WHY IS THE SKY DARK AT NIGHT?

Hiya, Sean Lally, Physics guy here. Today on "How do we know that?" we're talking about the night sky and what it looks like to us. So, here’s a classic question for you – why is the sky dark at night?

So, what do you think? Take a minute to think about it.

I’ll bet that you’re thinking about day and night being caused by the rotation of the Earth, toward and away from the Sun. And that is true.

However…. That’s not the end of the story.

Imagine going outside on a good night and counting each and every star you can see. How many stars would you count? Quick, what’s your guess?

Now, are you seeing all the stars that exist? No. How many stars do exist?

Did you guess millions? Billions? Billions of billions? You’re getting warmer.

The actual number is certainly not known, but there are on the order of 10^12 galaxies, and each may have on the order of 10^12 stars. That gives an ballpark estimate of 10^24 stars. That’s really, really, really big. No wait, that’s an understatement.

It is this many:

1,000,000,000,000,000,000,000,000 stars.

If you started counting from birth, one star per second for you entire life, could you count that high? How long would it take you? A month? A year? Your lifetime? Multiple lifetimes???

Oh by the way, how would one come up with this number? What’s a decent way to estimate the number of stars in the universe? Imagine that you have some technology – say, a nice telescope. Maybe even the Hubble Telescope!

So, back to the point of the lesson. With all of these stars, why is the sky dark at night. Think about the question again.

Or how about this question? Imagine staring at a forest full of trees. Given a dense forest, would you expect to light at the other end? Why or why not?

Back to the universe. 10^24 is a HUGE number of stars – one would think that with all of that light hitting us, the sky should be brilliant at night. And yet it is not. Hmmmmm.

Let’s think about this. What are some possible reasons why we do not see a brilliant sky at night?

• Do we have an unobstructed view of all stars, or are some blocked?
• Is there some interstellar matter that absorbs starlight?
• Are all stars of the same brightness, regardless of their distance from us?
• Is the universe populated with a mostly constant number density of stars?
• Is the universe infinitely large or infinitely old?
• Does the inverse-square law of light hold for distant stars, or does light obey some other law?
• Does the motion of distant stars affect the brightness that we see?

Can you think of others? What might be your answers to these questions? As it turns out, there are reasonable scientific answers to each of these.

This problem, often called “Olber’s Paradox” (though Henry Olber, who described it in 1823, was certainly not first person to do so), does not have a simple answer. Indeed, one really might expect to have a bright night sky. Why?

Imagine the Earth at the center of series of thin spheres of stars. Each sphere has a certain number of stars “on” it. As you get farther from Earth, the light from each individual star decreases (inverse square relationship: 1/4πr^2), but the number of stars per sphere actually increases (square relationship for surface area of sphere: 4πr^2). These two effects cancel each other out, so each sphere has effectively the same total brightness.

If the universe actually were infinite in size, we likely would have a bright night sky. So, it seems as though the universe is not infinite in size (though there are substantial mathematical objections to this argument). The better answer has to do with the age of the universe – it is NOT infinite. Moreover, stars have only existed for some of that time. And given an expanding universe, it is easy to see that starlight from many, many stars has simply not reached us yet. Enough time has not yet existed!

Well, that’s all for now. See ya soon, see ya on the Moon!

Further Reading

Barbara Ryden – Cosmology
(I have borrowed heavily from Ryden’s chapter 2 for this lesson.)
Edward Robert Harrison - Darkness at Night: A Riddle of the Universe
http://www.esa.int/esaSC/SEM75BS1VED_index_0.html

All text and images copyright 2009 Sean Lally, except where noted.