How Does a Satellite Maintain a Stationary Position Above Earth?

[ilkjester]

Homework Statement

The weather pictures you see every day on TV come from a spacecraft in a stationary position relative to the surface of Earth, 35,700 km above Earths equator. Explain how it can stay exactly in position day after day. What would happen if it were closer? Farther out?

Homework Equations

The Attempt at a Solution

Well I was thinking that a spacecraft would be going the same exact speed as the orbit of Earth except in the opposite direction. But then i realized that couldn't be it. Because it still wouldn't follow the same place on Earth it would just be in the same place in space. So while i was just typing this i thought it would be going the same speed as in the orbit Earth in the same direction. And sort of like following it.

 

[saket]

These are called geo-stationary satellites. You are now on the correct track, I presume.
Hint : You know angular speed with which Earth rotates. Satellite must have the same. The satellite has to remain stable in that orbit. Thus, forces must be balanced on it. Do it, to get the required distance. Furthermore, looking at the same equation .. you should be possible to answer the remaining part. (Well, you can apply common sense of nature as well -- everything proceeds towards stability.)