Answer:
The center of mass of the Earth–Moon system is 4.613 × 10⁶ m from center of the Earth.
Explanation:
Let the reference point be the center of the Earth
[tex]X_{Cm = \frac{M_eX_e +M_mX_m}{M_e+M_m}[/tex]
Where;
Xcm is the distance from center of the Earth =?
Me is the mass of the Earth = 6 × 10²⁴ kg
Xe is the center mass of the Earth = 0
Mm is the mass of the moon = 7 × 10²² kg
Xm is the center mass of the moon = 4 × 10⁸ m
[tex]X_{Cm = \frac{M_eX_e +M_mX_m}{M_e+M_m} = \frac{M_e(0) +M_mX_m}{M_e+M_m} = \frac{ M_mX_m}{M_e+M_m}}\\\\X_C_m = \frac{7 X 10^{22}*4X10^8}{6X10^{24}+7X10^{22}} =\frac{28 X10^{30}}{607X10^{22}}\\\\ X_C_m = 4.613 X10^6 m[/tex]
Therefore, the center of mass of the Earth–Moon system is 4.613 × 10⁶ m from center of the Earth.
