# The relation between the light of full moon and the distance between the sun and the earth

If we want the full moon to be 2 times more bright,how we should change the distance between the sun and the earth?

The strength of the light from the Sun scales with the inverse square of distance [note 1]. That means that we would need to have the Earth-Moon system at $\frac{1}{\sqrt{2}}$ (approx 0.7) AU for the full Moon to be twice as bright [note 2].
• I can't understand why you answer $\frac { 1 } { \sqrt { 2 } }$, would you please explain more? – user115608 Apr 8 '16 at 9:56