How is the gravity on moon different from the gravity on earth?

It's not. The law of gravity operates on the moon precisely as it does on Earth,

according to the exact same mathematical formula.

The mathematical formula says that the gravitational force of attraction between

two objects is proportional to the product of their masses, and inversely proportional

to the square of the distance between their centers, where the proportionality

constant is the Newtonian 'G'.

This formula accurately predicts the weight of an object on Earth, and also predicts

its weight on the moon with equal accuracy.

Because of the significant difference between the masses of the Earth and moon,

and between their radii, an object on the moon's surface weighs only about 16.5%

of what the same object weighs on the Earth's surface.