Gravity, Satellites, Apparent Weightlessness

Weightlessness: Free Fall• Suppose for a rocket flying awayfrom the Earth’s center, the rocketthrust is decreased so that therocket falls back toward the Earthwith acceleration a• The astronaut feels the floorpushing up on him with a forceequal to F N = m (g-a) (exactly thesame as the elevator problem).• Now suppose the thrust is reducedto zero and the rocket begins tofree fall toward the Earth → a = g →F N = m (g-a) = 0 and the astronautexperiences weightlessness.• This holds true for any object infree fall including objects in orbit.• Einstein’s Equivalence Principle →General RelativityNormalforce F NmaIf a = g = 9.8 m/s 2 →F N = 0 WeightlessnessAn Orbiting Satellite• A satellite of mass m in acircular orbit around aplanet of mass M• Gravity provides thecentripetal force:g(r)GMm v2 m orbitr rv orbit2= CentripetalAccelerationrmM6