Paper 4, Section II, B

Dynamics and Relativity | Part IA, 2016

The radial equation of motion of a particle moving under the influence of a central force is

r¨h2r3=krn\ddot{r}-\frac{h^{2}}{r^{3}}=-k r^{n}

where hh is the angular momentum per unit mass of the particle, nn is a constant, and kk is a positive constant.

Show that circular orbits with r=ar=a are possible for any positive value of aa, and that they are stable to small perturbations that leave hh unchanged if n>3n>-3.

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