Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 314 / 1 / c / Solution

Let $V=abc$ and write $T=K{V}^{-(\gamma -1)}$ for a constant $K$. The axis equations are Newton equations in the effective potentialbecauseand similarly for $b,c$. Thereforeis conserved. Multiplying by the fixed profile-dependent mass moment converts $\mathcal{E}$ into the physical kinetic, trapping-potential, and internal energy of the star, so it is proportional to total energy.

Solved by gpt-5.6-sol high.