How much gravity does the moon have compared to earth?

The gravity on the Moon is about 17% what it is on the Earth. So if you weigh 200 pounds on Earth, you will weigh 34 pounds on the Moon.

How many g's do you feel on the Moon? 

The acceleration due to gravity on the surface of the Moon is approximately 1.625 m/s2, about 16.6% that on Earth's surface or 0.166 ɡ.

Why do astronauts fall on the moon?

The Apollo astronauts on their way to and from the Moon were still in an Earth orbit, still “falling around Earth.” When close to the Moon, they fell under its gravitational tug and entered lunar orbit, thus falling around our natural satellite in the same way.