Question

At its greatest distance from Earth, the moon experiences a gravitational force of 1.78 E 20 N. The mass of the Earth is 5.97 E24 kg. The mass of the moon is 7.35 E22 kg. What is the distance between the Earth and the moon at that point if G = 6.67 E−11 N*m2/kg2?4.06 E 5 km1.65 E 17 km1.65 E 8 km4.06 E 14 km

Answer 1

Given

F = 1.78e20 N

m_e = 5.97e24 kg

m_m = 7.35e22 kg

G = 6.67e-11 nm2/kg2

Procedure

$\begin{gathered} F=\frac{Gm_em_m}{r^2} \\ r=\sqrt[]{\frac{Gm_em_m}{F}} \\ r=\sqrt[]{\frac{6.67e-11\cdot5.97e24\cdot7.35e22}{1.78e20}} \\ r=4.06e8\text{ m} \end{gathered}$