Calculating the Radius of a Geosynchronous Satellite Orbit Around Earth

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To calculate the radius of a geosynchronous satellite orbiting Earth, the orbital period is established as 24 hours or 86400 seconds. The relevant equation for orbital motion is v = 2(pi)(r)/T, which describes the relationship between orbital radius and period. However, gravitational force must also be considered, leading to the equation F_gravity = G(m1*m2)/r^2, where G is the gravitational constant and m1 and m2 are the masses involved. The solution requires integrating these equations to find the radius R from the center of the Earth. Understanding the interplay between gravitational force and orbital mechanics is crucial for solving the problem.
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Homework Statement


http://i241.photobucket.com/albums/ff4/alg5045/MUG_co_6.jpg

A satellite that goes around the Earth once every 24 hours is called 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 R 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:

G=6.67*10^-11
mass of the Earth = 5.98*10^24 kg
radius of the Earth = 6.38*10^6 m


Homework Equations





The Attempt at a Solution



I have no idea how to even begin this problem.
 
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What is a geosynchronous satellite's orbital period? What are the relevant equations regarding orbital period?
 
The orbital period is 24 hours or 86400 seconds. I think the relevant equation is v = 2(pi)(r)/T.
 
You aren't incorporating gravity. You need to do that.
 

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