# The newest fashion statement: the Personal Satellite!

It's the latest craze to sweep the nation: the Personal Satellite, a shiny little ball which floats in mid-air as it orbits around your head.

The standard model is a sphere of mass m = 0.008 kg with little, tiny rocket engines all over its surface. The engines fire in exactly the right direction, and with exactly the right force, to keep the ball moving in a perfect circle of radius R = 1 m around one's head.

Sally programs her PS to orbit her head with a period of P = 3 seconds.

1. Draw a free-body diagram showing all the forces acting on the PS
2. How large must the vertical force provided by the rockets be?
3. How large must the horizontal force provided by the rockets be?
4. Describe the total force exerted by the rockets on the PS as a vector.

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Astronaut Al lives deep in space, far from the Earth and Moon. He decides to get a PS of his own ... but instead of powering it with little rockets, Al tries to use GRAVITY to keep the PS circling around his head.

Will it work?

1. How much force would it take to make the PS orbit Al's head with a radius of R = 1 m and a period of P = 3 seconds?
2. How strong is the gravitational force between Al's head and the PS? (Hint: ask the instructor for clues)

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