Radius of geosynchronous orbit using the standard 6.67X10^-11 law of gravity and

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5.98X10^24 mass of earth? How do you find the radius of a geosynchronous orbit using
G=6.67X10^-11 N m^2/kg^2 for the standard gravitational law
M=5.98X10^24 kg for the mass of the earth

the equations the teacher gave us are
v=d/t
Vc=sqrt GM/r

What is the radius and how do i do it?

Or do i need the velocity of the earth to do it? He says we don't, but i think we do.

thanks
 
d = the circumference = 2 pi r
t = 24 hours
v = d/t

also, lets see a = v^2/r = GM/r^2
therefore v = sqrt GM/r
your teacher's formula is correct!

therefore
d/t = sqrt GM/r
2 pi r/(24 hours) = sqrt GM/r

You are going to have to move both "r" to the same side, you will get a 3/2 power. If you can't finish from here, and you ask, I will come back and finish -- or check your work.
 
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