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

Thanks for your help.

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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].

Note 1: The fact that the Sun is not a point source of light has only a very minor effect on the scaling. Note 2: Technically, it will be slightly brighter because more of the absorbed radiation will be radiated away in the visible spectrum. This is however also a negligible effect.

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  • $\begingroup$ I can't understand why you answer $ \frac { 1 } { \sqrt { 2 } } $, would you please explain more? $\endgroup$ – user115608 Apr 8 '16 at 9:56
  • $\begingroup$ @user115608 "The inverse of the square root of how much more light." $\endgroup$ – Hohmannfan Apr 8 '16 at 10:52
  • $\begingroup$ "The strength of the light from the Sun scales with the inverse square of distance",why it is so? $\endgroup$ – user115608 Apr 8 '16 at 11:07
  • $\begingroup$ @user115608 Check out the inverse square law here: en.wikipedia.org/wiki/Inverse-square_law $\endgroup$ – Hohmannfan Apr 8 '16 at 11:24
  • $\begingroup$ Coincidentally, that close to the orbital distance of Venus. If you doubled tge the brightness of the moon like this you also double the brightness of the sun, and probably cook most of life on Earth. $\endgroup$ – James K Apr 9 '16 at 7:02

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