The weight of an object on the earth is the force with which the earth attracts the object. In the same way, the weight of an object on the moon is the force with which the moon attracts that object.

The mass of the moon is less than that of the earth. Due to this, the moon exerts a lesser force of attraction on objects. Let the mass of an object be m. Let its weight on the moon be W_{m}. Let the mass of the moon be M_{m} and its radius be R_{m} .

By applying the universal law of gravitation, the weight of the object on the moon will be

W_{m} = G M_{m} x m / R_{m}^{2}

Let the weight of the same object on the earth be We. The mass of the earth is M and its radius is R.

we have, We = G M x m / R^{2}

Substituting the values from , we get

Wm = G X 7.36 X 10^{22 } kg x m / (1.74 X 10^{6} m )^{2}

W_{m} = 2.431 x 10^{10}G x m

W_{e} = 1.474 x 10^{11} G x m

Dividing Eq. (1) by Eq. (2), we get

W_{m} / W_{e} = 2.431 x 10^{10}G x m / 1.474 x 10^{11} G x m

W_{m} / W_{e} = 0.165 = 1 / 6

Weight of the object on the moon / Weight of the object on the earth = 1 / 6

Weight of the object on the moon = (1/6) × its weight on the earth.