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I remember reading Galileo's 'Dialogue Concerning the Two Chief World Systems' where Salviati and Sagredo explain how the moon would be almost entirely dark if it were a perfect sphere but after discussing this with a friend recently I wonder whether Galileo's argument might actually be wrong.

If you follow the following link on page 69, Sagredo gives the following argument:

'If the moon were smooth as a mirror, only a very small part would show itself to the eyes of a peson as illuminated by the sun, although an entire hemisphere would be exposed to the sun's rays. The rest would remain, to this observer's eyes, unilluminated and therefore invisible'

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  • $\begingroup$ What argument did Salviati give? What argument did you and your friend give? We can't comment if you don't go into more detail of why it's possible Galileo's argument might be wrong. $\endgroup$ – Tweej Apr 11 '16 at 10:21
  • $\begingroup$ I just added a reference to the argument of Salviati, as summarized by Sagredo. $\endgroup$ – user29305 Apr 11 '16 at 10:46
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That depends on how literal you want to be. If the moon were perfectly spherical, but the dust on top were the same, it would be just as bright as it is now.

However take that to a literal extreme replacing the moon with a perfect sphere, most of the light hitting the moon would not bounce to your eye but would reflect based on the angle in which it hits. It would turn the moon into a gigantic spherical mirror. And as such, the sun's light would be represented by a tiny bright dot representing the small point where the sun's light would have to hit in order to reach your eye.

It would certainly be bright but not much brighter than the brightest star in the sky, while most of the rest of the moon would reflect the blackness of space.

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  • $\begingroup$ @jean Link? I would love to read that. $\endgroup$ – Neil Apr 11 '16 at 11:56
  • $\begingroup$ pretty sure if it was a What If answer at some point humanity is wiped from earth by a focused energy beam $\endgroup$ – jean Apr 11 '16 at 13:59
  • $\begingroup$ @jean spherical mirrors do not focus beams. $\endgroup$ – Asher Apr 11 '16 at 20:06
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    $\begingroup$ @NeuroFuzzy, if diameter of the Sun is $\phi$, distance from Sun to the Moon $d$ and diameter of the Moon is $\phi_M$, the virtual image of the Sun created by the Moon would have diameter $\frac{1}{4}\frac{\phi_M}{d}\phi$. This is about 8km. The image would be located under Moon's surface but close. From Earth, object of this size on the Moon would appear as a dot. $\endgroup$ – Ján Lalinský Apr 11 '16 at 23:21
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    $\begingroup$ It's probably worth pointing out that it's not really the shape but rather the material that determines how the object looks. A perfectly spherical absorber/emitter will probably obey Lambert's law and thus be uniformly lit. An irregular perfect mirror will have many speckles of light over its surface. Galileo assumed all matter reflected, rather than absorbing and reemitting, which turns out not to be a very good model for things. $\endgroup$ – user10851 Apr 12 '16 at 2:58

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