In planetary motion, the reduced mass of a system [itex]\mu[/itex] is used in order to study the motion of the planet [itex]m[/itex] in the non-inertial frame of the star [itex]M[/itex]. Using [itex]\mu[/itex] the trajectory of [itex]m[/itex] turns out to be a conic. But this is the trajectory of the planet [itex]m[/itex] as seen from the star [itex]M[/itex], correct? I read that in the CM frame the trajectories are still conics (ellipses for istance) but that the focus is in the CM. Moreover the Sun (or the star) also follows a conic trajectory with focus in the CM of the system. Is the trajectory of the planet seen in CM frame different from the one calculated using [itex]\mu[/itex] (and so the one in the [itex]M[/itex] frame)?