Question: Why don't astronauts feel weightlessness in moon while they do in artificial satelite orbiting the earth?

Answer: 
The moon itself has so much mass, about $\frac{1}{81}$ of earth an this mass is responsible for the attraction, not the attraction from earth,(the mass of the satellites is too small to measure the attraction) The attraction from earth keeps satellites and the moon on there circular or elliptic tracks.
It's a problem which reflect on the simple Newton's Gravity Law. Moon has enough mass for attraction, satellites haven't got enough mass to attract bodies as moon does.