How come moonlight is silver?

Answer

There are two aspects to the answer.

The light we see from the Moon is indeed reflected sunlight. But the extent to which the light is reflected depends on the wavelength. In total, the Moon reflects about 10% of the sunlight, absorbs the rest, and then emits it back as infrared radiation. That 10% is an average across the spectrum: in blue light it is less, and it increases with wavelength.

That way, the Moon should be a little redder than the Sun, and it is. Yet we see them whiter. This is because the scattering of sunlight by the Earth’s atmosphere is also color dependent, with a stronger wavelength dependence than the reflectivity of the Moon. Scattering goes with the fourth power of the inverse wavelength, reflectivity is quite linear with it. This strong color dependence of the scattering ensures that most of the blue light from the sun is scattered (the sky is blue!), and that in a dusty atmosphere everything but red is filtered out when the sun goes down (and the light has to pass through a lot of atmosphere) .

We can clearly see that the scattering of sunlight by the Earth’s atmosphere makes the Sun redder than the reflection by the Moon during a total lunar eclipse. Then the Earth blocks the direct solar radiation on the Moon, but sunlight does reach the Moon through the sunlight deflected by the Earth’s atmosphere that reaches the Moon. We see the Moon a bit, in orange-red light.