Gravitational EnergyGravitational WorkGravitational PotentialKinetic Energy in CirclesKinetic Energy in OrbitEscape VelocityGravitational EnergyGravitational EnergyGravitational WorkGravitational WorkGravity on the surface of the Earth is a local Gravity on the surface of the Earth is a local consequence of universal gravitation.consequence of universal gravitation.How much work can an object falling from very far How much work can an object falling from very far from the Earth do when it hits the surface?from the Earth do when it hits the surface?2rGmMF rREERrRrGmMWdrrGmMWrdFWE112Gravitational PotentialGravitational PotentialThe work doesn’t depend on the path.The work doesn’t depend on the path.•Universal gravity is a conservative forceUniversal gravity is a conservative forceThe potential is set with The potential is set with UU = 0 at an infinite distance. = 0 at an infinite distance.•Gravity acts at all rangesGravity acts at all ranges•Gravity is weakest far from the sourceGravity is weakest far from the sourcerGmMUdrrGmMUr2Kinetic Energy in CirclesKinetic Energy in CirclesFor circular motion there For circular motion there speed is related to the speed is related to the centripetal acceleration.centripetal acceleration.•aa = = vv22//rrAn object moving in a circle An object moving in a circle has kinetic energy.has kinetic energy.•KK = ½ = ½mvmv22•KK = ½ = ½ marmar•KK = ½ = ½ F rF rThe kinetic energy is equal The kinetic energy is equal to half the work that could be to half the work that could be done.done.vrFKinetic Energy in OrbitKinetic Energy in OrbitThe kinetic energy for a The kinetic energy for a circular orbit is related to the circular orbit is related to the potential energy.potential energy.The total energy in a circular The total energy in a circular orbit can be described in orbit can be described in terms of either the kinetic or terms of either the kinetic or the potential energy.the potential energy.UKrGmMmvrGmMrmv22212222/)2(UEKEKKEUKEEscape VelocityEscape VelocityNegative total energy can be Negative total energy can be viewed as being captured by viewed as being captured by the force of gravity.the force of gravity.To get away from the To get away from the influence of gravity requires influence of gravity requires zero or positive energy.zero or positive energy.The minimum velocity is The minimum velocity is called the escape velocity. called the escape velocity. nextrGMvrGmMmvUKEesc202102On earth, vesc = 11.2
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