Artificial Gravity

We all know that a body will tend to “float” around in a space station orbiting Earth or in a spaceship cruising at a constant velocity with respect to the stars. Some films depict a dumbbell-shaped space station rotating about an axis through its middle perpendicular to the long axis in order to provide artificial gravity. What interesting behavior patterns might be experienced by an astronaut who walks across the axis from one end to the other?

Answer

Space stations and spaceships have been created by authors and screenwriters in a vast array of shapes and sizes. A rotating dumbbell shape has appeared in many space adventures, the rotation providing a pseudo gravity force for Earth creatures. The rotation about the center of mass perpendicular to the long axis provides a pseudo-acceleration acting radially outward called the centrifugal acceleration a_c = v²/r, where v is the tangential velocity value and r is the radial distance from the axis of rotation. The resulting centrifugal force is called a pseudo-force because the actual force is acting radially inward toward the axis of rotation to accelerate the object from its inertial straight-line motion. We must assume that the structural integrity of the space station remains intact that is, the station was designed for the rotation and for the allowed distributions of mass on board.

Using the relation for the angular velocity ω = v/r, we can express the centrifugal force as F_c = mrω². The whole spaceship has the same angular velocity about the rotation axis, so an object’s radial acceleration increases linearly with distance r from the rotation axis. An astronaut at one end of the dumbbell must climb that is, walk up a ladder and then down a ladder from one end to the other through the middle, where the radial acceleration is zero. The muscular effort required changes throughout the climb, so the sensations must be wonderful!