Applying Kepler's Third Law

The planet Xabros is orbiting the sun in an elliptical path with a major axis of length 2a2a. Doofenschmirz has a machine that can scale the length of the ellipse's major axis by a factor of kk: that is, after using the machine, Xabros will be in a path with a major axis of length 2ka2ka.

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

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