Past exam of the physics 1 paper of the University of Oxford / 2016 / 10 / iii

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- Solution iii

Solution

At the outer tangent point, the vis-viva equation gives

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

. This is below the outer circular Kepler orbit's speed

v_{1} = μ / r_{1}

. The second impulse is therefore also prograde:

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

It raises the pericentre to the outer radius, completing the circularization.

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