I know that if I have a two-body system, the sun and the earth, then the common centre of mass is orbited every 365 days. What about if I add another planet in, say jupiter? Does the sun still orbit the centre of mass every 365 days? With two bodies, their orbital period about the centre of mass is the same. But jupiter and earth have different orbital periods, so how do you know how often the sun orbits now, when there are two periods to choose from?