Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

The orbit of a geosynchronous satellite

You've all seen satellite images of weather patterns:


Thanks to Unisys

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 ....

(as you answer the following questions, use symbols in equations -- do NOT plug in any numbers until step 4)

  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.


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Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.