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Chapter 1: Q52E (page 267)

Find the position of centre of mass of the system of the Sun and Jupiter. (Since Jupiter is more massive than the rest of the solar planets combined, this is essentially the position of the center of mass of the solar system.) Does the center of mass lie inside or outside the sun? Use the data in Appendix F.

Short Answer

Expert verified

The center of mass is7.42脳108m from the center of the sun and is on the line connecting the centers of the Sun and Jupiter.

It lies just outside the sun.

Step by step solution

01

The known data

Let the origin be at center of the Sun.

Let x-axis lies along the line joining the center of the Sun and Jupiter.

Mass of the sunms=1.99脳1030kg

Mass of JupitermJ=1.90脳1027kg

Distance between centre of the Sun and Jupiter is7.78脳1011m m

So xS=0

And xJ=7.78脳1011m

02

Formulas used

Center of mass isx=mSxS+mJxJmS+mJ

03

Find the position of center of mass

Now center of mass isx=mSxS+mJxJmS+mJ

So

x=1.99脳1030kg0+1.90脳1027kg7.78脳1011m1.99脳1030kg+1.90脳1027kg=7.42脳108m

Hence, The center of mass is7.42脳108 m from the center of the sun and is on the line connecting the centers of the Sun and Jupiter.

The Sun鈥檚 radius is6.96脳108 m so center of mass lies just outside the sun.

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