Suppose that you can just barely see a certain star that is at a distance of 100 light years. How far away must a star that is 4 times more luminous be barely be seen/how about a star that is 100 times more luminous?

Answer 1

If you need to make a star to appear 4 times more luminous becuase it is because it is barely seen , then you will need to make the star appear 4 times dimmer than it would at 100 l.y. distance. The inverse propostional distance is the square root of 4 which means that you will have to double the distance by multiplying 2(the sq. rt. of 4) with 100 L.Yrs. which is equal to 200 Light Years.