A particle moves in a force field described by where k and a are positive.(a) Write the eq...

A particle moves in a force field described by

where k and a are positive.

(a) Write the equations of motion and reduce them to the equivalent one-dimensional problem. Use the effective potential to discuss the qualitative nature of the orbits for different values of the energy and the angular momentum.

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(b) Show that if the orbit is nearly circular, the apsides will advance approximately by πρ/a per revolution, where ρ is the radius of the circular orbit.