Category: Astronomy: Planetary Science

Directional Reset

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, Uncategorized1 Comment

Professor of Astronomy Cathleen O’Meara barges into Cal’s Coffee Shop. “There you are, Sy Moire! You numbskull! You addlepate! You … nincompoop! “

We’ve known each other since we were kids but I’ve rarely seen her this angry. “What have I done this time, Cathleen? I apologize, but what for?”

“That last post you put up. One of the hardest things to get across to planet science students is the Coriolis Effect. You got it exactly backwards, you lummox! Confused the be-jeepers out of half my students and it’s going to take a whole class period to unwind it.”

All those exclamation points sting when they strike home. “It did feel funny. All the sources I checked said Coriolis skews travel to the right in the northern hemisphere but I worked hard for hours on that video and it clearly shows ‘left‘.”

<sniff> “Stupid waste of time, chump! That video doesn’t show Coriolis.” <she grabs one of Cal’s graph-paper napkins and starts sketching> “Your balloon or whatever isn’t traveling north along Earth’s surface. It’s going out into space. That dark line tracks the thing’s shadow, or it would if you had the Sun behind it instead of off to the side. It has nothing at all to do with the cloud stream at the top of the hurricane and by the way those winds in the picture are outward, not inward as you’d’ve known if you’d’ve thought about for even a moment, blockhead! Here, look at a sideways view.”

“You’re saying my balloon’s not following the surface, it’s vectored away from the surface parallel to the north‑south axis. Also that the shadow points that I plotted on Earth trend westward only because the Earth turns west‑to‑east underneath the balloon. … Okay, I can see that. Goes so high up I guess it can’t be a balloon, huh?”

“Don’t try to deflect the conversation, nitwit. Figure out what you got wrong and put up a correction post that gives a proper account of Coriolis. Sorry, Cal, I’ll need my coffee in a sippy‑cup. Gotta go revise my lesson plan, again.”

She grabs her caffeine to‑go, flings me a final “Dolt! ” and storms out the door trailing a cloud of grumbles.

Vinnie’s open-mouthed. “Geez, Sy, she does have a temper.”

“You know it, Vinnie. Fortunately she saves it up for deserving occasions but don’t ever get her started on politics. So let’s see, what part of what I posted did I get right?”

“Well, there’s the part about Helsinki’s rotation around the Earth runs fewer kilometers per hour than Quito’s. That’s just fact, can’t argue with it.”

“Yeah, Mr Moire, and there’s Conservation of Momentum.”

“Right, Jeremy.” Synapses connect in my head. “Got it! Vinnie, what’s the rule between speed and orbit size?”

“The closer the faster. The Moon’s a quarter‑million miles away, takes a month to go round the Earth; the ESS is 250 miles up, circles us every 90 minutes. If you’re in some orbit and wanna go lower, you gotta speed up. Took me an hour to convince Larry that’s the way it works. He was all about centrifugal force forcing you outward, but if you want to get deeper in the gravity well you need the extra speed to balance the extra gravity.”

“That’s the rule for space orbits, alright, but things work exactly the opposite for travel on the surface of a rotating sphere. Gravity pulls centerward with the same strength everywhere so gravity’s not what balances the centrifugal force.”

“What does?”

“Geometry. In space orbits, velocity and kinetic energy increase toward the core. On a sphere’s surface, the highest velocity is farthest away from the rotational axis, at the equator. Velocity falls off to zero at both poles. Every latitude has its characteristic velocity and kinetic energy. Suppose you’re loose on Earth’s northern hemisphere and moving east too fast for your latitude. You’ll drift southward, away from the axis, until you hit a latitude that matches your speed. Meanwhile, because you’re moving east the landscape will flow westward beneath you. The blend is the Coriolis Effect.”

“So if I’m slower than my latitude I drift north and Coriolis sends me east?”

“Cathleen would agree, Jeremy.”

~ Rich Olcott

When It’s Not The Same Frame – Never Mind

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, UncategorizedLeave a comment
  • Author‘s note — Please ignore everything below the separator line. It’s bogus. No excuses, it’s just wrong. I intend to embarrass Vinnie and Sy just as soon as I get my head straight. My apologies to every reader, especially teachers, that I’ve confused.

“Hey, Sy, I couldn’t help overhearing—”

<chuckle> “Of course not, Cal. Overhearing what?”

“When you said Quito goes round the world twice as fast as Helsinki. That can’t be true! Things would collide and we’d get all kinds of earthquakes and stuff.”

“Well, sure, Cal, if those two airports moved relative to each other. But they don’t, they’re stuck 10750 kilometers apart just like they’ve always been. I hated flying that route. Mountains to dodge at both ends, in between there’s bad weather a lot of the time and no place good to set down if something goes wrong. … Wait — different speeds — it’s frames again, ain’t it, Sy?”

“Exactly, Vinnie, even though it’s not black holes for a change. Relative to an inertial frame on the Earth’s surface, the Earth itself doesn’t move and neither does either city. Relative to a Sun‑centered frame, though, the Earth spins on its axis once every 24 hours. In the Sun’s frame, Quito on Earth’s 40‑thousand kilometer Equator does 1666 kilometers per hour. Helsinki’s at 60° North. Its circle around the spin axis is only 20 thousand kilometers so its linear speed is 833 kilometers per hour even though it does the same 15 degrees per hour that Quito does.”

“Hi, Mr Moire. Welcome back. I couldn’t help overhearing—”

<chuckle> “Of course not, Jeremy. Overhearing what?”

“You talking about places on Earth moving different speeds. We just studied about that in Dr O’Meara’s planet science class but it’s still loose in my head. It has to do with why storms go counterclockwise, right?”

“It has everything to do with that, except the counterclockwise storms are only in the northern hemisphere. Southern hemisphere storms rotate the other way.”

“I got this, Sy. Bring up that movie you got on Old Reliable, the one that shows the northern hemisphere. Yeah, that one. Jeremy, some guy in a balloon is the dark line on his way from Kansas to the North Pole to meet Santa. In his frame the earth is moving left‑to‑right relative to his northbound course. See how the red star’s moving?”

“Yeah, it’s moving towards sunrise so his movie’s got the rotation right. Why Kansas?”

“‘Cause he’s got a good long shot over flatlands before any mountains or big lakes get in the way, okay? So, the other section of Sy’s movie is like it was shot from a satellite in geostationary orbit. In its frame the Earth is standing still, but the balloon guy’s swerving to his left which is west. Also counterclockwise.”

“Mmm, okay. So you’re saying that in our earthbound frame we see northerly winds getting twisted to their left which is west but it’s really the Earth turning under the atmosphere and that’s why hurricanes turn the way they do.”

“There are other ways to analyze it, guys.”

“Like what, Sy?”

“Let’s get back to Quito and Helsinki. In the northern hemisphere the latitude lines make shorter circles as you go north so your distance traveled per day gets smaller.”

“Makes sense, yeah.”

“Right. Your balloon guy’s at rest somewhere in the Earth’s frame before he starts his trip so the satellite sees him traveling eastward at say 1200 kilometers per hour. The atmosphere around him is doing about the same. Suppose he suddenly moves a few hundred kilometers north where the atmosphere’s moving significantly slower but he still has his original eastward momentum. What happens?”

“He gets slowed down.”

“Why?”

“Drag from the slower air. He dumps some of his momentum to the air molecules.”

“Conservation of Momentum does apply, Vinnie. That’s an explanation I see a lot in the pop‑sci press, but I’m not happy with it. An astronaut in a shuttlecraft going point‑to‑point across the airless Moon would see the same between‑frames contrast.”

“Oh! Newton’s First Law says you can’t change momentum unless an external force acts on you. So that’s the Coriolis Force, Mr Moire?”

“It’s related, Jeremy. Gravity restricts planet‑bound travelers to surface motion. Geometry and the force of gravity give that westward push in the planet’s frame to northbound objects in the northern hemisphere. The balloon guy and the astronaut don’t observe the Coriolis Effect unless they look out the window.”

~ Rich Olcott

When It’s Not The Same Frame

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, UncategorizedLeave a comment
  • Author‘s note — Please ignore everything below the separator line. It’s bogus. No excuses, it’s just wrong. I intend to embarrass Vinnie and Sy just as soon as I get my head straight. My apologies to every reader, especially teachers, that I’ve confused.

“Hey, Sy, I couldn’t help overhearing—”

<chuckle> “Of course not, Cal. Overhearing what?”

“When you said Quito goes round the world twice as fast as Helsinki. That can’t be true! Things would collide and we’d get all kinds of earthquakes and stuff.”

“Well, sure, Cal, if those two airports moved relative to each other. But they don’t, they’re stuck 10750 kilometers apart just like they’ve always been. I hated flying that route. Mountains to dodge at both ends, in between there’s bad weather a lot of the time and no place good to set down if something goes wrong. … Wait — different speeds — it’s frames again, ain’t it, Sy?”

“Exactly, Vinnie, even though it’s not black holes for a change. Relative to an inertial frame on the Earth’s surface, the Earth itself doesn’t move and neither does either city. Relative to a Sun‑centered frame, though, the Earth spins on its axis once every 24 hours. In the Sun’s frame, Quito on Earth’s 40‑thousand kilometer Equator does 1666 kilometers per hour. Helsinki’s at 60° North. Its circle around the spin axis is only 20 thousand kilometers so its linear speed is 833 kilometers per hour even though it does the same 15 degrees per hour that Quito does.”

“Hi, Mr Moire. Welcome back. I couldn’t help overhearing—”

<chuckle> “Of course not, Jeremy. Overhearing what?”

“You talking about places on Earth moving different speeds. We just studied about that in Dr O’Meara’s planet science class but it’s still loose in my head. It has to do with why storms go counterclockwise, right?”

“It has everything to do with that, except the counterclockwise storms are only in the northern hemisphere. Southern hemisphere storms rotate the other way.”

“I got this, Sy. Bring up that movie you got on Old Reliable, the one that shows the northern hemisphere. Yeah, that one. Jeremy, some guy in a balloon is the dark line on his way from Kansas to the North Pole to meet Santa. In his frame the earth is moving left‑to‑right relative to his northbound course. See how the red star’s moving?”

“Yeah, it’s moving towards sunrise so his movie’s got the rotation right. Why Kansas?”

“‘Cause he’s got a good long shot over flatlands before any mountains or big lakes get in the way, okay? So, the other section of Sy’s movie is like it was shot from a satellite in geostationary orbit. In its frame the Earth is standing still, but the balloon guy’s swerving to his left which is west. Also counterclockwise.”

“Mmm, okay. So you’re saying that in our earthbound frame we see northerly winds getting twisted to their left which is west but it’s really the Earth turning under the atmosphere and that’s why hurricanes turn the way they do.”

“There are other ways to analyze it, guys.”

“Like what, Sy?”

“Let’s get back to Quito and Helsinki. In the northern hemisphere the latitude lines make shorter circles as you go north so your distance traveled per day gets smaller.”

“Makes sense, yeah.”

“Right. Your balloon guy’s at rest somewhere in the Earth’s frame before he starts his trip so the satellite sees him traveling eastward at say 1200 kilometers per hour. The atmosphere around him is doing about the same. Suppose he suddenly moves a few hundred kilometers north where the atmosphere’s moving significantly slower but he still has his original eastward momentum. What happens?”

“He gets slowed down.”

“Why?”

“Drag from the slower air. He dumps some of his momentum to the air molecules.”

“Conservation of Momentum does apply, Vinnie. That’s an explanation I see a lot in the pop‑sci press, but I’m not happy with it. An astronaut in a shuttlecraft going point‑to‑point across the airless Moon would see the same between‑frames contrast.”

“Oh! Newton’s First Law says you can’t change momentum unless an external force acts on you. So that’s the Coriolis Force, Mr Moire?”

“It’s related, Jeremy. Gravity restricts planet‑bound travelers to surface motion. Geometry and the force of gravity give that westward push in the planet’s frame to northbound objects in the northern hemisphere. The balloon guy and the astronaut don’t observe the Coriolis Effect unless they look out the window.”

~ Rich Olcott

That Lump in The Table

On By rolcottIn Astronomy: Planetary Science, Chemistry, UncategorizedLeave a comment

The Acme Building Science and Pizza Society is back in session. It’s Cal’s turn to deal the cards and the topic. “This TV guy was talking about rare earths that China’s got a lock on and it’s gonna mess up our economy, but he didn’t say what they are or why we should care about them. What’s goin’ on?”

Vinnie passes but Susan tosses a chip into the pot. “The rare earths are oxides of the lanthanide elements—”

“Wait, they’re from the planet that the Strange New Worlds engineering prof is from?”

“Put in a chip, Vinnie, you know the rules.” <He does.> “No, they have nothing to do with Pelia or her home planet. She’s a Lanthanite, these elements are lanthanides. Although these days we’re supposed to call them lanthanoids because ‑ides are ionic compounds like oxides.”

It’s not Kareem’s turn yet but he chuckles and flips in a chip. “Funny. The geology community settled on meteoroids as rocks floating in space, meteors when they flash through the sky, and meteorites when they hit the ground. I don’t think there’s such a thing as a meteoride. Sorry, Susan, go on.”

“As a matter of fact, Kareem, I once did a high‑rated downhill mountain bike path in Arizona called the Meteoride. Once. Didn’t wipe out but I admit I used my brakes a whole lot. Where was I? Oh, yes, the lanthanides. They’re a set of fourteen near‑identical twins, chemistry so similar that it took decades of heroic effort by 19th‑century Swedish chemists in the long, cold Swedish nights to separate and identify them.”

Benfey‘s “Periodic Snail” Image by DePiep under CC BY-SA 3.0

“Similar how?”

“They all act like aluminum.” <pulls laptop from her purse, points to two stickers on its lid> “You’ve all at least heard of the Periodic Table, right? Back in the mid-1800s, the chemists had isolated dozens of chemical elements, enough that they could start classifying them. They didn’t know what atoms were yet but they had developed ways to measure average atomic weights. Some theorists played with the idea of arranging elements with similar chemistries according to their atomic weights. Mendeleev did the best job, even predicting three elements to fill empty slots in his tabulation. These guys in the lime green row and the pale pink bulge were his biggest puzzlement.”

“Why’s that? They’re all spread out nice.”

“Because like I said, Vinnie, they all have pretty much the same chemistry. Aluminum’s a soft silvery metal, oxidizes readily to a 3+ ion and stays there. Same for almost all the lanthanides. Worse yet, all their atoms are nearly the same size, less than 8% difference from the largest to the smallest.”

“Why’s that make a difference?”

“Because they can all fit into the same crystalline structure. Nineteenth‑century chemistry’s primary technique for isolating a metallic element was to dissolve a likely‑looking ore, purify the solution, add an organic acid or something to make crystalline salts, burn away the organics, add more acid to dissolve the ash, purify the solution and re‑crystallize most it. Do that again and again until you have a provably pure product. All the lanthanide ions have the same charge and nearly the same size so the wrong ions could maliciously infiltrate your crystals. It took a lot of ingenious purification steps to isolate each element. There were many false claims.”

Kareem contributes another chip. “Mm‑hm, because geology doesn’t use chemically pure materials to create its ores. Four billion years ago when our planet was coated with molten magma, the asteroids striking Earth in the Late Heavy Bombardment brought megatons of stone‑making lithophile elements. The lanthanides are lithophiles so random mixtures of them tended to concentrate within lithic silicate and phosphate blobs that later cooled to form rocky ores. Industry‑scale operations can tease lanthanides out of ores but the processes use fierce chemicals and require close control of temperature and acidity. Tricky procedures that the Chinese spent billions and decades to get right. For the Chinese, those processes are precious national security assets.”

Cal’s getting impatient. “Hey, guys, are we playing cards or what?”

~ Rich Olcott

Why Those Curtains Ripple

On By rolcottIn Astronomy: Planetary Science, Physics: Electromagnetism, UncategorizedLeave a comment

I’m in the scone line at Cal’s Coffee when suddenly there’s a too‑familiar poke at my back, a bit right of the spine and just below the shoulder blade. I don’t look around. “Morning, Cathleen.”

“Morning, Sy. Your niece Teena certainly likes auroras, doesn’t she?”

“She likes everything. She’s the embodiment of ‘unquenchable enthusiasm.’ At that age she’s allowed.”

“It’s a gift at any age. Some of the kids in my classes, they just can’t see the wonders no matter how I try. I show them aurora photos and they say, ‘Oh yes, red and green in the sky‘ and go back to their phone screens. Of course there’s no way to get them outside late at night at a location with minimal light pollution.”

“I feel your pain.”

“Thanks. By the way, your aurora write-ups have been all about Earth’s end of the magnetic show. When you you going to do the rest of the story?”

“How do you mean?”

“Magnetism on the Sun, how a CME works, that sort of thing.”

“As a physicist I know a lot about magnetism, but you’re going to have to educate me on the astronomy.”

Plane‑polarized Lorentz (electromagnetic) wave
 Electric (E) component is red
 Magnetic (B) component is blue
(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)
Licensed under CC ASA3.0 Unported

“Deal. You go first.”

<displaying an animation on Old Reliable> “We’ll have to flip between microscopic and macroscopic a couple times. Here’s the ultimate micro — a single charged particle bouncing up and down somewhere far away has generated this Lorentz‑force wave traveling all alone in the Universe. The force has two components, electric and magnetic, that travel together. Neither component does a thing until the wave encounters another charged particle.”

“An electron, right?”

“Could be but doesn’t have to be. All the electric component cares about is how much charge the particle’s carrying. The magnetic component cares about that and also about its speed and direction. Say the Lorentz wave is traveling east. The magnetic component reaches out perpendicular, to the north and south. If the particle’s headed in exactly the same direction, there’s no interaction. Any other direction, though, the particle’s forced to swerve perpendicular to both the field and the original travel. Its path twists up- or downward.”

A charged particle traversing a Lorentz wave

“But if the particle swerves, won’t it keep swerving?”

“Absolutely. The particle follows a helical path until the wave gives out or a stronger field comes along.”

“Wait. If a Lorentz wave redirects charge motion and moving charges generate Lorentz waves, then a swerved particle ought to mess up the original wave.”

“True. It’s complicated. You can simplify the problem by stepping back far enough that you don’t see individual particles any more and the whole assembly looks like a simple fluid. We’ve known for centuries how to do Physics with water and such. Newton invented hydrodynamics while battling the ghost of Descartes to prove that the Solar System’s motion was governed by gravity, not vortices in an interplanetary fluid. People had tried using Newton‑style hydrodynamics math to understand plasma phenomena but it didn’t work.”

<grinning> “I don’t imagine it would — all that twistiness would have thrown things for a loop.”

“Haha. Well, in the early 1940s Swedish physicist Hannes Alfven started developing ideas and techniques, extending hydrodynamics to cover systems containing charged particles. Their micro‑level electromagnetic interactions have macro‑level effects.”

“Like what?”

“Those aurora curtains up there. Alfven showed that in a magnetic field plasmas can self‑organize into what he called ‘double layers’, pairs of wide, thin sheets with positive particles on one side against negative particles in the other. Neither sheet is stable on its own but the paired‑up structure can persist. Better yet, plasma magnetic fields can support coherent waves like the ones making that curtain ripple.”

“Any plasma?”

“Sure.”

“Most of the astronomical objects I show my students are associated with plasmas — the stars themselves, of course, but also the planetary nebulae that survive nova explosions, the interstellar medium in galactic star‑forming regions, the Solar wind, CMEs…”

“Alfven said we can’t understand the Universe unless we understand magnetic fields and electric currents.”

~ Rich Olcott

Colors Made of Air

On By rolcottIn Astronomy: Planetary Science, Physics: Electromagnetism, UncategorizedLeave a comment

Teena’s whirling around in the night with her head thrown back. “I LUVV AURORAS!! They’re SO beautiful beautiful beautiful!”

“Yes, they are, Teena. They’re beautiful and magical, and for me it’s even better because they’re Physics at work right in front of us. Well, above us.”

“Oh, Sy, give it a rest.”

“No, really, Sis. I look at a rainbow and I’m dazzled by its glory against the rainclouds but I’m also aware that each particular glimpse of pure color comes to me by refraction through one individual droplet. Better yet, I appreciate the geometry that presents the entire spectrum in perfectly circular arcs. Marvels supported by underlying marvels. These curtains are another example of beauty emerging from hidden sources.”

“What do you mean?”

“Remember Teena’s teacher’s magnetic force lines that were organized and revealed by iron filings? Auroras are a bit like that, except one level deeper. Again we don’t see magnetic fields directly. What we do see is light coming to us from oxygen and nitrogen atoms that are bombarded by rampaging charged particles.”

“Wait, Uncle Sy, we learned that charges make magnetic fields when they move.”

“That, too. It works both ways, which is why they call it electromagnetism. A magnetic field steers protons and electrons which make their own field to push back on the first one. But my point is, the colors in each curtain and the curtains themselves tell us about the current state of the atmosphere and Earth’s magnetic field.”

“Okay, I can see how magnetic fields up there could steer charged particles to certain parts of the sky, but how does that tell us about the atmosphere? What do the colors have to do with it? Is this more rainbows and geometry?”

“Definitely not. Sis. Rainbows are sunlight refracted through water droplets. Aurora light’s emitted by atoms in our own atmosphere. Each color is like a fingerprint of a specific atom in specific circumstances. The uppermost reds, for instance come from oxygen atoms that rarely touch another atom of any kind. They’re at 150 or more kilometers altitude, way above the stratosphere. There aren’t many of them that far up which is why the curtain tops sort of fade away into infinity.”

Aurora, photo by AstroAnthony
licensed under CC BY-SA 4.0

“Oooo, now it’s going green and yellow!”

“Mm-hm, the bombardment’s reaching further now. Excited oxygen atoms emit green lower down in the atmosphere where collisions happen more often and don’t give the red‑emitters a chance to do their thing. The in‑between yellow isn’t really there — it’s what your eye tells you when it sees pure red and pure green overlapping.”

“Why do the curtains have that sharp lower edge, Sy? Surely we don’t run out of oxygen there.”

“Quite the reverse. That level’s about 100 kilometers up. It’s where the atmosphere gets so thick that collisions drain away an excited atom’s energy before it gets a chance to shine.”

“But why are there curtains at all? Why not simply fill the sky with a smooth color wash?”

IMAGE view of Aurora australis
Credit: NASA, public domain

“Mars gets auroras like that, or at least Perseverance just spotted one. We don’t, thanks to our well‑ordered magnetic field. Mars’ field is lumpy and too weak to funnel incoming charged particles to special spots like our poles. Actually, those curtains are just segments of rings that go all around Earth’s magnetic axis. The rings usually lurk about 2/3 of the way to our poles but a really strong solar event like this one can push them closer to the Equator.”

“Mars gets auroras? Uncle Sy, how about other planets?”

“Them, too, but theirs mostly don’t look like ours. You’d have to be able to see X‑rays on Mercury, for instance. Venus gets a general green glow for the same reason that Mars does. Jupiter is Texas for the Solar System — everything’s bigger there, including auroras in every color from X‑ray to infrared. Strong ordered field, so I’m sure there’s curtains up there.”

Sis yanks out her writer’s‑companion notebook and scribbles without looking down…
  ”Curtains made of colors
   Colors made of air.“

Aurora, photo by Bellezzasolo
licensed under CC BY-SA 4.0

~ Rich Olcott

Sky Lights

On By rolcottIn Astronomy: Planetary Science, Physics: Electromagnetism, UncategorizedLeave a comment

“Mom! Uncle Sy! Come outside NOW before it goes away!”

“Whah— oooh!”
 ”An aurora! Thanks for calling us.”

“Glowing curtains rippling across the sky! Spotlights shining down through them! Where do those come from?”

“From the Sun, Teena.”

“C’mon, Sy. The Sun’s 93 million miles away. Even if that bright streak up there is as much as 10 miles across, which I doubt, the beam from the Sun would be only a teeny‑tiny fraction of a degree wide. Not even magnetars send out anything that narrow.”

“Didn’t say it’s a beam, Sis. The whole display comes from the Sun as single package. Sort of. Sometimes.”

“Even for you, little brother, that’s a new level of weasel‑wording.”

“Well, it’s complicated.”

“So unravel it. Start from the beginning.”

“Okay. The Sun’s covered in plasma—”

“Eww!”

“Not that kind of plasma, Teena. This is mostly hydrogen atoms except they’re so hot that the electrons and protons break away from each other and travel separately. What have they told you in school about magnets?”

“Not much. Umm … electric currents push on magnets and that’s how motors work, and magnets push on electrons and that’s how a generator works. Oh, and Mr Cox laid a sheet of paper on top of a magnet and sprinkled iron filings on it so we could see the lines of force, but when I asked him what made the magnetism ’cause I didn’t see any wires he started talking about electrons in iron atoms and then the bell rang and I had to go to Spanish class.”

The shape of the bar magnet’s field, disclosed by iron filings chaining together.

<sigh> “The clock rules, doesn’t it? Anyway, he was on the right track, but I want to get back to those lines of force. Were they there before he sprinkled on those filings?”

“Mmm … Mom would say, ‘That’s a good question,’ but how could you know? I’m gonna say they were.”

“Your Mom would be right, but sorry, you’re wrong. With no iron filings in the picture, the magnetic field is nice and smooth, everywhere just the same or maybe only a little bit stronger or weaker than neighboring points. No lines. Conditions change when you put the first bit of iron anywhere in the field. As Mr Cox was probably saying when the bell interrupted, the electrons in the grain’s iron atoms align orbitals with the magnetic field. The alignment affects the surrounding field and that pulls in other iron bits that change the field even more.”

“But wouldn’t that make just a solid iron blob?”

“No, because a magnetic field has both strength and direction. Once the first particle points along the field, the iron bits it recruits rotate to point mostly in the same direction. You wind up with a chain of specks tracing out where they’ve acted together to alter the field. The chain’s surrounded by spaces where the field’s been stressed.”

“And then lotsa chains make lotsa lines, yeah!”

“I see where you’re headed, Sy. You’re going to claim that the vertical lines we see in the curtains trace out the Sun’s magnetic field.”

“Not quite, Sis. There’s only one magnetic field, a combination of Earth’s field, the Sun’s field, and the magnetic fields contained in whatever the Sun throws our way. Way out here Earth’s field is about ten thousand times stronger than the Sun’s is, but the fields inside a CME can range up to 10% or 20% of Earth’s. The moving curtains up there are the result of a magnetic tussle between us and a CME or maybe a flare’s outflow.”

CME blast (red‑orange) impacting Earth ‘s magnetic field (blue lines)
Credit: NASA/GSFC/SOHO/ESA

“But there aren’t any iron filings up there, Uncle Sy!”

“True, but there are free charged particles in the ionosphere thanks to UV radiation from the Sun. A free electron caught in a magnetic field whips into a tight spiral. Its field gets neighbor particles spiraling. Pretty soon you wind up with a chain of them spiraling together, lining up like the filings do.”

“The spotlights?”

“Probably ion blobs embedded in the CME, but that’s a guess.”

Aurora, photo by W.carter
licensed under CC BY-SA 4.0

~ Rich Olcott

Surf Lake Loki? No, Thanks.

On By rolcottIn Astronomy: Planetary Science, Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Vinnie’s been eavesdropping (he’s good at that). “You guys said that these researcher teams looked at how iron and sulfur play together at a bunch of different temperature, pressures and blend ratios. That’s a pretty nice chart, the one that shows mix and temperature. Got one for pressure, like the near‑vacuum over Loki’s lava lake on Io?”

“Not to my knowledge, Vinnie. Of course I’m a lab chemist, not a theoretical astrogeochemist. Kareem’s phase diagram is for normal atmospheric pressure. I’d bet virtually all related lab work extends from there to the higher pressures down toward Earth’s center. Million‑atmosphere experiments are difficult — even just trying to figure out whether a microgram sample’s phase in a diamond anvil cell is solid or liquid. Right, Kareem?”

“Mm‑hm, but the computer work’s hard, too, Susan. We’ve got several suites of software packages for modeling whatever set of pressure-temperature-composition parameters you like. The problem is that the software needs relevant thermodynamic data from the pressure and temperature extremes like from those tough‑to‑do experiments. There’s been surprises when a material exhibited new phases no‑one had ever seen or measured before. Water’s common, right, but just within the past decade we may have discovered five new high‑pressure forms of ice.”

“May have?”

Artist’s concept of Loki Patera,
a lava lake on Jupiter’s moon Io
Credit: NASA/JPL-Caltech/SwRI/MSSS

“The academics are still arguing about each of them. Setting aside that problem, modeling Io’s low‑pressure environment is a challenge because it’s not a lab situation. Consider Cal’s pretty picture there. See those glowing patches all around the lava lake’s shore? They’re real. Juno‘s JIRAM instrument detected hot rings around Loki and nearly a dozen of its cousins. Such continual heat release tells us the lakes are being stirred or pumped somehow. Whatever delivers heat to the shore also must deliver some kind of hot iron‑sulfur phase to the cooler surface. That’ll separate out like slag in a steel furnace.”

“It’s worse than that, Kareem. Sulfur’s just under oxygen in the periodic table, so like oxygen it’s willing to be gaseous S2. Churned‑up hot lava can’t help but give off sulfur vapor that the models will have to account for.”

I cut in. “It’s worse than that, Susan. I’ve written about Jupiter’s crazy magnetic field, off‑center and the strongest of any planet. Io’s the closest large moon to Jupiter, deep in that field. Sulfur molecules run away from a magnetic field; free sulfur atoms dive into one. Either way, if you’re some sulfur species floating above a lava lake when Jupiter’s field sweeps past, you won’t be hanging around that lake for long. Most likely, you’ll join the parade across the Io‑to‑Jupiter flux tube bridge.”

Susan chortles. “Obviously not an equilibrium. It’s a steady state!”

“Huh?” from everyone. Cal gives her, “Steady state?”

“Chemical equilibrium is when a reaction and its reverse go at equal rates, right, so the overall composition doesn’t change. That’s the opposite of situations where there’s a forward reaction but for some reason the products don’t get a chance to back‑react. Classic case is precipitation, say when you bubble smelly H2S gas through a solution that may contain lead ions. If there’s lead in there you get a black lead sulfide sediment that’s so insoluble there’s no re‑dissolve. Picture an industrial vat with lead‑contaminated waste water coming in one pipe and H2S gas bubbling in from another. If you adjust the flow rates right, all the lead’s stripped out, there’s no residual stink in the effluent water and the net content of the vat doesn’t change. That’s a steady state.”

“What’s that got to do with Loki’s lake?”

“Sulfur vapors come off it and those glowing rings tell us it’s giving off heat. It’s just sitting there not getting hotter and probably not changing much in composition. There’s got to be sulfur and heat inflow to make up for the outflow. The lake’s in a steady state, not an equilibrium. Thermodynamic calculations like Gibbs’ phase rule can’t tell you anything about the lake’s composition because that depends on the kinetics — how fast magma comes in, how fast heat and sulfur go out. Kareem’s phase diagram just doesn’t apply.”

~ Rich Olcott

A Lazy Summer Day at 1400°C

On By rolcottIn Astronomy: Planetary Science, Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Susan Kim and Kareem are supervising while Cal mounts a new poster in the place of honor behind his cash register. “A little higher on the left, Cal.”

“How’s this, Susan? Hey, Sy, get over here and see this. Ain’t it a beaut?”

“Nice, Cal. What’s it supposed to be? Is that Jupiter in the background?”

“Yeah, Jupiter all right. Foreground is supposed to be a particular spot on its moon Io. They think it’s a lake of molten sulfur!”

“No way, from that picture at least! I’ve seen molten sulfur. It goes from pale yellow to dark red as you heat it up, but never black like that.”

“It’s not going to be lab-pure sulfur, Susan. This is out there in the wild so it’s going to be loaded with other stuff, especially iron. But the molten sulfur I’ve seen in volcanoes is usually burning with a blue flame. I guess the artist left that out.”

“No oxygen to burn it with, Kareem. Why did you mention iron in particular?”

“Yeah, this article I took the image from says that lake’s at 1400°C. I thought blast furnaces ran hotter than that.”

I’ve been looking things up on Old Reliable. “They do, Cal, typically peaking near 2000°C.”

“So if this lake has iron in it, why isn’t the iron solid?”

“Same answer as I gave to Susan, Cal. The iron’s not pure, either. Mixtures generally melt or freeze at lower temperatures than their pure components. Sy would probably start an entropy lecture—”

“I would.”

“But I’m a geologist. Earth is about ⅓ iron. That’s mixed in with about 10% as much sulfur, mostly in the core where pressures and temperatures are immense. We want to understand conditions down there so we’ve spent tons of lab time and computer time to determine how various iron‑sulfur mixtures behave at different temperatures and pressures. It’s complicated.” <brings up an image on his phone> “Here’s what we call the system’s phase diagram.”

“You’re going to have to read that to us.”

Adapted from Walder and Pelton
Click image to expand

“I expected to. Temperature increases along the y‑axis. Loki’s temp is at the dotted red line. Left‑to‑right we’ve got increasing sulfur:iron ratios — pure iron on the left, pure sulfur on the right. The idea is, pick a temperature and a mix ratio. The phase diagram tells you what form or forms dominate. The yellow area, for instance, is liquid — molten stuff with each kind of atom moving around randomly.”

“What’s the ‘bcc’ and ‘fcc’ about?”

“I was going to get to that. They’re abbreviations for ‘body‑centered cubic’ and ‘face‑centered cubic’, two different crystalline forms of iron. The fcc form dominates below that horizontal line at about 1380°C, converts to bcc above that temperature. Pure bcc freezes at about 1540°C, but add some sulfur to the molten material and you drive that freezing temperature down along the blue‑yellow boundary.”

“And the gray area?”

“Always a fun thing to explain. It’s basically a no‑go zone. Take the point at 1400°C and 80:20 sulfur:iron, for instance. The line running through the gray zone along those red dots, we call it a tie line, skips from 60:40 to 95:5, right? That tells you the 60:40 mix doesn’t accept additional sulfur. The extra part of the 80:20 total squeezes out as a separate 95:5 phase. Sulfur’s less dense than iron so the molten 95:5 will be floating on top of the 60:40. Two liquids but they’re like oil and water. If you want a uniform 80:20 liquid you have to shorten the tie line by raising the temp above 2000°C.”

“All that’s theory. Is there evidence to back it up?”

“Indeed, Sy, now that Juno‘s up there taking pictures. When the spacecraft rounded Io last February JunoCam caught several specular reflections of sunlight just like it had bounced off mirrors. At first the researchers suspected volcanic glass but the locations matched Loki and other hot volcanic calderas. The popular science press can say ‘sulfur lakes’ but NASA’s being cagey, saying ‘lava‘ — composition’s probably somewhere between 10:90 and 60:40 but we don’t know.”

Artist’s concept of Loki Patera,
a lava lake on Jupiter’s moon Io
Credit: NASA/JPL-Caltech/SwRI/MSSS

~ Rich Olcott

The Trough And The Plateau

On By rolcottIn Astronomy: Planetary Science, Mathematics, UncategorizedLeave a comment

Particularly potent pepperoni on Pizza Eddie’s special tonight so I dash to the gelato stand. “Two dips of pistachio in a cup, please, Jeremy, and hurry. Hey, why the glum look?”

“The season’s moving so slowly, Mr Moire. I’m a desert kid, used to bright skies. I need sunlight! We’re getting just a few hours of cloudy daylight each day. It seems like we’re never gonna leave this pattern. Here’s your gelato.”

“Thanks. Sorry about the cloudiness, it’s the wintertime usual around here. But you’re right, we’re on a plateau.”

“Nosir, the Plateau’s the Four Corners area, on the other side of the Rockies, miles and miles away from here.”

<chuckle> “Not the Colorado Plateau, the darkness plateau. Or the daylight trough, if you prefer. Buck up, we’ll get a daylight plateau starting in a few months.” <unholstering Old Reliable> “Here’s a plot of daylight hours through the year at various northern latitudes. We’re in between the red and green curves. For folks south of the Equator that’d just turn upside‑down, of course. I added a star at today’s date in mid‑December, see. We’re just shy of the winter solstice; the daylight hours are approaching the minimum. You’re feeling stressed because these curves don’t change much day-to-day near minimum or maximum. In a couple of weeks the curve will bend upwards again. Come the Spring equinox, you’ll be shocked at how rapidly the days lengthen.”

“Yeah, my Mom says I’m too impatient. She says that a lot. Okay, above the Arctic Circle they’ve got months‑long night and then months‑long day, I’ve read about that. I hadn’t realized it was a one‑day thing at the Circle. Hey, look at the straight lines leading up to and away from there. Is that the Summer solstice? Those low‑latitude curves look like sine waves. Are they?”

“Summer solstice in the northern hemisphere, Winter solstice for the southerners. The curves are distorted sines. Ready for a surprise?”

<Looks around the nearly empty eatery.> “With business this slow I’m just sitting here so I’m bored. Surprise me, please.”

“Sure. One of the remarkable things about a sine wave is, when you graph its slopes you get another sine wave shifted back a quarter. Here, check it out.”

“Huh! When the sine wave’s mid-climb, the slope’s at its peak. When the sine wave’s peaking, the slope’s going through zero on the way down. And they do have exactly the same shape. I see where you’re going, Mr Miore. You’re gonna show me the slopes of the daylight graphs to see if they’re really sine waves.”

“You’re way ahead of me and Old Reliable, Jeremy.” <frantic tapping on OR’s screen> “There, point‑by‑point slopes for each of the graphs. Sorta sine‑ish near the Equator but look poleward.”

“The slopes get higher and flatter until the the Arctic Circle line suddenly drops down to flip its sign. Those verticals are the solstices, right?”

“Right. Notice that even at the Circle the between‑solstice slopes aren’t quite constant so the straight lines you eye‑balled aren’t quite that. North of the Circle the slopes go nuts because of the abrupt shifts between varying and constant sun.”

Link to larger image

“How do you get these curves, Mr Moire?”

“It’s a series of formulas. Dust off your high school trig. The Solar Declination Angle equation is about the Sun’s height above or below the horizon. It depends on Earth’s year length, its axial tilt and the relative date, t=T‑T0. For these charts I set T0 to the Spring equinox. If the height’s negative the Sun’s below the horizon, okay?”

“Sine function is opposite‑over‑hypotenuse and the height’s opposite alright or we’d burn up, yup.”

“The second formula gives the the Hour Angle between your longitude and whichever longitude has the Sun at its zenith.”

“Why would you want that?”

“Because it’s the heart of the duration formula. When you roll all three formulas together you get one big expression that gives daylight duration in terms of Earth’s constants, time of year and your location. That’s what I plotted.”

“How about the slope curves?”

“Calculus, Jeremy, d/dt of that combined duration function. It’s beyond my capabilities but Old Reliable’s up to it.”

~ Rich Olcott