Map dtt Sapling Learning macmillan learning The figures show a hypothetical plan

Question

Map dtt 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- 2.3863 x 100 kg mA 1.9513 x108 kg mg-68307x 1026 kg mc-8.6951 x1027 kg Number AUm (0, 1.0135) TC (0.3751, 1.2553) (0.3429, 0) -18495, 0) (0, 0) (0,-0.4491) (-0.8443, -0.6035)

Explanation / Answer

Both coordinates of Center of mass should be at same location.

So, for x coordinate of Center of mass,

(0.3751*6.8307e26+0.3429*1.9513e28) = (-1.8495*6.8307e26 - 0.8443*8.6951e27+2.3863e30*x)

x =0.006517 AU

Similarly

Now y coordinate of Center of mass,

(1.2553*6.8307e26+1.0135*8.6951e27) = (-0.4491*1.9513e28 - 0.6035*8.6951e27+2.3863e30 y)

y =0.00992362 AU

d = sqrt (x^2 +y^2)

= sqrt(0.0.006517^2 +0.00992362^2)

= 0.011872216 AU

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