Lecture4 Energy Stability Viral Theorm

Lecture4 Energy Stability Viral Theorm - Energy, Stability,...

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Energy, Stability, and the Virial Theorem 2/6/09 Astronomy 309R - Spring 2009 1
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2/6/09 Astronomy 309R - Spring 2009 2 Kinetic and Potential Energy • Any moving object has positive kinetic energy , which equals to one half, times the object’s mass, times the object’s velocity squared . • Any object in the presence of other objects has negative gravitational potential energy , which is proportional to the product of the masses of the two objects, and inversely proportional to their distance.
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2/6/09 Astronomy 309R - Spring 2009 3 Energy vs. Momentum • Is not associated with specific direction. • Its value can be positive or negative. • Need not be associated with motion. • Is conserved in a truly isolated physical system. • Is associated a specific direction (i.e., the direction of motion). • Its magnitude is always positive. • Is always associated with motion. • Is conserved in a physical system not acted on by an external force.
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2/6/09 Astronomy 309R - Spring 2009 4 Stability A self-gravitating system of stars, like a galaxy or a galaxy cluster, is stable if in face of any small perturbation , the system returns to its previous state. A system that is not stable undergoes a violent rearrangement, or an instability , when slightly perturbed. Gravitational fragmentation is one form of instability. In nature and in the universe,
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Lecture4 Energy Stability Viral Theorm - Energy, Stability,...

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