WHEN YOU WISH UPON A STAR…

Obviously the classic song ends that phrase with “your dreams come true.” Then, as I’m sure you’ve seen, some smartass decided to put a modern and more cynical spin on the phrase with some iteration of the following:

when-you-wish-upon-a-star-that-star-is-dead-just-like-your-dreams

Unfortunately, that smartass was also a dumbass. Here’s why.

First of all, the phrase “you’re a few lightyears late” is absurd. A light year is a unit of distance, not time, despite the presence of the word “year.” This is your first clue that the person who came up with this delightfully snarky yet woefully misinformed little turn of phrase may not, in fact, know what the fuck they’re talking about.

Secondly comes the idea that “that star is dead.” This, no doubt, comes from the idea that stars are really far away (true) and that the light from said stars takes a long time to get here (true), so the star may have died a long time ago and we just can’t tell yet. That’s where this goes astray. TIME TO DO SOME MATH.

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First of all, how many stars do you think are actually visible to the naked eye? I’ll let you think about it for a second. Nope, you’re wrong. It’s a lot less than that. In “normal” conditions (read: not indoors or in the daytime or in Los Angeles ever), we can see about 3,000 stars in the sky. In good conditions, like out in the desert or at high altitude, that number goes up to about 6,000. All told, the total number of stars visible to a normal human eye from the surface of the Earth is in the area of 10,000.

Now, how long do those stars live? Totally depends. Big stars have more mass, which means more gravity compressing the core, which means higher rates of fusion, which means they run out of fuel and die faster. Those stars live for about 10 million years. Smaller stars burn cooler, slower, and longer, and live for about 10 billion years (a thousand times longer). Most live about 5 billion.

The final question is how far these stars are from Earth. The closest star to Earth is Proxima Centauri, which is a little over four light years away. Unfortunately, it’s so small and cool and red that we can’t actually see it with the naked eye, so we refer to it as Alpha Centauri, which is not a single star but a three-star system made up of Proxima Centauri, Alpha Centauri A, and Alpha Centauri B. On the other end of the spectrum, the farthest star we can see easily with the naked eye is Deneb, in the constellation Cygnus. Deneb is around 1500 light years away. In flawless viewing conditions, it’s possible to see stars as dim as V762 Cas, which is almost 15,000 light years away, but even then it’s difficult and most of the time it’s impossible. the average distance to a visible star is about 300 light years.

This makes the math pretty simple. For a star to be what I’ll call a “ghost star,” meaning it’s already dead but we can’t tell yet, it would have to have died more recently than the amount of time it’d take for its light to get here. If a star is 1,000 light years away and died 500 years ago, it would qualify because it’ll be another 500 years before we realize it’s dead.

Now, the math:

I’m going to do the math backwards here so that the full weight of reality will crash all the harder upon you. First, I’ll do it for the extremes. In order to maximize the chances of a ghost star, we’ll assume that all the stars we can see are short-lived, burning brightly for a mere ten million years before flaming out or exploding. We’ll also assume that they’re very far away, maximizing the chances that the light of their death has not yet reached us. And we’ll also assume that we can see the full 10,000 of them, just to give us the best chance at spotting a dead one.

If the stars were all 15,000 light years away, we’d need them to be in the last 15,000 years of their lives to be ghosts. If a star lives ten million years, there’s a 0.15% chance that it’s in the final 15,000 years of its life. Multiply that by 10,000 stars and we get 15 dead stars, somewhere up in the sky, that don’t look dead yet.  That’s not bad, but keep in mind, that’s for the whole sky, and that’s the most extreme example.

Now let’s do the math realistically. The average star is 300 light years away, so it would have to have died in the last 300 years for it to count as a “ghost star.” If the average star lives 5 billion years, then only 0.000006% of stars are in the final 300 years of their life. Multiply that by the average number of stars visible in the night sky (only 3000, not the 10,000 I used before), and a more realistic number is .0005%. That’s the probability that any of the stars in the sky — not any individual star, but the whole sky full of them — is already dead. Put another way, there’s only a one-in-200,000 chance that there’s a ghost star visible from Earth.*

There’s another aspect to this that I haven’t even mentioned: stars die in fairly predictable ways.  This means that astronomers can look at almost any given star and tell you, with extreme certainty, whether it’s in the “final” phases of its life or not.  Betelgeuse is the most prominent example because it’s definitely dying and relatively close by, so when it does explode (and it will), it’ll be pretty amazing to look at.

orion1

It’s the red one in the upper left corner of Orion, as seen in that photo above.  Unfortunately, to say that it’s definitely in the last phases of its life is a little like borrowing someone else’s car and seeing the gas light on.  You know it’s going to run out, but you don’t really know when.  On a stellar scale, it means that Betelgeuse might blow up tomorrow, or it might blow up in half a million years, when the mole people have wrested control of the surface and enslaved what’s left of humanity.  It’s not possible to be more precise than that.

Most stars, on the other hand, aren’t even dying.  Astronomers can look at them and say with 100% certainty that based on the color and brightness of the star, it is definitely nowhere near the end of its life, let alone near enough to be a “ghost” star.  So the odds are pretty long even if it were a crapshoot, and it’s not.

On the one hand, then, you can take comfort in the permanence of the stars. When you look up into the inky blue darkness of the night sky, resplendent with thousands of tiny pinpricks of light, you can rest easy knowing that in all likelihood, every one of those merrily twinkling stars is still there. It was there eons before you walked this earth and it will be there for eons to follow. It will not move or fade. The stars will always be there for you.

On the other hand, not a single of of those thousands of tiny pinpricks of light, merrily twinkling in the inky blue darkness of the night sky, gives the tiniest fraction of a shit about you or your wishes. You might as well wish on the wad of lint you scraped out of the dryer filter. Stop wasting your time on ridiculous superstitions and get on with your life.

*[EDIT 03/17: Turns out I did quite a lot (all) of the math wrong because decimals and scientific notation and percentages are hard.  The point still remains that there are basically no stars visible from Earth that have already died.]

One thought on “WHEN YOU WISH UPON A STAR…

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  1. Your math actually seems to have some problems.

    If the stars were all 15,000 light years away, we’d need them to be in the last 15,000 years of their lives to be ghosts. If a star lives ten million years, there’s a 0.15% chance that it’s in the final 15,000 years of its life.

    Correct so far.

    Multiply that by 10,000 stars and we get a 15% chance that, somewhere up in the sky, there’s a dead star that doesn’t look dead yet.

    Actually, no. That means you can expect approximately 15 actual dead stars up there. (Assuming ages are truely equally distributed, which has its own problems.) The chance of there being none at all is 0.0000302% if my calculator gets this right (((100-0.15)/100)^10,000), which I wouldn’t want to bet on, but it’s certainly very small – approximately one in three millions.

    That doesn’t mean you can pick a given star and there’s a one-in-six chance it’s dead,

    In fact, that chance is still one in 667. It’s not dependent on how many there are.

    Now let’s do the math realistically. The average star is 300 light years away, so it would have to have died in the last 300 years for it to count as a “ghost star.” If the average star lives 5 billion years, then only 0.000006% of stars are in the final 300 years of their life.

    Correct.

    Multiply that by the average number of stars visible in the night sky, and a more realistic number is 0.00018%.

    Actually, you can expect 3000*0.000006/100 or 0.00018 such stars on average, which number isn’t very illustrative, but the chance of there being none at all is ((100-0.000006)/100)^3000, or 99.9820016%, so the chance for at least one is 0.0179984%, one in 5556.

    That’s the probability that any of the stars in the sky — not any individual star, but the whole sky full of them — is already dead. Put another way, there’s only a one-in-5000 chance that there’s a ghost star visible from Earth.

    That one’s correct again, because you forgot the factor of 100 that % sign implies.

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