# PS2 - Phys601/F11/Problem Set 2 Due(upgraded 2.1H Kepler...

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Phys601/F11/Problem Set 2 Due 09/19/11 (upgraded) 2.1H Kepler Problem A particle of mass m moves in the 1/r gravitational potential of a fixed massive point object of mass M. Let k=GMm and p = m v . Let L = r x p be the angular momentum with r (t) being the position vector from the center of the mass M. Use the constancy of angular momentum L and the energy E to formulate first order differential equations in t for r(t) and φ (t). Find from these a differential equation in φ for the orbit r( φ ). By making the substitution u = 1/r, solve the resulting equation (look up the integral) to find an expression for r( φ ). Compare with Eq (3.55) in the text. For what values of E would you get a circle, an ellipse, a parabola, and a hyperbola. 2.2H Laplace-Runge-Lenz vector A particle of mass m moves in the gravitational field of a fixed massive point object of mass M. Let k=GMm and p = m v . Let L = r x p be the angular momentum with r (t) being the position vector from the center of the mass M. (a)

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## This note was uploaded on 12/29/2011 for the course PHYSICS 601 taught by Professor Hassam during the Fall '11 term at Maryland.

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PS2 - Phys601/F11/Problem Set 2 Due(upgraded 2.1H Kepler...

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