 Solution

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

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

r

v_{c} (r) = 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 by

Δ v_{1} = \frac{k}{r _{1}} (\frac{2 r _{2}}{r _{1} + r _{2}} - 1) .

r_{2}

the satellite must again accelerate in the direction of motion to circularize, by

Δ v_{2} = \frac{k}{r _{2}} (1 - \frac{2 r _{1}}{r _{1} + r _{2}}) .

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