Pas de deux

Ever heard of Antichthon? 

Sometimes called "Counter-Earth," Antichthon is a hypothesized (now known to be nonexistent) planet in the same orbit as Earth, but on the other side of the Sun.  And, therefore, invisible to earthbound observers.  It was first proposed by the fourth century B.C.E. Greek philosopher Philolaus, who argued against the prevalent geocentric models of the day.  Philolaus thought that not only was there another planet on the opposite side of the Sun from the Earth, he believed that the Sun and all of the planets were orbiting around a "Central Fire" exerting an unseen influence at a distance.  Thus, more or less accidentally, landing something near the truth, as the entire Solar System does revolve around the center of the Milky Way galaxy.

None of Philolaus's ideas, however, were based upon careful measurements and observations; another popular notion of his time was that celestial mechanics was supposed to be beautiful, and therefore you could arrive at the right answer just by thinking about what the most elegant possible model is.  (Nota bene: I took a class called Classical Mechanics in college, and what I experienced was not "beauty" and "elegance."  Mostly what it seemed like to me was "incredibly difficult math" and "intense frustration."  So honestly, maybe Philolaus was on to something.  If I could have gotten a better grade in Classical Mechanics by dreaming up pretty but untestable claims about planets we couldn't see even if we wanted to, I'd'a been all over it.)

Anyhow, Antichthon doesn't exist, which we now know for sure both because probes sent out into the Solar System don't see a planet opposite the Earth when they look back toward the Sun, and by arguments from the physics of orbiting bodies.  Kepler showed that the planets are in elliptical orbits, so even if Antichthon was out there, it wouldn't always be 180 degrees opposite to us, meaning that periodically it would peek out from behind the Sun and be visible to our telescopes.  Plus, an Earth-sized planet across from us would experience gravitational perturbations from Venus that would make its orbit unstable -- again, meaning it wouldn't stay put with the Sun in the way.

But there's no particular reason why there couldn't be two planets in the same orbit.  Way back in 1772, the brilliant astronomer and mathematician Joseph-Louis Lagrange found that there were stable points that small bodies could occupy, under the influence of two much larger orbiting objects (such as the Sun and the Earth).  There are, in fact, five such points, called "Lagrange points" in his honor:

[Image licensed under the Creative Commons Xander89, Lagrange points simple, CC BY 3.0]

And you can see that L3 is actually directly across from the Earth -- so Philolaus was before his time.  (Once again, though, not because he'd done the mathematics, the way Lagrange did.  It was really nothing more than a shrewd guess.)  In fact, there are three points that could result in a stable configuration of two planets sharing an orbit -- L3, L4, and L5.

The reason all this comes up is that scientists at the Madrid Center for Astrobiology have found for the first time a possible candidate for this elusive configuration -- around a T-Tauri type star called PDS 70 in the constellation of Centaurus.  The pair of planets, which appear to be gas giants, one of them three times the size of Jupiter, take 119 Earth years to circle their parent star once.

"Planets in the same orbit have so far been like unicorns," said study co-author Jorge Lillo-Box.  "They are allowed to exist by theory, but no one has ever detected them."

The discovery is so unusual that -- understandably -- the scientists are hesitant to state too decisively that it's proven.  Their paper, which appeared in the journal Astronomy and Astrophysics, indicates that they will continue to gather data from the ESO (European Southern Observatory) and ALMA (Atacama Large Millimeter Array) in Chile through 2026 to bolster their claim.

In any case, it's fascinating that a strange guess made 2,400 years ago by an obscure Greek philosopher, then shored up with rigorous mathematics by a French/Italian astronomer 250 years ago, has finally been shown to exist -- two planets locked in a celestial pas de deux, 370 light years away.  

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The celestial dance

It's interesting how the approach to science has changed in the last four centuries.

It's easy to have the (mistaken) impression that as long as we humans have been doing anything scientific, we've always done it the same way -- looked at the evidence and data, then tried to come up with an explanation.  But science in Europe before the eighteenth-century Enlightenment was largely done the other way around; you constructed your model from pure thought, based on a system of how you believed things should act, and once you had the model, you cast about for information supporting it.

It's why Aristotle's statement that the rate of speed of a falling object is directly proportional to its mass stood essentially unchallenged for over a millennium and a half despite the fact that it's something any second grader could figure out was wrong simply by dropping two different-sized rocks from the same height and observing they hit the ground at exactly the same time.  As odd as it is to our twenty-first century scientific mindset, the idea of figuring out if your claim is correct by testing it really didn't catch on until the 1700s.  Which is why the church fathers got so hugely pissed off at Galileo; using a simple experiment he showed that Aristotle got it wrong, and then followed that up by figuring out how things up in the sky moved (such as the moons of Jupiter, first observed by Galileo through the telescope he made).  And this didn't result in the church fathers saying, "Whoa, okay, I guess we need to rethink this," but their putting Galileo on trial and ultimately under permanent house arrest.

That "think first, observe later" approach to science plagued our attempts to understand the universe for a long time after Galileo; people first came up with how they thought things should work, often based on completely non-scientific reasons, then looked for data to support their guess.  That we've come as far as we have is a tribute to scientists who were able to break out of the straitjacket of what the Fourth Doctor in Doctor Who called "not altering their views to fit the facts, but altering the facts to fit their views."

One of the best examples of this was the seventeenth-century astronomer Johannes Kepler.  He was a deeply religious man, and lived in a time when superstition ruled pretty much everything -- in fact, Kepler's mother, Katharina (Guldenmann) Kepler, narrowly escaped being hanged for witchcraft.  Kepler, and most other European astronomers from his time and earlier, were as much astrologers as scientists; they expected the heavens to operate by some kind of law of divine celestial perfection, where objects moved in circles (anything else was viewed as imperfect) and their movements had a direct effect on life down here on Earth.

At the beginning, Kepler tried to extend his conviction of the mathematical perfection of the cosmos to the distances at which the planets revolved around the Sun.  He became convinced that the spacing of the planets' orbits was determined by conforming to the five Platonic solids -- cube, dodecahedron, tetrahedron, icosahedron, and octahedron -- convex polyhedra whose sides are made up only of identical equal-sided polygons.  He tried nesting them one inside the other to see if the ratios of their spacing could be made to match the estimated spacing of the planets, and got close, but not close enough.  One thing Kepler had going for him was he was firmly committed to the truth, and self-aware enough to know when he was fudging things to make them fit.  So he gave up on the Platonic solids, and went back to "we don't know why they're spaced as they are, but they still travel in perfect circles" -- until careful analysis of planetary position data by the Danish observational astronomer Tycho Brahe showed him again that he was close, but not quite close enough.

This was the moment that set Kepler apart from his contemporaries; because instead of shrugging off the discrepancy and sticking to his model that the heavens had to move in perfect circles, he jettisoned the whole thing and went back to the data to figure out what sort of orbits did make sense of the observations.  After considerable work, he came up with what we now call Kepler's Laws of Planetary Motion, including that planets move in "imperfect" elliptical, not circular, orbits, with the Sun at one focus.

Start with the data, and see where it drives you.  It's the basis of all good science.

[Image licensed under the Creative Commons Gonfer, Kepler-second-law, CC BY-SA 3.0]

What got me thinking about Kepler and his abandonment of the Platonic-solid-spacing idea was a paper this week in Astronomy & Astrophysics showing that even though Kepler initially was on the wrong track, there are sometimes odd mathematical regularities that pop up in the natural world.  (A well-known one is how often the Fibonacci series shows up in the organization of things like flower petals and the scales of pine cones.)  The paper, entitled "Six Transiting Planets and a Chain of Laplace Resonances in TOI-178," by a team led by Adrien Leleu of the Université de Genève, showed that even though hard data dashed Kepler's hope of the motion of the heavens being driven by some concept of mathematical perfection, there is a weird pattern to the spacing of planets in certain situations.  The patterns, though, are driven not by some abstract philosophy, but by physics.

In physics, resonance occurs when the physical constraints of a system make them oscillate at a rate called the "natural frequency."  A simple example is the swing of a pendulum; a pendulum of a given length and mass distribution only will swing back and forth at one fixed rate, which is why they can be used in timekeeping.  The motion of planets (or moons) is also an oscillating system, and a given set of objects of particular masses and distances from their center of gravity will tend to fall into resonance, the same as if you try to swing a pendulum at a different rate than the rate at which it "wants to go," then let it be, it'll pretty much immediately revert to swinging at its natural frequency.

The three largest moons of Jupiter exhibit resonance; they've locked into orbits that are the most stable for the system, which turns out to be a 4:2:1 resonance, meaning that the innermost (Io) makes two full orbits in the time the next one (Europa) makes a single orbit, and four full orbits in the time it takes for the farthest (Ganymede).

This week's paper found a more complex resonance pattern in five of the planets around TOI-178, a star two hundred light years away in the constellation Sculptor.  It's a 18:9:6:4:3 resonance chain -- the nearest planet orbits eighteen times as the farthest orbits once, the next farthest nine times as the farthest orbits once, and so on.  This pattern was locked in despite the fact that the planets are all quite different from each other; some are small, rocky planets like Earth, others low-density gaseous planets like Neptune.

"This contrast between the rhythmic harmony of the orbital motion and the disorderly densities certainly challenges our understanding of the formation and evolution of planetary systems," said study lead author Adrien Leleu, in an interview with Science Daily.

So the dance of the celestial bodies is orderly, and shows some really peculiar regularities that you wouldn't have guessed.  But unlike Kepler's favored (but ultimately abandoned) idea that the perfect heavens had to be arranged by perfect mathematics, the Leleu et al. paper shows us that those patterns only emerge by analysis of the data itself, rather than the faulty top-down attempt to force the data to conform to the way you think things should be.  Once you open your mind up to going where the hard evidence leads, that's when the true wonders of the universe begin to emerge.

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Just last week, I wrote about the internal voice most of us live with, babbling at us constantly -- sometimes with novel or creative ideas, but most of the time (at least in my experience) with inane nonsense.  The fact that this internal voice is nearly ubiquitous, and what purpose it may serve, is the subject of psychologist Ethan Kross's wonderful book Chatter: The Voice in our Head, Why it Matters, and How to Harness It, released this month and already winning accolades from all over.

Chatter not only analyzes the inner voice in general terms, but looks at specific case studies where the internal chatter brought spectacular insight -- or short-circuited the individual's ability to function entirely.  It's a brilliant analysis of something we all experience, and gives some guidance not only into how to quiet it when it gets out of hand, but to harness it for boosting our creativity and mental agility.

If you're a student of your own inner mental workings, Chatter is a must-read!

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

A planetary Tilt-o-Whirl

A long-standing unsolved puzzle in physics is the three-body problem, which despite its name is not about a ménage-à-trois.  It has to do with calculating the trajectory of orbits of three objects around a common center of mass, and despite many years of study, the equations it generates seem to have no general solution.

There are specific solutions for objects of a particular mass starting out with a particular set of coordinates and velocities, and lots of them result in highly unstable orbits.  Take, for example, this one, which involves three objects of equal masses, starting out with zero velocity and sitting at the vertices of a scalene triangle:

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

It's a problem that has application to our understanding of double and triple star systems, which seem to be quite common out there in the cosmos.  For people like me, who are fascinated with the possibility of extraterrestrial life, it's especially important -- because if the majority of planets in orbit around a double star (or worse, a triple star) follow unstable trajectories, that would represent a considerable impediment to the evolution of life.  Such planets would have wildly fluctuating climates, a possibility that resulted in a plot twist on the generally abysmal 1960s science fiction show Lost in Space, even though when it came up (1) the writers evidently didn't know the difference between a planet's rotation and its revolution, with the result that the blazing heat wave and freezing cold only lasted a few hours each, and (2) in subsequent episodes they conveniently forgot all about it, and it was never mentioned again.

Be that as it may, now that we have a vastly-improved ability to detect extrasolar planets and determine their orbits around their host star(s), it's given us more information about what kinds of trajectories these complex systems can take.  For example, consider the system GW Orionis, which was the subject of a paper last week in Science.

GW Orionis is a trio of young stars, two of which are quite close together, and the third further away.  The two closer ones are whirling around pretty quickly, and the third making long swoopy dives in toward (and then away from) the others.

Complicated enough, but add to that a set of proto-planetary rings.  Three of them, in fact.  And unlike our own rather sedate star system, where all the planets except for Pluto are orbiting within under seven degrees' tilt with respect to a flat plane -- even Pluto's orbit is only tilted by fifteen degrees -- this system is kind of all over the place.

Here's an artist's conception of what GW Orionis looks like, based on the measurements and observations we have:

[Image courtesy of L. Calçada/ESO, S. Kraus et al., University of Exeter]

Pretty cool-looking.  Given our lack of knowledge of (in this case) six-body problems -- the three stars and the three planetary rings -- no one knows for sure if this is going to be a long-lasting, stable system, or if it will eventually collapse or fly apart.  It seems likely that the system would be a planetary Tilt-o-Whirl, and any orbits formed would be as chaotic as the animation I included above, but honestly, that's just a guess.

However, it's entertaining to think of what life would be like on a planet with three suns in the sky.  One more even than Tatooine:

The more we scan the skies, the more awe-inspiring things we find.  I'm glad to live in a time when our ability to study the stars has improved to the point that we're able to consider not just systems like our own, but the vast array of possibilities that are out there.  One thing's for certain: if you are into astronomy, you'll never be bored.

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Humans have always looked up to the skies.  Art from millennia ago record the positions of the stars and planets -- and one-off astronomical events like comets, eclipses, and supernovas.

And our livelihoods were once tied to those observations.  Calendars based on star positions gave the ancient Egyptians the knowledge of when to expect the Nile River to flood, allowing them to prepare to utilize every drop of that precious water in a climate where rain was rare indeed.  When to plant, when to harvest, when to start storing food -- all were directed from above.

As Carl Sagan so evocatively put it, "It is no wonder that our ancestors worshiped the stars.  For we are their children."

In her new book The Human Cosmos: Civilization and the Stars, scientist and author Jo Marchant looks at this connection through history, from the time of the Lascaux Cave Paintings to the building of Stonehenge to the medieval attempts to impose a "perfect" mathematics on the movement of heavenly objects to today's cutting edge astronomy and astrophysics.  In a journey through history and prehistory, she tells the very human story of our attempts to comprehend what is happening in the skies over our heads -- and how our mechanized lives today have disconnected us from this deep and fundamental understanding.

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

Homing in on Tatooine

I remember the first time I ran into the concept that the Earth's relatively circular orbit might not be universal amongst the planets out there in the universe.

I shudder to admit that it was on the generally abysmal 1960s science fiction series Lost in Space.  The brave crew of the Jupiter 2 are stranded on a strange planet, and initially the whole place seems to be a frozen wasteland.  But after a journey via their "chariot" (as they call their tank-like wheeled transport vehicle), they find the temperature is seesawing wildly -- at first it seems to be heading to cold temperatures that will eliminate all possibility of life, but unexpectedly the mercury begins to rise, and what was a crossing on solid ice turns into a treacherous sea voyage (the chariot, fortunately, has amphibious capabilities).

The explanation we're given is that the planet they're on has a very elliptical orbit, so it experiences huge temperature changes.  Unfortunately, the writers of the show apparently did not understand that there's a difference between a planet's rotation and its revolution, so they depict the excruciatingly hot temperatures when the planet is at its perigee as only lasting a minute or two, so all the Robinsons had to do was hide under a reflective shelter for a little bit to avoid getting cooked.

So good idea, lousy execution, which can be said of much of that series.

A more fundamentally startling change in my perception of what it'd look like on another planet occurred when I saw Star Wars for the first time, and hit the iconic scene where Luke is looking toward the horizon as sunset occurs on Tatooine -- and there are two suns in the sky.  Tatooine, it seems, orbits a binary star -- something I'd honestly never thought about before then.

Being a science nerd type, I wondered what the shape of a planet's orbit would be if it were moving around two centers of gravity, and found pretty quickly that my rudimentary knowledge of Newton's Laws and Kepler's Law were insufficient to figure it out.

Turns out I wasn't alone; physicists have been wrestling with the three-body problem for a couple of hundred years, and there is no general solution for it.  Three objects orbiting a common center of gravity results in a chaotic system, where the paths of each depend strongly on initial conditions (and some configurations are unstable and result in either collisions or one of the objects being ejected from the system).

It is known, however, that there are points in a three-body system called Lagrange points (after their discoverer, the French mathematician and astronomer Joseph-Louis Lagrange) which result in a stable configuration in which each of the orbiting bodies stays in the same locked position relative to the other, so the entire system seems to turn as one.  Some of the moons of Jupiter (the so-called Trojan moons) sit at the Lagrange points for that system, a pattern that seems to be stable indefinitely.  (Note that from the Earth perspective, an object at the L3 Lagrange point would never be visible -- leading conspiracy wackos to postulate that it could be a place for alien spacecraft to be hiding.)

[Image licensed under the Creative Commons Xander89, Lagrange points simple, CC BY 3.0]

Things only get worse when you add additional objects.  The only way to approximate the configuration of the orbits is to input the specific initial parameters and use computer modeling software to determine a solution; there is no general set of equations to predict what it will look like.

What brings this up is a paper this week in The Astrophysical Journal that went beyond the theoretical, and found actual data from binary star systems with planets to see what the various orbits looked like.  In "The Degree of Alignment between Circumbinary Disks and Their Binary Hosts," by a team led by Ian Czekala of the University of California - Berkeley, we read about new observations from the Atacama Large Millimeter/submillimeter Array (ALMA), which tells us that not only might objects orbiting a binary star exhibit chaotic paths, they might not all orbit in the same plane.

Because of the way planets form -- coalescence of dust and debris from a flat ring surrounding the host star -- planetary systems seem mostly to be aligned with each other.  In our own Solar System, the eight planets all orbit within seven degrees of the Earth's orbital plane (excluding, sadly, Pluto, which still hasn't recovered its planet status, and has an orbital tilt of just over seventeen degrees).

But apparently there are exceptions.  Some binary stars have planets that orbit in a highly tilted ellipse with respect to the orbit of the two stars around their own center of mass.  How this could happen -- whether the planets condensed from a ring that was already tilted for some reason, or that the three-body chaos warped the orbits after formation -- isn't known.  "We want to use existing and coming facilities like ALMA and the next generation Very Large Array to study disk structures at exquisite levels of precision," study lead author Czekala said, "and try to understand how warped or tilted disks affect the planet formation environment and how this might influence the population of planets that form within these disks."

Which is pretty cool.  While it won't solve the more general difficulty of the three-body problem (and the four-, five-, six-, etc. body problems), it will at least give some empirical data to go on with which to analyze other systems ALMA finds.

So we're homing in on Tatooine.  For what it's worth, it looks like the overall situation might be more similar to Star Wars than it is to Lost in Space.

Which is a good thing in a variety of respects.

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Any guesses as to what was the deadliest natural disaster in United States history?

I'd speculate that if a poll was taken on the street, the odds-on favorites would be Hurricane Katrina, Hurricane Camille, and the Great San Francisco Earthquake.  None of these are correct, though -- the answer is the 1900 Galveston hurricane, that killed an estimated nine thousand people and basically wiped the city of Galveston off the map.  (Galveston was on its way to becoming the busiest and fastest-growing city in Texas; the hurricane was instrumental in switching this hub to Houston, a move that was never undone.)

In the wonderful book Isaac's Storm, we read about Galveston Weather Bureau director Isaac Cline, who tried unsuccessfully to warn people about the approaching hurricane -- a failure which led to a massive overhaul of how weather information was distributed around the United States, and also spurred an effort toward more accurate forecasting.  But author Erik Larson doesn't make this simply about meteorology; it's a story about people, and brings into sharp focus how personalities can play a huge role in determining the outcome of natural events.

It's a gripping read, about a catastrophe that remarkably few people know about.  If you have any interest in weather, climate, or history, read Isaac's Storm -- you won't be able to put it down.

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