The orbit of Pluto is elongated with an eccentricity of 0.25. What is the approximate ratio of Pluto's orbital speed at perihelion to its orbital speed at aphelion?

May 24, 2016

$\sqrt{\frac{5}{3}}$

Explanation:

Use $v = \sqrt{\mu} \left(\left(\frac{2}{r}\right) - \left(\frac{1}{a}\right)\right)$, perihelion = $a \left(1 - e\right)$ and aphelion $= a \left(1 + e\right)$.

Here e = 0.25, approximately.

Now, for any planet, the ratio of the speeds at perihelion and aphelion becomes

$\sqrt{\frac{1 + e}{1 - e}}$ and here it is $\sqrt{\frac{1.25}{0.75}} = \sqrt{\frac{5}{3}}$.