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?. r. R E. Gravitational Potential. The work doesn’t depend on the path.
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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? r 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
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 = ½ F r The kinetic energy is equal to half the work that could be done. Kinetic Energy in Circles v F r
The kinetic energy for a circular orbit is related to the potential energy. The total energy in a circular orbit can be described in terms of either the kinetic or the potential energy. Kinetic Energy in Orbit
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. On earth,vesc= 11.2 km/s next