A star system consists of a primary star and several planets. The total mass of the system (star plus all planets) is $M_0$. At a certain instant, all the planets are aligned with the star along a single axis. At this instant, the barycenter (center of mass) of the system is located at a distance $r_0$ from the center of the star. Suppose an additional planet of mass $m$ were also present on this axis, located at a distance $4r_0$ from the center of the star, in the same direction as the original barycenter. The barycenter of this augmented system would instead be at a distance $2r_0$ from the center of the star. What is the mass $m$ of the additional planet? (Answer in term of $M_0$)