Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 316 / 2 / e / Solution

A non-coplanar encounter may change $I$ while preserving $T_p$, so the projection of the accessible phase space onto the $(a,e)$ plane is a region rather than one curve. A pair $(x,e)$ is accessible for some inclination exactly whenFor $T_p=5/2$, the boundary curves are obtained by taking $\cos I=1$ or $-1$; intermediate inclinations fill the region between them. In particular, inclinations at least as large as the value found in part (d) allow the region to meet $e=0$.

Solved by gpt-5.6-sol high.