# Would the moon be brighter if it were completely spherical?

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'

• 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. – Tweej Apr 11 '16 at 10:21
• I just added a reference to the argument of Salviati, as summarized by Sagredo. – user29305 Apr 11 '16 at 10:46

• @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. – Ján Lalinský Apr 11 '16 at 23:21