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Kepler's Law

A satellite i...

Question

A satellite is moving in elliptical orbit around a fixed planet. If eccentricity of ellipse is e = 0.4 then ratio of maximum speed to minimum speed of satellite is (Answer upto two digits after the decimal point.)

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Solution

By conservation of angular momentum,
$\Rightarrow m v_{1} r_{1} = m v_{2} r_{2}$

$\frac{v_{1}}{v_{2}} = \frac{r_{2}}{r_{1}} = \frac{1 + e}{1 - e} = \frac{1.4}{0.6}$

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