# The orbit of a geosynchronous satellite

You've all seen satellite images of weather patterns:

In order to provide continuous coverage of one section of the Earth -- such as the Eastern US -- a satellite must have a very special orbit: it must have a period of (almost) exactly 24 hours. If it does, then it will seem to hover directly over one area on Earth.

How can we cause a satellite's orbit to have a period of P = 24 hours? Hmmm. Maybe we just need to find the right orbital radius R ....

1. What is the speed v of a geosynchronous satellite? Your answer should have some factor of R in it ...
2. What is the centripetal acceleration of this satellite? Your answer should still have R in it ...
3. What is the acceleration due to gravity for this satellite? Again, your equation should have some factor of R.
4. Solve for the orbital radius R at which gravity provides the required centripetal acceleration.
5. How far above the surface of the Earth is this?
6. Let's make a scale model of the Earth and some satellites. I'll place a soccer ball at the front of the classroom, to represent the Earth.
• How far away from the soccer ball should I place a model of the ISS?
• How far away from the soccer ball should I place a model of a geosynchronous satellite?