 Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2016/10/ii/solution

a = (r_{0} + r_{1}) /2

. The vis-viva equation gives the transfer speed at the inner tangent point,

v_{p} = \frac{μ}{r _{0}} \frac{2 r _{1}}{r _{0} + r _{1}} .

Both old and new velocities are tangential there, so the required first impulse is prograde, with

Δ v_{1} = \frac{μ}{r _{0}} (\frac{2 r _{1}}{r _{0} + r _{1}} - 1) .

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