Does the earth's gravity make the moons gravity?

The gravity on earth is 9.8m/s^2 I believe the gravity on the moon is 1.6m/s^2

Gravity on the moon has exactly the same characteristics and behavior as it has on Earth and everywhere else. It causes a pair of forces between any two objects, that are proportional to the product...

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The gravitational force of the moon is 1/6 that of the earth.

The earth's gravity is approximately 9.8m/s^2 The gravity on the moon is I believe 1.6m/s^2 So when you are on the moon, you are about 6 times lighter. Hope this helps!