The eccentric heavens

For a lot of people, the most disquieting thing about science is the way it's moved humanity farther and farther from its position as the center of the universe.

It's why the heliocentric model met with such resistance.  That the Earth was at the center, and all celestial objects move in circles around it, seemed not only common sense but to fit with the biblical view of the primacy of humans as being created in the image of God.  Copernicus and Galileo ran afoul of the church because their findings contradicted that -- especially when Galileo was the first to see the four largest moons of Jupiter (now known as the "Galilean moons" in his honor), and it was clear they were circling Jupiter and not the Earth -- meaning there are celestial objects that don't obey the model of the entire universe being geocentric.

Another blow was dealt to this idea when Johannes Kepler used data by Danish observational astronomer Tycho Brahe to show that the planets weren't even in circular orbits -- i.e., the heavens were not neat, tidy, and divine, with everything moving in "perfect circles."  That idea didn't die easily.  It'd been known since the time of Ptolemy (second century C.E.) that perfectly circular orbits with the Earth at the center didn't produce predictions that matched the actual positions of the planets, so Ptolemy and others tried desperately to salvage the model by having them move in "epicycles" -- smaller circles that loop-the-loop around a point that itself travels in a circle around the Earth.  But that didn't quite do it, either.  Instead of scrapping the model, Ptolemy introduced epicycles around the epicycles, resulting in an orbital pattern so complex it's almost funny (but still, supposedly, "perfect").

The Ptolemaic model of the universe [Image is in the Public Domain]

But that didn't quite work either, even if you followed Copernicus's lead, put the Sun at the center, and adjusted the planetary orbits accordingly.  The discrepancies bothered Kepler until he finally had to concede that the objects in the Solar System didn't move in circles around the Sun, but in "imperfect" ellipses with the Sun at one focal point.  A measure of how far off the orbit is from being circular -- the "flatness" of the ellipse, so to speak -- is called the eccentricity.  Some planets have very low eccentricity; their orbits are nearly circular.  Of the planets in the Solar System, Venus has the lowest eccentricity, at 0.0068.  Mercury has the highest, at 0.2056.

There's no reason why it couldn't go a lot higher, though.  Comets have highly eccentric orbits; Halley's Comet, for example, has an orbital period of 76 years and an eccentricity of 0.9671.

Could an actual planet have a very eccentric orbit?  Yes, but it would create the climate from hell, hot when it's at the perihelion of its orbit and freezing cold when it's at the aphelion.  Even the old Lost in Space looked at this possibility; very early on, the Robinsons find that the average temperature on the planet where they're stranded is dropping, and the Robot figures out this is because the planet is in a highly elliptical orbit.  This means, of course, that if they survive the intense cold, they're in for a period of intense heat when the planet reaches the other side of its orbit.  Unfortunately, this clever plot point got fouled up because the writers evidently didn't know the difference between a planet's rotation and its revolution, so when the peak cold and peak heat come, it only lasts for a few minutes.  For example, in a highly dramatic scene, the intrepid family take shelter under reflective tarps when the planet's sun is at its closest, and some of the tarps burst into flame, but five minutes later, things are cooling off.

Disaster averted, unless you count the traumatic eye-rolls experienced by viewers who knew even the rudiments of astronomy.

The reason this comes up is because of the discovery of an exoplanet with the highest eccentricity known.  A paper in Astronomy & Astrophysics last week describes a planet orbiting a red dwarf star about 188 light years away, which is over twice the size of the Earth, and has an orbital eccentricity of about 0.5.  This means that in its 35-day orbit, the average temperature fluctuates between -80 C and 100 C -- a frozen wasteland at aphelion and a boiling blast furnace at perihelion, with brief periods in between where the temperature might be tolerable.

"In terms of potential habitability, this is bad news," said Nicole Schanche, an astronomer at the University of Bern and lead author of the paper, in what has to be understatement of the year.

So the whole "Goldilocks zone" issue for finding habitable exoplanets -- an orbital distance resulting in temperatures where water could exist as a liquid, which isn't too hot or too cold, but "just right" -- isn't as simple as it sounds.  The average temperature might be in the right range, but if the planet has an eccentric orbit, the average may not tell you much.  It's like the old quip that if you have one foot encased in ice and the other one in a pot of boiling water, on average you're comfortable.

Not only that, but there's the problem of tidal locking -- when the rotation and revolution rate are equal, so the same side of the planet always faces its sun.  Once again, this might result in an average temperature that is reasonably good, but only because one side is getting continuously cooked while the other is in the deep freeze.  It might be possible to live on the boundary between the light and dark sides -- a place where the planet's star is forever on the horizon -- but there, you'd find a different problem.  Because of the process of convection, in which fluids flow in such a way as to distribute heat evenly, on that twilight margin there'd be catastrophic upper-level winds from the hot to the cold side and equally strong ones at the surface from the cold to the hot side, putting that thin zone smack in the center of the Convection Cell from Hell and rendering even that area effectively uninhabitable.

So we're lucky to live where we do.  Or, more accurately, if the Earth had any of the aforementioned problems, we wouldn't be here.  But this further reinforces my awareness of what a beautiful, awe-inspiring, and scarily inhospitable place the universe is.  And whether there are other places out there that are as clement as the Earth, where life as we know it could evolve and thrive, remains very much to be seen.

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Like many people, I've always been interested in Roman history, and read such classics as Tacitus's Annals of Imperial Rome and Suetonius's The Twelve Caesars with a combination of fascination and horror.  (And an awareness that both authors were hardly unbiased observers.)  Fictionalized accounts such as Robert Graves's I, Claudius and Claudius the God further brought to life these figures from ancient history.

One thing that is striking about the accounts of the Roman Empire is how dangerous it was to be in power.  Very few of the emperors of Rome died peaceful deaths; a good many of them were murdered, often by their own family members.  Claudius, in fact, seems to have been poisoned by his fourth wife, Agrippina, mother of the infamous Nero.

It's always made me wonder what could possibly be so attractive about achieving power that comes with such an enormous risk.  This is the subject of Mary Beard's book Twelve Caesars: Images of Power from the Ancient World to the Modern, which considers the lives of autocrats past and present through the lens of the art they inspired -- whether flattering or deliberately unflattering.

It's a fascinating look at how the search for power has driven history, and the cost it exacted on both the powerful and their subjects.  If you're a history buff, put this interesting and provocative book on your to-read list.

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

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!]