 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-4/10c/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

\overset{r}{¨} - r \dot{θ}^{2}

, so

\overset{r}{¨} - r \dot{θ}^{2} = - \frac{k}{r ^{2}} .

h = r^{2} \dot{θ}

. Substitution of

\dot{θ} = h / r^{2}

yields

\overset{r}{¨} = - \frac{k}{r ^{2}} + \frac{h ^{2}}{r ^{3}} .

The last term is the centrifugal part of the radial effective potential.

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