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Gravitational Energy Gravitational Work Gravity on the surface of the Earth is a local consequence of universal gravitation. How much work can an object falling from very far from the Earth do when it hits the surface? W F dr r F GmM r2 GmM dr 2 r r 1 1 W GmM r RE W RE RE Gravitational Potential The work doesn’t depend on the path. • Universal gravity is a conservative force The potential is set with U = 0 at an infinite distance. • Gravity acts at all ranges • Gravity is weakest far from the source GmM dr 2 r GmM U r U r Kinetic Energy in Circles For circular motion there speed is related to the centripetal acceleration. • a = v2/r An object moving in a circle has kinetic energy. • K = ½mv2 • K = ½ mar • K=½Fr The kinetic energy is equal to half the work that could be done. F r v Kinetic Energy in Orbit The kinetic energy for a circular orbit is related to the potential energy. mv2 GmM r r2 1 2 GmM mv 2 2r 2K U The total energy in a circular orbit can be described in terms of either the kinetic or the potential energy. E K U E K (2 K ) E K E U /2 Escape Velocity Negative total energy can be viewed as being captured by the force of gravity. To get away from the influence of gravity requires zero or positive energy. The minimum velocity is called the escape velocity. E K U 0 1 2 GmM mv 0 2 r vesc 2GM r On earth, vesc = 11.2 km/s next