Explain why mercury, venus, and the moon do not have significant erosion. relate erosional activity to planetary size and distance from the sun.

Enus does have some erosion but not as much as Earth or Mars. Some Erosion is caused by the atmosphere a planet has and more specifically the activity of that atmosphere. On Earth, wind and rain wear down mountains over millions of years. On Mars there is wind and dust storms that do the same. The atmosphere on Venus is extremely dense and very sluggish at the surface so there is erosion but it's very slow. Mercury and the Moon do not have atmospheres so there is no erosion. 

There is also erosion caused by liquid running over the surface, rivers for example. A planet or moon needs to have an atmosphere to have this feature. 

It takes a certain amount of gravity to hold an atmosphere in place. Mercury is almost big enough but has the add disadvantage of being closer to the Sun which keeps it hot enough to boil off any atmosphere. The Moon is simple to small to hold on to an atmosphere.