Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 4 / 10C / c / iii / Solution

The transfer ellipse has semi-major axis and semi-minor axisConservation of angular momentum gives constant areal velocity $h/2$. The satellite sweeps half the ellipse, whose area is $\pi ab/2$, soUsing part (i),This is half the orbital period from Kepler's third law.