Past Papers

If you have a verified solution to a past paper question, please send it to me and I will add it here.

Corrections: 1999

Anthony Challinor and I think that the answer to 1999 C10 should read

precesses through an angle of (pi/4) (d/r_0) per orbit

not

precesses through an angle of (3 pi/2) (d/r_0) per orbit.

An examiner has confirmed that our answer is correct.

Solutions

1999 C10

(sketch)
The effective potential is

 U'(r) = k(r+d)^2 / 2 + J^2/(2 m r^2)

The orbital frequency \Omega is given by

 \Omega^2 = (k/m) ( 1 + d/r_0 ) .

The frequency of simple harmonic oscillations in the effective potential, \omega, is given by

 \omega^2 = 4 (k/m) ( 1 + (3/4) d/r_0 ) .

So the perturbed orbit is roughly an ellipse, and, if we assume the perturbation is purely radial (so J is unaffected), the angle of precession per orbit is

          \pi d / ( 4 r_0 ) ,

the sense of the precession being the same as the sense of the orbit.

David MacKay <mackay@mrao.cam.ac.uk>

Last modified: Mon Jan 31 17:38:47 2000