Hi, first off, please excuse me if this doesn't sound clear, but it here goes anyway. I'm taking an Astronomy class in which we're asked to solve equations by taking the ratio instead of plugging in numbers. Even after the professor walked me through an answer I'm still having trouble with it, and it's making me feel "slightly" less than intelligent. Here's a sample of what she's asking us to do:

The two stars rotate around their common center of mass with a period of 1 year. If we increase the distance to 200AU, what will the new period be?

The formula to solve this is p² = a^3, where p = period, and a= semimajor axis

Here's the answer she gave me for this:

Pold = 1yr

Pnew² = 2³ Pold²

Can someone please help me understand how?