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

A circular orbit of radius $r$ has speed $v_c(r)=\sqrt{k/r}$. On the transfer ellipse, the velocity is tangential at both apsides and has magnitude $h/r$. The first prograde burst therefore changes the speed byAt $r_2$ the satellite must again accelerate in the direction of motion to circularize, byThese are the two impulses of a Hohmann transfer.