Why is the weight of an object on the moon 1 6 th its weight on the earth?

Weight of an object is the product of mass and the acceleration due to gravity. The acceleration due to gravity g = G M R 2 . Let M e a n d M m be the masses of the earth and the moon, respectively. And, R e a n d R m be their radii. The weight of an object of mass m on the earth surface W g = G M e m R e 2 The weight of an object of mass m on the moon surface W m = G M m m R m 2 Hence the required ratio W g W m = G M e m R e 2 ÷ G M m m R m 2 = M e M m × R m 2 R e 2 We know that Celestial Body Mass (kg) Radius (m) Earth 5.98 × 10 24 6.37 × 10 6 Moon 7.36 × 10 22 1.74 × 10 6 Hence, W g W m = 5.98 × 10 24 7.36 × 10 22 × 1.74 × 10 6 6.37 × 10 6 2 = 6 The weight on the surface of the moon will be 1 / 6 times that on the earth.