Satellite Motion

Low Orbit  A container falls off the space station while in low earth orbit. It will move A) straight down toward Earth. A) straight down toward Earth. B) curving slowly down toward Earth. B) curving slowly down toward Earth. C) in the same orbit as the space station. C) in the same orbit as the space station. D) ever farther away due to lower mass. D) ever farther away due to lower mass. E) rapidly away into space. E) rapidly away into space.

Short Period  An object in space would go in a straight line without another force.  Gravity supplies a force to hold objects in circular orbits.  In low orbit the period is related to the gravitational acceleration. no gravity gravity Low Earth orbit period: T < 90 min.

Geosynchronous Orbit  In higher orbits, the gravitational force is significantly less than on the surface. Use the force of universal gravitation.Use the force of universal gravitation. F grav = G M m / r 2F grav = G M m / r 2  The height for a satellite with a 24 hr period can be found. radius: r = 4.22 x 10 7 m altitude is r km = 36,000 km

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. Earth a F net F net = mg a = g v v

Weightlessness  Objects in free fall exert no normal force. F net = -ma = -mg + F NF net = -ma = -mg + F N If a = g, F N = 0If a = g, F N = 0  The same is true in orbit. F net = ma r = F grav + F NF net = ma r = F grav + F N If a r = F grav /m, F N = 0If a r = F grav /m, F N = 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.Acceleration is on the inside pointing inward.  There is a corresponding centripetal force for object on the inside wall. Satellite a F

Station Gravity  The centripetal force is like an elevator accelerating upward. F net = ma r = F NF net = ma r = F N  The net force must be due to a normal force. Experience as weightExperience as weight If r  2 = g then it matches earth’s gravity.If r  2 = g then it matches earth’s gravity. Satellite a F next