Question

The earth and moon are seperated by a

Answer 1

Answer:

4674568 m or 4675 km

Explanation:

Let x be the distance from the center of the mass system to the center of the earth. This means the distance from the center of the mass system to the center of the moon is $3.85*10^8 - x$. For the masses to balance out, we have the following equation:

$m_e*x = m_m*(3.85*10^8 - x)$

where $m_e$ is the mass of Earth, and $m_m$ is mass of the moon

$5.98 * 10^{24}x = 7.35*10^{22}(3.85*10^8 - x)$

We can divide both sides by $10^{22}$

$598x = 7.35*3.85*10^8 - 7.35x$

$605.35x = 2829750000$

$x = 2829750000/605.35 \approx 4674568 m$ or 4675 km