Skeptophilia (skep-to-fil-i-a) (n.) - the love of logical thought, skepticism, and thinking critically. Being an exploration of the applications of skeptical thinking to the world at large, with periodic excursions into linguistics, music, politics, cryptozoology, and why people keep seeing the face of Jesus on grilled cheese sandwiches.

Saturday, November 6, 2021

The ghoul's head and the three-body problem

Ever heard of Algol?

Known to astronomers as Beta Persei, it's the second-brightest star in the constellation of Perseus.  It was singled out as strange a long time ago.  Even in a small telescope it looks like a single star, but in 1881 it became the first identified eclipsing binary, a pair of stars orbiting around a common center of gravity with the orbital plane lined up so that from our perspective, one passes in front of the other.  Because one of the stars is dimmer than the other, when the dimmer one crosses in front of the brighter one, the brightness of the pair appears to diminish -- the transit takes ten hours and happens every 2.86 days, so it's regular as clockwork.

The first certain mention of Algol's variability was by Italian astronomer Geminiano Montanari in 1667, but way before that the star had a reputation for being uncanny.  The name Algol comes from the Arabic رأس الغول (raʾs al-ghūl) -- "the head of the ghoul."  The Greeks, who named the constellation in which it resides Perseus, thought that Algol was the Gorgon's head that the hero was carrying.  The ancient Hebrews called it Rōsh ha Sāṭān (Satan's head).  These are similar enough that they probably come from a common source, but the Chinese as well thought there was something evil about it; they called Algol and the stars surrounding it Dà Líng -- the Mausoleum.

So even if there's no certain evidence that the ancients knew about Algol's odd variability, it seems pretty likely.

What no one realized until recently is that Algol is weirder even than that.  To see just how strange it is, first a brief physics lesson.

Some of the great names of physics and astronomy in the sixteenth and seventeenth centuries -- Galileo Galilei, Tycho Brahe, Johannes Kepler, and Isaac Newton, especially -- used highly accurate data on planetary positions to conclude that the planets in the Solar System go around the Sun in elliptical orbits, all powered by the Universal Law of Gravitation.  The mathematical model they came up with worked to a high degree of accuracy, allowing earthbound astronomers to predict where the planets were in the sky, and also such phenomena as eclipses.

Lucky for them, though, that the Sun is so massive.  Because the Sun is huge -- it has a thousand times more mass than the largest planet, Jupiter -- its gravitational pull is big enough that it swamps the pull the planets exert on each other.  For most purposes, you can treat each orbit as independent two-body problems; you can (for example) look at the masses, velocities, and distances between the Sun and Saturn and ignore everything else for the time being.  (Interestingly, it's the slight deviation of the orbit of Uranus from the predictions of its position using the two-body solution that led astronomers to deduce that there must be another massive planet out there pulling on it -- and in 1846 Neptune was observed for the first time, right where the deviations suggested it would be.)

I said it was "lucky" that the mass imbalance is so large, but I haven't told you how lucky.  It turns out that all you have to do is add one more object of close to the same size, and you now have the three-body problem -- a big problem, because physicists have been unable to find a general solution to the equations it generates.  You can pick the parameters (mass, separation distance, initial velocity, and so on) and have a computer model what the orbits would look like, but there's no overarching set of mathematical equations that physicists can use on any other system with different parameters.  The unifying model just doesn't exist, or at least hasn't been discovered yet.

Worse still, most individual three-body systems generate chaotic orbits.  Here's a rather mesmerizing gif showing one of them:

[Image is licensed under the Creative Commons Dnttllthmmnm, Three-body Problem Animation with COM, CC BY-SA 4.0]

The reason this comes up  is a paper in The Astrophysical Journal showing that Algol isn't a simple double star system, with two stars orbiting their common center of gravity like Newton said.  In the 1950s astronomers figured out that the known binary system (Algol A and Algol B) is in an orbit with a third star (Algol C), with the whole trio orbiting their center of gravity once every 1.86 years, and presumably tracing out some kind of bizarre Spirograph pattern like the one in the gif.

But the recent paper showed that it's not even that simple.  Algol isn't a weird, chaotic three-star system.

The "star" we call Algol is apparently made up of at least seven stars all moving in a complex dance around their collective center of gravity.

Algol is in our stellar neighborhood -- only ninety light years away -- so why haven't they been observed until now?

"The paradox is that Algol A is 'too bright,' " said astrophysicist Lauri Jetsu, author of the paper, in an interview with Science Daily.  "It can hide these new companion candidate stars even from our most powerful modern space telescopes, just like our Sun can hide all other stars during daytime...  Even the cutting-edge equipment onboard the Gaia satellite could not detect these new companion candidates.  Future interferometric observations may be used to directly confirm the existence of at least some of Algol's companions."

I find it fascinating that even in a part of physics that is usually considered pretty well sussed-out -- classical mechanics, the study of objects in motion -- there are unsolved problems that the experts consider very close to intractable.  Further reinforcing the notion that the universe doesn't seem to feel obliged to choose how it acts based upon whether humans find it comprehensible.  It does what it does, leaving us to try to explain how on earth (or off it) that kind of thing could happen -- in this case, seven massive objects all whirling around each other in apparently stable orbits.

It's a little like the famous (if apocryphal) story about bumblebees -- that physicists have analyzed their mass, wing size, wing beat frequency, and so on, and have come to the conclusion that bumblebees can't fly.  The bumblebees, not knowing this, go ahead and fly anyway.  Here, the seven members of the Algol system are apparently unaware that the steps of their cosmic dance is beyond what our current physics can explain, but it doesn't stop them from dancing.

Think of that the next time you look at the night sky, and see the bright blue pinpoint of the ghoul's head twinkling against the blackness.


My master's degree is in historical linguistics, with a focus on Scandinavia and Great Britain (and the interactions between them) -- so it was with great interest that I read Cat Jarman's book River Kings: A New History of Vikings from Scandinavia to the Silk Road.

Jarman, who is an archaeologist working for the University of Bristol and the Scandinavian Museum of Cultural History of the University of Oslo, is one of the world's experts on the Viking Age.  She does a great job of de-mythologizing these wide-traveling raiders, explorers, and merchants, taking them out of the caricature depictions of guys with blond braids and horned helmets into the reality of a complex, dynamic culture that impacted lands and people from Labrador to China.

River Kings is a brilliantly-written analysis of an often-misunderstood group -- beginning with the fact that "Viking" isn't an ethnic designation, but an occupation -- and tracing artifacts they left behind traveling between their homeland in Sweden, Norway, and Denmark to Iceland, the Hebrides, Normandy, the Silk Road, and Russia.  (In fact, the Rus -- the people who founded, and gave their name to, Russia -- were Scandinavian explorers who settled in what is now the Ukraine and western Russia, intermarrying with the Slavic population there and eventually forming a unique melded culture.)

If you are interested in the Vikings or in European history in general, you should put Jarman's book in your to-read list.  It goes a long way toward replacing the legendary status of these fierce, sea-going people with a historically-accurate reality that is just as fascinating.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

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