Space Elevator 09
Space Elevator 09 : Physics of Space Elevators: (1) Apparent Gravitational Field: A space elevator cable rotates along with the rotation of the Earth. Objects fastened to the cable will experience upward centrifugal force that opposes some of, all of, or more than, the downward gravitational force at that point. The higher up the cable, the stronger is the upward centrifugal force and the more it opposes the downward gravity. Eventually it becomes stronger than gravity above the geosynchronous level. Along the length of the cable, this (downward) actual gravity minus the (upward) centrifugal force is called the apparent gravitational field. The apparent gravitational field can be represented this way: The downward force of actual gravity decreases with height: The upward centrifugal force due to the planet's rotation increases with height: Together, the apparent gravitational field is the sum of the two: where g is the acceleration of actual gravity or apparent gravity down (negative) or up (positive) along the vertical cable (m s?2), a is the centrifugal acceleration up (positive) along the vertical cable (m s?2), G is the gravitational constant (m3 s?2 kg?1) M is the mass of the Earth (kg) r is the distance from that point to Earth's center (m), ? is Earth's rotation speed (radian/s). At some point up the cable, the two terms (downward gravity and upward centrifugal force) equal each other, objects fixed to the cable there have no weight on the cable. This occurs at the level of the stationary orbit. This level (r1) depends on the mass of the planet and its rotation rate. Setting actual gravity and centrifugal acceleration equal to each other gives: On Earth, this level is 35,786 km (22,236 mi) above the surface, the level of geostationary orbit. Seen from a geosynchronous station, any object dropped off the tether from a point closer to Earth will initially accelerate downward. If dropped from any point above a geosynchronous station, the object would initially accelerate up toward space
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