# Detecting Multiple Planets Around a Star

Staff Emeritus
Gold Member
In the Doppler shift or radial velocity method for detecting exoplanets, it is assumed that the orbital period of the star's planetary companion is equal to the period of the star's detected wobble. I'm assuming that this fact comes straight from the solution to the two-body problem.

My question is, what if a star has multiple planets in orbit around it? Say, for example, we were viewing our solar system from afar. Would we be able to detect anything other than Jupiter? I guess this is an n-body problem, although it seems that the typical thing to do is to assume that the interaction between each planet and the parent star is much greater than the interactions among planets, which can be ignored. So, I guess that this is like 8 independent two-body problems, each of which gives a solution that is a good (zeroth-order? first-order?) solution for that planet's orbit.

What's confusing me is that the solution to each two-body problem would have you believe that the parent star wobbles with a period equal to the orbital period of the second object. So, how could the sun wobble "around" the barycentre on 8 different timescales? What does the wobble look like if there are multiple planets, and how are we supposed to know that they are there?