# What makes the Moon and Venus shine?

Is there some substance on Venus or some kind of material, because neither bodies have any source of light.

• Virtually everything reflects light to some degree. Apr 8, 2016 at 6:04
• The cheese. It's the cheese. Apr 8, 2016 at 12:54
• – uhoh
Mar 25, 2020 at 6:06

The sun is an excellent source of light for all the planets and moons, although it gets a little dodgy way out near Pluto. The moon reflects about 10% of the sunlight that hits it, that's why we see it. Venus' albedo is about 0.75, what with its clouds and all. That means 75% of the sunlight that hits it is reflected back into space for us to see.

Obviously Wayfaring Stranger is right, but it doesn't really answer why the moon shines. I mean, it's a long way away and very dim. 10% is a low albedo, and if you put a rock with 10% albedo 239,000 miles away, we wouldn't be able to see it.

Or would we? The point is, the moon is a large rock. So large that its apparent angular diameter is $$1/2$$ a degree. That means it takes up an area $$1/2$$ a degree by $$1/2$$ a degree (give or take a factor of $$\pi/4$$). Now it doesn't matter how far away the moon is, what matters is the angular diameter, because that's how much light reaches your eye. To put this another way, the apparent brightness of any particular 1 meter square patch falls off as $$1/d^2$$, where $$d$$ is the distance to the moon, but the radius of the moon increases as $$d$$ if the angular diameter remains constant, so the number of such patches increases as $$d^2$$, which cancels.

So the moon has the same brightness as an American quarter at arm's length would have if (a) the quarter were made of rock with albedo 10% and (b) the quarter was somehow in daylight, despite the fact that you are not. Even if you were both in daylight, you could see that quarter, but the fact that it's in daylight and you're not makes is very visible, because your eyes have adjusted to everything else being dark, and it appears to shine.

Venus has a smaller angular diameter (it varies, but up to $$1/60$$ of a degree) but its albedo is 7-8 times greater. Again, it's the fact that Venus is big that makes it shine, even if it looks like a dot to the naked eye.

• +1 This is basically right. Keeping the Sun-Moon distance constant, the brightness of the Moon or any extended object per unit solid angle remains essentially constant as we move farther away from it. Walls don't get brighter when we walk towards them. It breaks down when the angular size decreases until it reaches our resolution limit and the object becomes unresolved or star-like. But until them it's nearly flat.
– uhoh
Mar 25, 2020 at 3:27