Question

The mass of the Earth is 6 × 1024 kg, the mass of the Moon is 7 × 1022 kg, and the center-to-center distance is 4 × 108 m. How far from the center of the Earth is the center of mass of the Earth–Moon system? Note that the Earth's radius is 6.4 × 106 m.

Answer 1

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

$X_{Cm = \frac{M_eX_e +M_mX_m}{M_e+M_m}$

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

$X_{Cm = \frac{M_eX_e +M_mX_m}{M_e+M_m} = \frac{M_e(0) +M_mX_m}{M_e+M_m} = \frac{ M_mX_m}{M_e+M_m}}\\\\X_C_m = \frac{7 X 10^{22}*4X10^8}{6X10^{24}+7X10^{22}} =\frac{28 X10^{30}}{607X10^{22}}\\\\ X_C_m = 4.613 X10^6 m$

Therefore, the center of mass of the Earth–Moon system is 4.613 × 10⁶ m from center of the Earth.