Question

why the gravity on moon is one-sixth as compared to the gravity of earth?

Answer 1

The gravitational force exerted an object depends on its mass; the mass of the moon is much lesser than the mass of the earth. Hence the acceleration due to gravity is also much lesser.

Answer 2

Because the distance from the center of the Moon to its surface is only about a quarter of the distance between the center of the Earth and its surface. Since its mass is 80 times less than that, its surface gravity is 13/80 or about one sixth of Earth's.