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

## "Artificial Gravity" and Circular Orbits

• Spaceships and space stations in orbit around the Earth are weightless environments. Because the ships and their contents orbit the earth together, they experience identical accelerations, and move together.
• The only significant force experienced by space stations and their contents is the force of gravity due to the Earth; thus, the stations -- and their contents -- are in freefall.
• If an astronaut aboard a space station releases a ball, it continues in its orbit around the Earth, as does he. So the ball doesn't appear to fall.
• But if a space station rotates around its axis, then the walls of the station must exert a centripetal force on the objects within; otherwise, those objects would not move around the center of the station.
• The centripetal force exerted by the walls of a rotating space station causes objects to behave in some ways as if they had weight: balls fall, humans compress the springs on scales. We call the effects of the centripetal force artificial gravity.
• The magnitude of the artificial gravity on a rotating space station can be expressed by its centripetal acceleration:
```                                   v^2
artificial "g"  = ------
R
```
• When objects move around the Earth in circular orbits, the Earth's gravitational force provides the centripetal force they need:
```
grav force    =   centripetal force

G Me M               v^2
----------     =   ----------
R^2                R
```
And thus one can solve for the speed of a body in an orbit of radius R:
```                                            G Me
v        =   sqrt ( ------ )
R
```

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