# The mass of the moon is 7.36×1022kg and its distance to the Earth is 3.84×108m. What is the gravitational force of the moon on the earth? The moon's force is what percent of the sun's force?

Jan 5, 2017

$F = 1.989 \cdot {10}^{20} k g \frac{m}{s} ^ 2$
3.7*10^-6%

#### Explanation:

Using Newton's gravitational force equation

$F = \frac{G {m}_{1} {m}_{2}}{{r}^{2}}$

and assuming that the mass of the Earth is

${m}_{1} = 5.972 \cdot {10}^{24} k g$

and ${m}_{2}$ is the given mass of the moon with $G$ being

$6.674 \cdot {10}^{-} 11 N {m}^{2} / {\left(k g\right)}^{2}$

gives $1.989 \cdot {10}^{20} k g \frac{m}{s} ^ 2$ for $F$ of the moon.

Repeating this with ${m}_{2}$ as the mass of the sun gives

$F = 5.375 \cdot {10}^{27} k g \frac{m}{s} ^ 2$

This gives the moon's gravitational force as 3.7*10^-6% of the Sun's gravitational force.