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**.

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

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?

- 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**? - How strong is the gravitational force between Al's head and the PS?
*(Hint: ask the instructor for clues)*

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