Why should counting a small patch of craters on the moon show the same distribution as asteroids in the solar system ?

Counting a small patch of craters on the Moon shows the same distribution of asteroids in the Solar System because of one main factor, that's the lack of atmosphere on the Moon. The lack of atmosphere on the Moon allows asteroids and meteors to have a free pass towards it's surface, thus the concentration of craters made by them is much larger, while on the other planets and Moons there atmosphere, at some more dense, at some less dense, but it affects the asteroids and meteors and cracks and burns them in most cases, so when they fall on the surface they are to little to make any significant impact and create a crater.

Dis the answer you perception is how you see the world 

The correct option to this statement would be true