1. Gravitational Energy

2. 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 RERE

3. Gravitational Potential  The work doesn’t depend on the path. Universal gravity is a conservative forceUniversal gravity is a conservative force  The potential is set with U = 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 source

4. Kinetic Energy in Circles  For circular motion there speed is related to the centripetal acceleration. a = v 2 /ra = v 2 /r  An object moving in a circle has kinetic energy. K = ½mv 2K = ½mv 2 K = ½ marK = ½ mar K = ½ F rK = ½ F r  The kinetic energy is equal to half the work that could be done. v r F

5. Kinetic Energy in Orbit  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.

6. 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. next On earth, v esc = 11.2 km/s