HW2 - Physics 110, Problem set #2 Due April 14, 2010 1. (25...

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Physics 110, Problem set #2 Due April 14, 2010 1. (25 pts) In lecture (3) I showed that perturbing a circular orbit in 2 / 1 r central force field will result in stable “oscillations” around the unperturbed solution. These small oscillations are in fact the difference between a circular orbit and a slightly elliptical one. Repeat the calculation and show that a circular orbit is also stable against perturbations in the z direction. Use the methods and notations used in the class. 2. (25 pts) A mass is dropped from the top of a tower (height 10m) located on the equator. Ignore the air friction. Approximate the Earth as a sphere, with 24 10 6 × = M Kg , 6 10 4 . 6 × = R m , 2 1 3 11 10 7 . 6 × = s Kg m G . Include the effects of the Coriolis force, the centrifugal force, and the corrected gravitational acceleration at a nonzero elevation. Think carefully about the relative contributions of various effects and make approximations. a.
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