# Applying Kepler's Third Law

Classical Mechanics Level pending

The planet Xabros is orbiting the sun, in an elliptical path with major axis of length $$2a$$. Doofenschmirz has a machine that can scale the length of the ellipse's major axis by a factor of $$k$$: that is, after using the machine, Xabros will be in a path with major axis of length $$2ka$$. If Doofenschmirz's evil plan is to double the orbital period of Xabros, what is $$k$$?

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