Compare the gravitational forces exerted by the sun and the moon on earth. Which exerts a greater force on earth ?

Given:
Mass of sun, $M_{s} = 4 \times 10^{31} k g$
Mass of moon, $M_{m} = 6.3 \times 10^{22} k g$
Distance between sun and earth, $R_{s e} = 1.3 \times 10^{12} m$
Distance between moon and earth, $R_{m e} = 4.5 \times 10^{8} m$
[3 Marks]

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Solution

Force exerted by the sun on earth is:
$F_{s} = \frac{G M_{s} M_{e}}{r_{s e}^{2}}$ -(1)
[1 Mark]

Force exerted by moon on the earth is:
$F_{m} = \frac{G M_{m} M_{e}}{r_{m e}^{2}}$ ...(2)
[1 Mark]

Dividing equation (1) by equation (2), we get:
$\frac{F_{s}}{F_{m}} = \frac{G M_{s} M_{e}}{r_{s e}^{2}} \times \frac{r_{m e}^{2}}{G M_{m} M_{e}}$
$\frac{F_{s}}{F_{m}} = \frac{M_{s}}{M_{m}} \times \frac{{r_{m e}}^{2}}{{r_{s e}}^{2}}$
$\frac{F_{s}}{F_{m}} = \frac{4 \times 10^{31}}{6.3 \times 10^{22}} \times {(\frac{4.5 \times 10^{8}}{1.3 \times 10^{12}})}^{2}$
$\frac{F_{s}}{F_{m}} = 76.07$
[1 Mark]

The force exerted by the sun on earth is about 76 times the force exerted by the moon on earth.

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Compare the gravitational forces exerted by the sun and the moon on earth. Which exerts a greater force on earth ? Given: Mass of sun, Ms=4×1031 kg Mass of moon, Mm=6.3×1022 kg Distance between sun and earth, Rse=1.3×1012 m Distance between moon and earth, Rme=4.5×108 m [3 Marks]