Why isn't the night sky full of stars?

posted Feb 1, 2015, 1:34 PM by Patrick Poole
Starry sky, from ForestWander (wiki)
You’ve probably heard that there are quite a lot of stars in the universe, and there is definitely a huge amount visible on a very dark night. Why doesn’t all that light wash out the dark spots in the sky, so that we see no black at all? This is actually a question that’s been debated a lot over the centuries called Olbers’ paradox, with even figures like Edgar Allen Poe weighing in. Today is the first time I’m talking about a question submitted to the Ask Questions page. Thanks for the great question!






The universe is 13.8 billion years old, and the speed of light is finite, so the light from most of the stars has not reached us

So if all those stars are around us emitting light, and they are more or less evenly distributed, shouldn’t the night sky be full of light? There are a couple of reasons why not.

One of the big ones is that the light from most of those stars hasn’t had enough time to reach us. Light travels at 3x108 meters every second, or 9.5x1015 meters every year. Those are huge distances, so rather than list all those zeros every time we can use the units of light-seconds and light-years. For example, the nearest star to us, Proxima Centauri, is 4x1016 meters away, or about 4.2 light years. That means it takes light from Proxima Centauri 4.2 years to reach us—or, put another way, the light that you can see from Earth when you look there is light that left Proxima Centauri 4.2 years ago. So really you’re seeing 4.2 years into the past.

The universe is incredibly old—13.8 billion years—but it’s also incredibly vast. Because light can only go so fast, there is a region of space around the Earth beyond which we cannot see—there are certainly more stars beyond this region, but the light from them hasn’t had time to reach us yet.

Observable universe with outside stars

It turns out this volume is a bit bigger than the 13.8 billion light years you might expect. Expansion that occurred in the early times of the universe pushed this volume of visible space, called the observable universe, up to about 84 billion light years. That’s still small enough (comparatively) to rule out seeing quite a lot of the stars in the universe.

Estimates for the number of stars in the observable universe are around 10 billion trillion (1022)

It’s tough to determine exactly how many stars are in the universe that we can see, but it’s clear the number is enormous. Part of what makes this fact difficult to obtain is the sheer size of the number—we can’t have people just count them, it would take too long—but there is also the standard problem of astronomy where the only tool you have for knowing anything about the universe is by what the universe sends towards the Earth. We can also send our own probes out, but only to very close objects, certainly not to other stars. So astronomers have to come up with clever ways to measure things based on observations of the light and particles that are sent toward their detectors on the Earth and knowledge of the principles of physics.

Estimating the number of stars in our galaxy is a good example of this synergy of detection and physics understanding. The Milky Way is rotating about its center, and special radio telescopes can determine the speed of stars near the edge of the galaxy. It turns out that the speed of rotation depends on the mass of the whole galaxy—based on the observed speed we can estimate the mass of our galaxy as the same as 100 billion of our suns. There are plenty of stars with mass more or less than our sun, but it’s a pretty good guess to say that there are somewhere around 100 billion stars in our galaxy.

That’s probably a good guess for most galaxies, based on other observations. So now we know the number of stars in one galaxy, we just need to know how many galaxies there are. The Hubble space telescope watched just one relatively tiny section of the night sky for over four months, adding up all the small amounts of light it saw from very, very distant stars in that region. The result was 10,000 galaxies visible in that small patch, and if you extrapolate that galaxy density up to the whole night sky, the resulting estimate is 100 billion galaxies all around us.

So our combined estimate is 100 billion stars per galaxy times 100 billion galaxies, or 10 billion trillion (1022) stars in the observable universe. That’s a huge number—that many 0.5 mm radius grains of sand would pile up to be the size of Mt. Everest!

Most of a star’s light won’t hit the Earth because we are so small and so far away

Stars emit an enormous amount of light, but they do so in all directions. The farther that light travels away from the source star, the more it gets spread out—this is just like the way sounds decrease in volume as the source gets farther from you, like we discussed back in the Doppler shift post.

This is why stars appear just as points of light in the night sky—of course they are really enormous, but they’re so far away we only see the light that is traveling directly from them towards the Earth. As an example, our own sun looks a lot different the farther out in the solar system you get. If you stand on the surface of Pluto, our sun wouldn’t look much bigger than any of the other stars in the sky. It would be much brighter though, but only enough to light up the surface about as much as the moon lights up Earth’s surface at night. This is because a lot of the sun’s light just misses Pluto because it travels so far to reach the little planetoid.

Most starlight misses us

The fraction of light that reaches us from even a close star can be very small. The human eye needs at least a few photons to detect light, so if less than that arrives from a distant star you won’t see it with your eyes! Modern telescopes with special detectors still have a chance, though—they can see this distant light by essentially doing a “long exposure”, leaving their camera shutters open to record those small amounts over a long period of time.

Additionally, light from some stars can be red-shifted out of the visible spectrum, or be blocked by interstellar clouds of dust, or be drowned out by nearby terrestrial lights

Those two points take care of most of the star light we might see, but there are still a few other things that keep the night sky dark. We discussed in the Doppler shift post how a wave appears changed if the source of that wave is moving with respect to the observer. There we were talking about sound and its frequency (or pitch) changing, but in the case of stars this frequency change translates to a color shift. Almost all galaxies are moving very fast away from us—which is evidence of some early behavior of our expanding universe, but that’s another post—and as a result their light is shifted toward the red end of the spectrum. It’s possible that the starlight can be redshifted so much that it’s no longer visible to the eye, but certain types of telescopes can still see them.

Another big problem with seeing more stars is if their small amount of light is drowned out by a brighter light source. This is definitely the case during the day, when the light from our sun easily dwarfs any light coming from another farther away star. Even at night, though, a full moon can prevent some stars from being seen. This is why large telescopes are often placed on mountains, or away from civilization—the light pollution from cities is especially bad at preventing starlight from being seen. If you ever want to watch a meteor shower, or just see the beautiful night sky in its full glory, drive out to the countryside as far away from city lights as you can.

Bonus physics—Twinkling stars

One last bit of star-related physics—have you ever wondered why stars twinkle? It turns out the light from the star can get scattered a bit by the water vapor and other molecules floating in our atmosphere. That starlight is essentially coming from just one point, so it’s easy for a bit of wind to come in and change the way that light scatters on its way to your eye one moment, and then change it again the next moment. You don’t notice this with something like the moon because it’s so large in the sky. Other stars “twinkle” with a definite pattern, which is evidence that there is some object passing regularly in front of them, like a planet orbiting that star, for example. This is one way that astronomers are searching for planets outside our solar system, but we’ll have to save that for another post.


Thanks to ForestWander (wiki) for the starry sky picture.
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