force will equal ma, as it is the net force acting on the satellite. After finding "r", make sure you subtract the radius of the Earth to get the height above the Earth at which the satellite orbits.
 

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