If there is a satellite in geosynchronous orbit

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In a geosynchronous orbit, the centripetal force acting on the satellite is equal to the gravitational force exerted by the Earth. The relevant equations for gravitational force (Fg) and centripetal force (Fc) are provided, allowing for the calculation of the satellite's distance from Earth. Given the satellite's mass, Earth's mass, and the orbital period, one can determine the altitude of the satellite above the Earth's surface. Setting Fc equal to Fg is valid since the gravitational force is what keeps the satellite in circular motion. Understanding this relationship is crucial for solving orbital mechanics problems.
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Homework Statement



Does the centripetal force equal the gravitational force?

Homework Equations



Fg = G(m1)(m2) / r^2
Fc = 4(pi^2)(m)(r) / T^2

The Attempt at a Solution



I have the mass of a satellite in geosynchronous Earth orbit. The period of Earth's orbit, and the Earth's radius and mass.
I need to find the distance of the satellite above earth.

Is it right to set Fc = Fg?
 
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As long as the satellite is traveling in a circular orbit around the Earth, the gravitational force provides the centripetal force. The geosynchronous orbit gives you the period time of the satellite.
 
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