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?

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Answer 1 · 2017-01-05T07:39:55

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

Using Newton's gravitational force equation

$F = \frac{G m_{1} m_{2}}{r^{2}}$ $F=(Gm_1m_2)/(r^2)$

and assuming that the mass of the Earth is

$m_{1} = 5.972 \cdot 10^{24} k g$ $m_1=5.972*10^24kg$

and $m_{2}$ $m_2$ is the given mass of the moon with $G$ $G$ being

$6.674 \cdot 10^{- 11} N \frac{m^{2}}{{(k g)}^{2}}$ $6.674*10^-11Nm^2/(kg)^2$

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

Repeating this with $m_{2}$ $m_2$ as the mass of the sun gives

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

This gives the moon's gravitational force as $3.7 \cdot 10^{- 6} %$ $3.7*10^-6%$ of the Sun's gravitational force.