Problem: If a satellite orbits a planet at a distance of 6541 kilometers from the center, at a speed of 7932 meters per second, then what is its centripetal acceleration? What gravitational force must the planet exert on the 4141 kg satellite in order to provide this acceleration?
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Solution: The centripetal force holding a satellite in a circular orbit must be equal to the gravitational force at that point.
For the current problem, the distance must be expressed in meters. 6541 kilometers is 6541(1000) meters. The centripetal acceleration required to keep the satellite in a circular orbit is thus
cent accel = ( 7932 m/s) ^ 2 / ( 6541 * 1000) meters = .9618 meters per second per second.
The force required to accelerate a 4141 kg satellite at this rate is 4141 kg ( .9618 m/s/s) = 3982 Newtons.