Reading by Starlight

Good astronomy: This one's easy: You can't.

• at night, which in turn means
• excluding the Sun

How it works:
You are reading a thriller, and the scene is set: the hero is alone in a dark field, on a warm, clear, moonless night. You know he is walking towards a trap, but he is unaware. Suddenly, he stops: by starlight, he can see the loose dirt in front of him where the landmine is buried. Stepping over it, he is saved! Hurray!

Actually, starlight is simply not bright enough to see anything by. If we take the author of the thriller at his exact word, then Our Hero will never see the loose dirt. Oops! KABOOM!! Another victim of Bad Astronomy.

This is a common misconception. There are about 6000 stars in the sky visible to the unaided eye, ranging in brightness from the star Sirius to stars you can only see by squinting. Hipparchus, an ancient Greek, arranged the brightnesses of stars into a magnitude scale: the brightest star was given a magnitude of 1, and the dimmest a magnitude of 6. His scale was later extended to represent all objects, even ones brighter than Hipparchus' first magnitude stars. The magnitude scale runs backwards, so a smaller number means a brighter object: Sirius, the brightest star (besides the Sun of course), has a magnitude of about -1.5, and the dimmest star visible has a mag of 6.0. Venus, the brightest planet, has a mag of about -4, the full Moon shines at -13, and the Sun in all its glory burns fiercely at a mag of -26.

Nowadays we have quantified (that is, used math to actually assign a relationship to) the scale. Each magnitude represents a brightness change of 2.5119 from the next. This way, a change of 5 magnitudes is 2.5119 ^ 5, or a factor of 100. The scale is logarithmic, which means each step is the result of a multiplication, not an addition: a star with a magnitude of 3 is about 2.5 times brighter than a star with a magnitude of 4. So the Sun, at mag -26, is 32 magnitude steps brighter than the dimmest star you can see: this means it is 2.5119 ^ 32 times brighter, or a whopping 6 trillion times!

Now, it's pretty easy to see by sunlight. You can even read fairly well by the full Moon, which is 2.5119 ^(13 - 26)=0.0000067 as bright as the Sun. But it's kind of tough. If the light were much dimmer, you wouldn't be able to read. Dimmer than that, and you won't be able to see at all.

But there are 6000 stars visible to the naked eye! If you add up all the light from the stars, would you be able to see well? Can Our Hero be saved?

Below is a graph of the magnitudes of all 6000 naked eye stars. Do you see how there are not many very bright stars? There are less than 200 brighter than third magnitude, and 600 brighter than fourth magnitude. The overwhelming majority of stars are dimmer than that. Even though there are lots of dim stars, their light doesn't add up to much. The second graph shows the same thing, except now the brightness is plotted, and I have arbitrarily chosen the brightest star to have a brightness of 1. The dimmest stars are 0.001 (1/1000) times as bright (note that the plot is on a logarithmic scale, which means each step in y is a factor of 10). Suppose you lumped together all the stars you can see in the sky into one star. How bright would it be? It turns out it would have a magnitude of about -5, or a little brighter than Venus. It is 8 magnitudes (1500 times) dimmer than the full Moon. Some people say you can actually see a shadow cast by the light of Venus, although I never have. Although our conglomerate star is a bit brighter than Venus, it simply isn't bright enough to read by.

Even worse, you cannot see all 6000 stars at the same time. The Earth itself blocks half the sky, so you can only see at most half the stars in the sky at any one time. Of course, there are lots of stars dimmer than sixth magnitude. Telescopes can take pictures of stars that are tremendously fainter than what the human eye can see; there are images of stars with magnitudes around 29! That is 23 magnitudes, or about a billion times fainter than what the unaided human eye can see! The problem is, even though there are lots of those dim stars, again they are simply too faint to add much light to our problem. Our Hero is doomed.

Or is he? In yet another twist, there is more than just the stars lighting up the night sky. Think about it: even in the darkest places, you can still usually see fairly well at night. This is because of sky glow. The sky itself glows softly, and can add up to a considerable amount of light. The main source of this glow is from light pollution: lights from cities, towns, parking lots, whatever, throw lots of light into the sky. Particles in the sky like smog, haze, clouds, even the air itself will reflect and scatter that light all over the sky, and you see that as a dull glow over the whole sky. If you live in a city you are pretty familiar with this! I received one email from an astronomer who says that he saw appreciable skyglow in Kenya, far from any cities. To be honest, I'm not sure what the source of this glow is. Someone else emailed me and said they could actually see well enough simply from the light from the Milky Way! Perhaps this is what the first person saw. There are other sources of background light: dust in the solar system reflects light back towards the Earth. This comes in two forms. First is the gegenschein, which is light from the Sun directly reflected back from the point on the sky opposite the Sun ("gegenschein" is German for "opposite" or "opposing" light). The other is called zodiacal light, which is light reflected back from dust in the plane of the solar system, which is what defines the zodiac. However, both of these forms of light are very faint, and do not add appreciably to overall skyglow. Anyway, the Milky Way itself is a collection of stars, so perhaps we simply need to expand our definition of starlight. It does appear that this glow is indeed enough to see by.

So if our hero is in Central Park in New York, he can easily see the landmine. But then of course it is nighttime, and he is more likely to simply be mugged. He may know his astronomy, but he doesn't know urban life!