Why is the weight of an object on the moon  $\frac{1}{6}th$  its weight on the earth?

The weight of an object on the moon would be given by

$W_{M}=G\frac{M_{M}m}{r_{_{M}}^{2}}$

where MM is the mass of the moon, m is mass of the body, rM is the radius of the moon and G is the gravitational constant.

The weight of an object on the Earth would be given by

$W_{E}=G\frac{M_{E}m}{r_{_{E}}^{2}}$

where ME and rare the mass and radius of the earth respectively.

$\frac{W_{M}}{W_{E}}=\frac{M_{M}r_{E}^{2}}{M_{E}r_{M}^{2}}$

The above ratio is approximately equal to 1/6 and this is why the weight of an object on the moon  (1/6)th of  its weight on the earth

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