Why would orbiting space stations that simulate gravity likely be large structures?

Answer 1

Artifical gravity is created by the outward acceleration (centrifugal force) as an object rotates around an axis of rotation. The magnitude of this outward acceleration is given by the centripetal acceleration, which is the opposing inward acceleration keeping the rotating object in circular orbit around the rotating object. In space, this would be done by rotating a space station until the centripetal acceleration is equal to the acceleration of gravity on Earth. Centripetal acceleration is given by the equation: Centripetal Acceleration = Velocity2/ Radius. As you can see, the magnitude of the centripetal acceleration is largely dependent upon the object's distance (distance) from the axis of rotation. Thus, in a space station that is fairly small (has a small radius), a standing astronaut will feel a different centripetal acceleration in his head than in his feet. Take the example of an astronaut standing up in a circular rotating space station with radius 5m and rotating at a speed of 7 m/s. At the astronauts feet (about 5 meters from the axis of rotation), the astronaut's centripetal acceleration will be given by the following equation. CA = 72/5 --> CA = 9.8 m/s2. This is roughly equal to Earth's gravitation acceleration. Now, lets see the magnitude of centripetal acceleration at the astronauts head. If the astronaut is 6 feet tall (about 1.83 meters), then the radius of rotation at the astronauts head is only 3.17 meters (5 meters - 1.83 meters). The speed of rotation will also be slower because the astronauts head, being closer to the axis of rotation, will have to complete a relatively smaller circle to complete one rotation in the same amount of time as the feet. After calculations, the resulting speed of rotation is 4.289 m/s rather than 7m/s. Thus, the centripetal acceleration at the astronauts head is given by the following equation: CA = 4.2892/3.17 --> CA=5.803 m/s2. Thus, we see a serious inconsistency between the centripetal acceleration at the feet of the astronaut and at the head of the astronaut (9.8 m/s2 at the feet and 5.803 m/s2 at the head). This difference would make the astronaut feel extremely uncomfortable and nauseated, rendering them unable to function at the high level needed for space. Instead, lets look at a large space station design. Take, for example, the Stanford Torus, a design that consists of a large 1.8 km in diameter rotating ring. At this large size, the space station would only need to rotate at one rotation per minute and at a rotating speed of 94.24 m/s in order to simulate Earth's gravitational acceleration. with a radius of 900m, the 1.83 meter difference between a astronaut's feet and head would be negligible and thus an astronaut would feel just as if he or she were on Earth. This is why space stations that intend to simulate gravity should be built large enough to minimize the significance of the difference between the radius of rotation of one's feet and one's head.