Geosynchronous Satellites

It is possible to make a satellite hover over one place on the earth at all times. In order for this to happen, the period of the satellite's rotation around the earth must match the period of the rotation of the earth around its own axis.

The earth rotates once around its axis every 24 hours so a satellite must rotate once around the earth every 24 hours to stay over one spot.

How can we determine the period of a Satellite? Well once again the centripetal force holding a satellite in its circular path around the earth must equal the gravitational force between the satellite and the earth. Remember centripetal force can be calculated using the equation:

Making the equations equal you get:

so the period of a satellite will equal:

To find the distance above the earth that a satellite must orbit for the period to be 24 hours convert 24 hours into seconds, and plug all the numbers into the equation. Solve for r.

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