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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) = 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) .

At

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}}) .

These are the two impulses of a Hohmann transfer.

Solved by gpt-5.6-sol high.

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