Applying Kepler's Third Law

The planet Xabros is orbiting the sun in an elliptical path with a major axis of length 2 a 2a . Doofenschmirz has a machine that can scale the length of the ellipse's major axis by a factor of k k : that is, after using the machine, Xabros will be in a path with a major axis of length 2 k a 2ka .

If Doofenschmirz's evil plan is to double the orbital period of Xabros, what is k ? k?

2 1 / 3 2^{1/3} 2 2 / 3 2^{2/3} 2 2 2 4 / 3 2^{4/3}

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