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

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- Solution i

Solution

The assumed orbital energy is

E = - μ m / (2 a)

. At a point a distance

r

from the planet,

\frac{1}{2} m v_{e}^{2} - \frac{μ m}{r} = - \frac{μ m}{2 a}, v_{e}^{2} = μ (\frac{2}{r} - \frac{1}{a}) .

This is the vis-viva equation. The semi-major axis and radius are measured from the gravitational focus where the planet lies.

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