Why the sky is dark at night © Getty Images

Why the sky is dark at night

The dark sky paradox, also known as Olbers’ Paradox, explains why, despite the infinite number of stars in the Universe, the sky at night appears black.

If you’ve ever looked up into the night sky and pondered why it is not completely full of the near-infinite number of stars out there, you would not be alone. In fact, it is one of the oldest puzzles in astronomy, but the answer is not only relatively simple, it’s also rather illuminating.

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In this extract from her book, Space: 10 Things You Should Know, astronomer and YouTuber Dr Becky explains the science behind this cosmological conundrum.


Why the Night Sky Is Dark

The question about why the night sky is dark has been posed by many physicists and philosophers over the millennia, from the Ancient Greeks through to twentieth-century astronomers.

It was popularised in the nineteenth century by a German called Heinrich Olbers; a doctor by day and an astronomer by night. While many others had described this problem before, Olbers formulated an explanation that was named after him: Olbers’ paradox, sometimes known as the dark sky paradox.

You might think there is a simple answer to this question: surely the night sky is dark because the Sun has set? But as the Earth spins on its axis to face us away from that great big life-giving ball of light that is ever present in our daytime sky, it turns towards uncountable numbers of other stars.

Heinrich Wilhelm Mathias Olbers © Getty Images
Heinrich Wilhelm Mathias Olbers © Getty Images

While these stars may be further away, there are a great many more of them – enough to make our home star seem rather insignificant. The answer is therefore rather more profound, giving us insight into the very nature of the Universe we live in.

Think back to what previous generations have considered to be true about the Universe. In the sky are the Sun, the Moon, the planets and the stars which would always rise again after setting. These things were known and they were a constant.

Based on these observations, our ancestors drew the following conclusions about the Universe:

  1. that it was the same in all directions because you see stars in every direction you look (we call this a homogeneous Universe)
  2. that it was unchanging, forever remaining the same, because nothing changed with each passing year (a static Universe)
  3. that the Universe was infinite, because as telescopes grew with the centuries, an evergrowing number of fainter stars were found in every part of the sky.

If all of these things about the Universe are true then every line of sight, every single place you look in space should eventually happen upon a star.

Imagine taking a small patch of sky, perhaps the size of your thumbnail, which held at arm’s length is about the size of the full Moon. Try it next time you’re looking at the night sky and you’ll find you’ll be able to block the Moon out of the sky with your thumb.

We are both well aware that in reality the Moon is a lot bigger than your thumb. In fact, if I assume my thumbnail is roughly circular and about 1.5 centimetres across, I could fit 50,000,000,000,000,000 of my thumbnails on the surface of the Moon.

The reason my single thumbnail can block out the whole Moon an arm’s length away from me down on Earth, is all down to perspective. If we imagine that my arm could grow to twice its length, then at twice the distance away it would take four of my thumbnails to block out the whole full Moon. Twice the distance again and it would take sixteen thumbnails.

Now if extending arms wasn’t enough of a stretch for you, imagine that my thumbnail also glows. The closer it is to me, the brighter it will appear. The further away it is, the fainter it will be. This is something we’re all familiar with from crossing roads at night – judging how far away a car is by how bright its headlights appear. Astronomers have known for a long time how much fainter things get with distance, and as with perspective it depends on the square of the distance.

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So if we go twice as far away, things get four times fainter, because 2² = 2 x 2 = 4. Three times further away, things get nine times fainter. Ten times further away, a hundred times fainter. So, if we go back to my glowing thumbnail on my extendable arm – at double the length of my arm, I’m going to need four glowing thumbnails to block out the Moon, but they’re going to be four times fainter. So the two effects cancel out to give you four thumbnails as bright as the thumbnail only one arm’s length from you.

Now imagine taking this to 100 times my arm length, where we’d have 10,000 thumbnails, which would be 10,000 times fainter and yet still as bright as a single thumbnail at one arm’s length – and so on until infinity.

Glowing thumbnails might be a slightly tenuous analogy but I rather like it. Because imagine that instead of a glowing thumbnail we’ve got a star, and instead of an arm’s length we’ve got a light year.

Even with these much larger objects and distances, the same truths hold as with the glowing thumbnail. If I have one star in a patch of sky at one light year away, I would have four in the same patch at twice the distance, which would be four times fainter.

Now imagine this across the whole sky. A sky which is homogenous, the same in all directions, and infinite. At every single light year step, in any direction we look, we’d have the same amount of brightness as a single star only a light year away. And with infinite number of light year steps the night sky would be blindingly bright! So why is the sky dark?

Edgar Allan Poe, of all people, once touched on this in one of his many essays:

Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy – since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all.

Edgar focused on only one reason the sky might be dark: because the Universe isn’t infinitely old. It has a certain age, in years, since its creation.

Adding that assumption to our three from above – and taking into account that it takes light time to get to us, travelling at its set speed limit – it follows that we can only see the light of the stars that has had enough time to get to us since the beginning of creation.

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We now know that the Universe was created in the Big Bang 13.8 billion years ago, so because light will take time to reach us, there will be an ‘observable universe’ beyond which we are blind and we can’t see any stars.

But the other thing we know from the theory of the Big Bang is that the Universe is not infinite. It has a finite size. So not only will light take time to reach us, but we won’t have an infinite number of light year steps along a single line of sight. As a result, we won’t have the infinite number of stars needed to make the night sky bright.

At the same time we must remember that the Universe is always growing, because space itself is expanding. This expanding of space stretches the light waves travelling across it. The further light travels in the Universe, the more it gets redshifted.

But space has expanded so much that all of the visible light from the most distant things in the Universe has been stretched beyond visible red light into infrared and even microwaves. These waves are no longer visible to our feeble human eyes and so the true brilliance of the night sky is, in reality, entirely hidden from us.

This is an edited extract from Space: 10 Things You Should Know by Dr Becky Smethurst, available now (£9.99, Orion)

This is an edited extract from Space: 10 Things You Should Know by Dr Becky Smethurst, available now (£9.99, Orion)

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