Problem Set 9

Due Sunday, November 18, 1pm, in metal homework locker outside B&L 166

Problem 8-22 in the text. Use Eq.(8.20) to explicitly solve for the particle trajectories, r(theta), and then discuss the trajectory behavior, in the following three cases: el²=mu*k, el²>mu*k, and el²<mu*k, where el is the angular momentum and mu is the mass. [15 points]
Problem 8-29 in the text. Hint: first determine the points on the moon's orbit which correspond to the maximum and minimum velocities. Then apply conservation of angular momentum to the motion at these points. [15 points]
A particle moves in an almost circular orbit in a central force field described by the screened Coulomb potential, U^sc=(-k/r)e^-r/a. Compute the total angle of rotation about the center of force, Delta theta, that the particle makes in going one period of oscillation from maximum radial distance to maximum radial distance (this gives the advance of the "apsidal angle" - see section 8.9). Assume that the variation in the radial distance, r_max-r_min is small compared to the average orbit radius r_o. Is the orbit of the particle in general closed or open? Hint: follow similar arguments as done in lecture for the force F=-k/rⁿ. [10 points]

Last update: Tuesday, August 14, 2007 at 5:37:41 PM.