Sapling Learning The figures show a hypothetical planetary two bodies are given

Question

Sapling Learning The figures show a hypothetical planetary two bodies are given in Astronomical Units (AU) In the first picture, the velocity of the center of mass of system is zero. Find the magnitude, ds, of the star's displacernent system at two different times. The spatial coordinates (x, y) of the ms-2.5085 x100 kg mA 2.928910 kg AU -6.8307 10 kg mc -7.3619 x10 kg Number e C (0, 1.0957) (0.6861, 1.5085) 0.3891, 0) (-1.4763, 0) 0,0) T(0,-03225) (-0.8443,-0.6999 Previous Give Up & View Solution Check Answer NextExit 9 Hint

Explanation / Answer

The x- and y-coordinates of the CM of the system must be fixed. So, we have
X: (ma*x, mb*x,...)
mS*0 + (2.9285 x 1028)*0.3891+ (6.8307 x 1026)*0.6861 + mC*0
= (2.5085 x 1030)*x + mA*0 - (6.8307 x 1026)*1.4763 - (7.3619 x 1027)*0.8443
x = 0.007578 AU

Y:
mS*0 + mA*0 + (6.8307 x 1026)*1.5085 + (7.3619 x 1027)*1.0957
= (2.5085 x 1030)*y - (2.9285 x 1028)*0.3225 - mB*0 - (7.3619 x 1027)*0.6999

y = 0.009445 AU

so d = sqrt(x² + y²) = sqrt[ (0.007578)2 + (0.009445)2] = 0.01211 AU

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