Classical Dynamics of Particles and Systems · Problem 8-36

Dynamics of a System of Particles — Marion & Thornton

Physics — Mechanics · central-force-apsidal-advance-yukawa

Problem

A particle moves in an almost circular orbit in a force field described by F(r)=−(k/r2)exp⁡(−r/a)F(r) = -(k/r^2)\exp(-r/a). Show that the apsides advance by an amount approximately equal to πρ/a\pi\rho/a in each revolution, where ρ\rho is the radius of the circular orbit and where ρ≪a\rho \ll a.

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