Two planets A and B orbit a star with coplanar orbital paths that don’t intersect. The major axes of the orbits are perfectly aligned, but the major axis of A is larger than that of B. A and B are observed to have eccentricities $0.5$ and $0.75$, respectively. What is the minimal possible ratio of semi-major axes of A to B?

Source: usaaao

Celestial Mechanics

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