Sometimes it's near, sometimes it's far

Geometry Level 3

A planet revolves around its star in an elliptical orbit of eccentricity \(0.6\), the star being at one of the ellipse's foci.

The planet is said to be at aphelion when the distance between the planet and the star its maximum; at perihelion, when the distance between the star and the planet is minimum.

If \(r_\text{ap}\) and \(r_\text{per}\) are the distances between the planet and the star at aphelion and perihelion respectively, then find \(\dfrac{r_\text{ap}}{r_\text{per}}\).

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