Respuesta :
Answer:
[tex]\bar x=4679496.086\ m=4679.496086\ km[/tex] from the center of the earth.
Explanation:
We have a system of Earth & Moon:
- we have the mass of earth, [tex]m_e=5.972\times 10^{24}\ kg[/tex]
- mass of the moon, [tex]m_m=7.348\times 10^{22}\ kg[/tex]
- distance between the center of the earth and the moon [tex]d=385000\ km[/tex]
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:
[tex]\bar x=\frac{m_e.x_e+m_m.x_m}{m_e+m_m}[/tex]
here:
[tex]x_e\ \&\ x_m[/tex] are the distance of the centers (center of masses) of the Earth and the Moon from the origin of the system.
[tex]x_e=0[/tex] ∵ since we have taken the point as the origin of the system.
[tex]x_m=d[/tex]
now putting the values in the above equation:
[tex]\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}}[/tex]
[tex]\bar x=4679496.086\ m=4679.496086\ km[/tex] from the center of the earth.
