"Artificial Gravity" and Circular Orbits

"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

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