Satellites in orbit such that they look like they don't move

[newtonistheman]

Homework Statement

Some communication satellites are put into a circular geosynchronius orbit in which the satellite remains above a certain postion on the Earth's equator as it orbits. Such a satellite would always be in the same position in the sky as seen from the transmitting or recieveing equipment of a communications broadcasting network. Find the angular speed of the satellites orbit necessary for it to reamin above the same point above the equator. What must be the orbitial radius of such a satellite?

Homework Equations

(GMm)\r^2=mw^2r
F=(GMm)\r^2

The Attempt at a Solution

I solved for w=squareroot(GM\r)
How am i to know what the radius is? I think i need another equation to input for the radius to find w. Then I can find the radius. Is this the right way to go?

 

[Hurkyl]

Another equation might be useful. Is there any information in the problem you haven't used? Is there any extra information you can extract from what you have used?

 

[andrevdh]

Your solution equation needs a rework.

What would the period of revolution, T, of such satellite be?

$$\omega = \frac{2 \pi}{T}$$

 

[newtonistheman]

but i don't know what the radius is

 

[andrevdh]

If you've got the period of revolution, $$T$$, you can calculate the angular speed with the formula in my previous post. The satellite completes $$2 \pi$$ radians (one revolution) during this time.