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Artificial Gravity Central Force There is no normal or tension force affecting things in orbit. Like falling bodies that accelerate, a satellite accelerates toward the earth. Gravity is a central force. orbital velocity centripetal acceleration Satellite Earth Force on Mass Newton’s law of acceleration applies to orbits. • Centripetal acceleration times mass is the force of gravity F The situation is the same for the satellite or any object in the satellite. a Earth Satellite or astronaut Free Fall The net force of an object in circular orbit matches the centripetal acceleration. This is the same for a freely falling object. Velocity does not change the force or acceleration. v Fnet a a=g Fnet = mg v Earth Weightlessness Objects in free fall exert no normal force. • Fnet = -ma = -mg + FN • If a = g, FN = 0 The same is true in orbit. • Fnet = mar = Fgrav + FN • If ar = Fgrav/m , FN = 0 Objects in orbit are weightless. Spin the Station A spinning station in orbit has a centripetal acceleration of its own. • Acceleration is on the inside pointing inward. There is a corresponding centripetal force for object on the inside wall. Satellite F a Station Gravity The centripetal force is like an elevator accelerating upward. • Fnet = mar = FN Satellite The net force must be due to a normal force. • Experience as weight W mar mrw 2 • If rw2 = g then it matches earth’s gravity. F a Centrifuge A centrifuge spins to create an artificial gravity. • Liquid separation • Pilot training • Amusement rides Gravitron The Gravitron is an amusement ride that uses centripetal force. • Rotates at 24 rpm • Diameter is 14 m W mar mrw 2 r 7m w (2 )( 24rpm)(1 min/ 60 sec) w 2.5rad/s rw 2 44m/s 2 4.5 g Centripetal Correction The spin of the earth creates a centripetal acceleration toward the axis of the earth. a = w2r The effect is like accelerating down in an elevator. Items weigh less at the equator.