Physics 235: Classical Mechanics
Prof. S. Teitel email@example.com ----- Fall 2001
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.
- A particle moves in an almost circular orbit in a central force field described by the screened Coulomb potential, Usc=(-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, rmax-rmin is small compared to the average orbit radius ro. 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]