Equation for Satellite in geosynchronous oribt

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To find the velocity of a satellite in geosynchronous orbit without using the radius, one must consider the orbital period of 24 hours and the relationship between angular velocity and linear velocity. The angular velocity can be calculated as 2π radians divided by the orbital period in seconds. For the second part, the radius can be determined using the centripetal force equation, which relates mass, angular velocity, and radius. This approach allows for the calculation of both velocity and radius without directly using the other variable in the respective equations. Understanding these relationships is crucial for solving the problem effectively.
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Homework Statement



Find Velocity of satellite in GS orbit around Earth but you cannot use r in the solution

And find r of satellite in GS orbit but you cannot use velocity in the solution

Homework Equations



V=Sqroot of G*Me/r, Me being the mass of the Earth but you can't use r from this equation

The Attempt at a Solution


I know at GS the satellite would travel around the Earth in 24 hours and a full revolution around a circle is 2pi, so i can get the angular revolution but then i can't figure out v without using r still
 
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The velocity depends on the radius r. I am not sure how they want you to answer the first part.

As for the second part, you can get out easily by using the centripetal force =mω2r
 
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