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

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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** ....

- What is the speed
**v**
of a geosynchronous satellite?
Your answer should have some factor of **R** in it ...
- What is the centripetal acceleration of
this satellite? Your answer should still have
**R** in it ...
- What is the acceleration due to gravity for this satellite?
Again, your equation should have some factor of
**R**.
- Solve for the orbital radius
**R**
at which gravity provides
the required centripetal acceleration.
- How far above the surface of the Earth is this?
- 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?
- How far away from the soccer ball should I
place a model of the Moon?

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