# What is the size of the gravitational force that Earth exerts on the Moon?

## The mass of the Moon is $7.35 \cdot {10}^{22} k g$, while that of Earth is $5.98 \cdot {10}^{24} k g$. The average distance from the center of the Moon to the center of Earth is $384 , 400 k m$.

We use Newton’s universal law of gravitation, $F = - G \frac{{m}_{1.} {m}_{2}}{r} ^ 2$ but be careful to convert the distance to base units (m)
$F = - 6.67 \times {10}^{-} 11 \frac{7.35 \times {10}^{22} \times 5.98 \times {10}^{24}}{384 \times {10}^{6}} ^ 2$
I get $F = - 1.99 \times {10}^{20}$ N
The minus sign in the answer is because force is a vector quantity, written as $\vec{F}$, so the direction matters and it is in the opposite direction to the distance as measured outwards from the Earth.