Map Sapling Learning macmillan learning The figures show a hypothetical planetar

Question

Map Sapling Learning macmillan learning The figures show a hypothetical planetary system at two different times. The spatial coordinates (x, y) of the bodies are given in Astronomical Units (AU). In the first picture, the velocity of the center of mass of the system is zero. Find the magnitude, ds, of the star's displacement. ms- 2.6307 x100 kg ma 2.6845 x1028 kg 70129 x 1026 kg mc 8.9173 x 1027 kg Number AU ms-7 (0, 14245) TC (0.8105, 1.2553) (0.3891, 0) (-1.5385, 0) (0, 0) (0,-0.2381) (-0.9709, -0.9409)

Explanation / Answer

The x- and y-coordinates of the CM of the system must be fixed, so

X:

mS*0 + 2.6845e28*0.3891 + 7.0129e26*0.8105 + mC*0

= 2.6307e30*x + mA*0 - 7.0129e26*1.5385 - 8.9173e27*0.9709

x = 0.007887835 AU

Y:

mS*0 + mA*0 + 7.0129e26*1.2553 + 8.9173e27*1.4245

= 2.6307e30*y - 2.6845e28*0.2381 - mb*0 - 8.9173e27*0.9409

y = 0.010782 AU

so d = ?(x² + y²) = 0.013359521 AU

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