Why Is the Night Sky Dark?
― With Countless Stars, the Sky Should Blaze Everywhere
“Because the Sun has set.” That is only half an answer. The universe holds countless stars like our Sun. If stars filled space without end, the night sky should glow everywhere like the surface of the Sun. In fact, the dark of night is evidence that the universe had a beginning.
It is a camping night. You switch off the lights and look up. The sky is packed with stars. A child says, “There are so many stars!”
A little later the child asks, “Stars are the same as the Sun, right? So why is it dark at night?” You answer, “Because the Sun has gone down.” The child replies, “But there are loads of stars.”
This is no slip of a child’s tongue. It is a real puzzle, and it troubled astronomers for more than 200 years.
There are only two reasons the night sky is dark
The universe began only about 13.8 billion years ago. Light has a limited speed, so light from farther away has not yet reached Earth. Our view ends before a wall of starlight can form.
The universe keeps expanding. The farther light has travelled, the more its waves are stretched on the way. It grows weaker and redder, and in the end becomes light our eyes cannot see. The night sky is still glowing everywhere, in light we cannot see.
First, let us see why people thought the night sky “should be dazzling”. Once that is clear, a dark sky suddenly looks strange.
Distant stars are dim. But there are more of them
The farther a star, the dimmer it looks. Double the distance and the brightness drops to one quarter. The light spreads in all directions and thins out. Hearing this, you might think distant stars can be ignored.
But look at Figure 1. Picture hollow layers of equal thickness stacked around the Earth. A layer at twice the distance has four times the surface area. If stars are spread through space at the same density, it also holds four times as many stars.
Each star is one quarter as bright. But there are four times as many. Multiply the two, and every layer sends the same amount of light. The layers pile up without end to the edge of the universe, so the light adds up without end too.
In reality, nearer stars hide farther ones, so the total is not infinite. Even so, in every direction your line of sight must eventually hit the surface of some star. The night sky would then be filled with the surface of the Sun, with no gaps. Day and night, the whole sky would be as bright as the Sun’s surface, at about 6000°C.
Answer one: the light has not arrived yet
This calculation hides an assumption. It assumes that the universe is infinitely old, and that light from any distance has already arrived.
The real universe had a beginning, put at about 13.8 billion years ago. Light travels only one light-year in a year. So we can see only as far as light has had 13.8 billion years to travel. Stars beyond that may exist, but their light is still on its way.
So how far would we have to see for stars to fill the sky? The calculation in the fold-out gives about 20 quadrillion light-years. That is more than a million times the range we can see in the universe.
Try the slider in Figure 2. As you extend the distance you can see, the share of sky filled with stars grows. At the present universe’s position, most of the sky is still gaps between stars. The night sky stopped while the wall of starlight was still being built.
Answer two: even the light that arrives has become invisible
The universe has been expanding ever since it began. Light from distant galaxies is stretched along with space on its journey. When a light wave is stretched, its colour shifts toward red, and the energy it carries weakens.
The most distant light we receive was given off by hot, bright gas soon after the universe was born. It was once a dazzling glow at several thousand degrees Celsius. It has been stretched about 1000 times, and now arrives from every direction in the sky as radio waves our eyes cannot see.
So the night sky really does glow everywhere. It is just that the light has been stretched into colours human eyes cannot see. Part of the snow on an untuned TV screen is said to be this radio signal mixed in.
This puzzle goes by the name of Olbers, a German physician and astronomer who discussed it in 1823. In 1848, the American novelist Edgar Allan Poe wrote in his prose poem “Eureka” that the gaps may look dark because the light has not yet reached us. In 1901, the physicist Lord Kelvin reached the same conclusion by calculating from the number and lifetimes of stars.
There is another way to look at it. A star like the Sun can shine for about 10 billion years. Even if the universe were infinitely old, stars burn out and new ones are born. Stars could not keep giving off enough light to fill the whole sky for ever.
Summary
If stars filled the universe without end, the night sky should blaze everywhere. It does not, because the universe had a beginning and light from far away has not arrived yet. On top of that, the light that does arrive is stretched by the expansion of the universe into radio waves we cannot see.
Night is dark not only because the Sun has set.
It is dark because the universe is still young.
For why stars cannot be seen in the daytime, see “Why can’t we see stars in the daytime?”. For how stars keep shining, see “How can stars keep shining for billions of years?”.
- On a clear night, hold a toilet-paper tube to one eye and look at a small patch of sky.
- Count the stars you can see inside the tube. Try it both in town and in a place with little light.
- Check that, even as the star count rises, the dark gaps between stars are far larger.
The darker the place, the more stars you see, but the sky never fills with stars. Beyond those gaps lies the universe whose light has not yet arrived. If you go out at night, watch your step and the traffic, and go with an adult.
For those who want more ― terms, formulas and links to textbooksWe state clearly which level each part belongs to, from middle-school science to university courses
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school earth science or physics
- High school+Advanced high-school material, or a textbook sidebar
- UniversityNot taught in high school; university courses in astrophysics and cosmology
- ResearchNot taught even at university as settled fact; researchers are still working on it
Middle schoolTerms: this phenomenon has a name
- Olbers’ paradox: The contradiction that, if stars are spread evenly without end, the night sky should be bright everywhere. It is named after Olbers, who discussed it in 1823.
- Light-year: The distance light travels in a year, about 9.5 trillion kilometres.
- Cosmic microwave background: Light from the early universe, stretched into radio waves (microwaves) that reach us from all over the sky.
Middle schoolHigh schoolChecking with a formula: how far until a line of sight hits a star?
Look straight at one point in the sky. We calculate how far, on average, your line of sight travels before it hits the surface of a star. If this distance is shorter than the range we can see in the universe, stars fill the sky. If it is longer, gaps remain.
| In symbols | L ＝ 1 ÷ ( n × π × R² ) |
| In words | Average distance to hit a star ＝ 1 ÷ (star density × area of one star’s “target”) |
| Where it comes from | Think of the line of sight as a tube with some width. The line of sight hits a star when exactly one star fits in a tube of length L. The condition is that the tube’s volume π × R² × L, times the density n, equals 1. |
| Symbol | Meaning and unit |
|---|---|
| L | Average distance until the line of sight hits a star (light-years) |
| n | Star density (stars per cubic light-year) |
| R | Radius of a star (light-years). Here we take it to equal the Sun’s |
| π | Pi (about 3.14) |
| Radius of the Sun | About 700,000 km (7 × 10⁵ km) |
| One light-year | About 9.5 trillion km (9.5 × 10¹² km) |
| Star density near the Sun | Said to be about 0.003 stars per cubic light-year |
| Age of the universe | About 13.8 billion years (distance light could travel: about 1.38 × 10¹⁰ light-years) |
| Star radius in light-years | (7 × 10⁵) ÷ (9.5 × 10¹²) ≒ 7.4 × 10⁻⁸ |
| Radius squared | 7.4 × 10⁻⁸ × 7.4 × 10⁻⁸ ≒ 5.5 × 10⁻¹⁵ |
| Area of one star’s “target” | 3.14 × 5.5 × 10⁻¹⁵ ≒ 1.7 × 10⁻¹⁴ |
| Density × target area | 0.003 × 1.7 × 10⁻¹⁴ ≒ 5.1 × 10⁻¹⁷ |
| Average distance to hit a star, L | 1 ÷ (5.1 × 10⁻¹⁷) ≒ 2.0 × 10¹⁶ |
| How many times the visible range | (2.0 × 10¹⁶) ÷ (1.38 × 10¹⁰) ≒ 1.45 × 10⁶ |
L is about 20 quadrillion light-years, roughly 1.45 million times the range we can see in the universe. And this assumes stars are as crowded as in the Sun’s neighbourhood. The real universe is almost empty between galaxies, so L is longer still, by many orders of magnitude.
| Visible range ÷ L (a guide to the share of sky filled by stars) | (1.38 × 10¹⁰) ÷ (2.0 × 10¹⁶) ≒ 6.9 × 10⁻⁷ |
By this calculation, only about one millionth of the sky is filled by star surfaces. The starting position in Figure 2 shows this value. Picture a full stadium of 50,000 seats: people would occupy just 0.03 of a seat.
High schoolHigh school+The inverse-square law of brightness, and redshift
High schoolThe brightness at distance r from a light source is inversely proportional to r squared, because the light spreads over a sphere of radius r (the inverse-square law). Meanwhile, the number of stars in a layer of equal thickness is proportional to the area of the sphere, that is, to r squared. The two cancel, so the light from each layer is constant whatever the distance. Figure 1 shows this relation.
High school+The stretching of the wavelength of distant light by the expansion of the universe is called cosmological redshift. The cosmic microwave background was emitted by gas at about 3000 kelvin, stretched about 1100 times, and is now observed as blackbody radiation at about 2.7 kelvin.
UniversityIts place in cosmology
Olbers’ paradox is used in introductory cosmology as a clue against a “steady, infinitely old universe”. In the current view, the main cause is the finite age of the universe (the “particle horizon”, the range from which light can reach us, is finite), and the redshift from expansion is a secondary effect. The cosmologist Edward Harrison showed this quantitatively. He also showed that the total energy stars can emit in their lifetimes is not enough to fill the sky. In formulas, the brightness of the background light follows from the Friedmann equations, which describe cosmic expansion, and from integrating the light along the line of sight.
📖 Derivations and further reading: Wikipedia, “Olbers’ paradox” (Japanese) ／ Wikipedia, “Cosmic microwave background” (Japanese)
ResearchWhat is still not clear
- Just how dark are the “gaps” of the universe? The New Horizons probe measured the darkness of the sky far from the Sun. It reported a sky brighter than known galaxies would predict, and the cause is still debated.
- When did the first stars in the universe light up? Light from early stars and galaxies should remain across the whole sky as infrared background light. Observations to measure its amount accurately are continuing.
- What is the universe like beyond the range we can see? We do not know how large the region the light has not yet reached is, or whether it is infinite.
So the content of this article, too, is “an explanation within what we know today”. Measuring the darkness of the night sky precisely is still one way of studying the history of the universe.
Links to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Middle school | Science, “Earth and the Universe” (stars, galaxies) | Stars are kin of the Sun; light-years |
| High school | Physics, “Light”; Earth science, “Structure of the Universe” | Inverse-square law of brightness, Figure 1 |
| High school+ | Earth science, “Expansion of the Universe and the Big Bang” | Redshift, cosmic microwave background |
| University | Astrophysics and cosmology | Particle horizon, Friedmann equations, Harrison’s argument |
| Research | Observational cosmology | Measuring the brightness of the cosmic background light |
| ― | Link to daily life | Looking up at night, the darkness of the gaps itself tells the age of the universe |
- Edward Harrison, Darkness at Night: A Riddle of the Universe, Harvard University Press, 1987
- Lord Kelvin, On Ether and Gravitational Matter through Infinite Space, Philosophical Magazine, 1901
- Wikipedia, “Olbers’ paradox” (Japanese)
- Wikipedia, “Cosmic microwave background” (Japanese)
- National Astronomical Observatory of Japan (国立天文台), ed., Rika Nenpyo (理科年表, Chronological Scientific Tables), Maruzen Publishing (values for stellar number density, the Sun’s radius and the light-year)
※This article is a general-audience science explainer. The figures given are guides and rough estimates to help you grasp the mechanism. The star density applies the value near the Sun to the whole universe as an assumption; the real average of the universe is said to be much lower.