The figures show a hypothetical planetary system at twodifferent times. The system has a star S and three planets, labeledA, B, and C. The table provides the mass of each body in thesystem, as well as their spatial coordinates (?,?) in their initialand final positions. The spatial coordinates of the bodies aregiven in Astronomical Units (AU). Body Mass (kg) Initital PositionFinal Position S ?S=2.0197×1030 (0,0) (?S,?S) A ?A=2.0735×1028(0.3429,0) (0,−0.5335) B ?B=6.6485×1026 (0.5617,1.2553) (−1.5385,0)C ?C=8.4729×1027 (0,1.6711) (−0.8021,−0.6035) The initial velocityof the center of mass of the system is zero. Find the magnitude ?Sof the star's displacement from the origin in its final position.An x y coordinate system. The star S is at the origin. Planet Alies on the positive x-axis. Planet B is in the first quadrant ofthe graph. Planet C lies on the positive y-axis. Initial PositionAn x y coordinate system. The star S is near the origin in thefirst quadrant. Planet A lies on the negative y axis. Planet B lieson the negative x axis. Planet C is in the third quadrant of thegraph. Final Position ?S= AU
