Question

How far is the center of mass of the Earth-Moon system from thecenter of the Earth? (Appendix C gives the masses of the Earth andthe Moon and the distance between the two.)

Answer 1

Answer:

$\bar x=4679496.086\ m=4679.496086\ km$ from the center of the earth.

Explanation:

We have a system of Earth & Moon:

• we have the mass of earth, $m_e=5.972\times 10^{24}\ kg$

• mass of the moon, $m_m=7.348\times 10^{22}\ kg$

• distance between the center of the earth and the moon $d=385000\ km$

Now we assume the origin of the system to be at the center of the earth.

Now for the center of mass of this system:

$\bar x=\frac{m_e.x_e+m_m.x_m}{m_e+m_m}$

here:

$x_e\ \&\ x_m$ are the distance of the centers (center of masses) of the Earth and the Moon from the origin of the system.

$x_e=0$ ∵ since we have taken the point as the origin of the system.

$x_m=d$

now putting the values in the above equation:

$\bar x=\frac{(5.972\times 10^{24}\times 0)+(7.348\times 10^{22}\times 385000\times 1000)}{5.972\times 10^{24}+7.348\times 10^{22}}$

$\bar x=4679496.086\ m=4679.496086\ km$ from the center of the earth.