Category: Astronomy: Planetary Science

The Coriolis Mandala

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, UncategorizedLeave a comment

“Cathleen, this Coriolis Effect‘s rule is so easy. The force always twists you to the right no matter which way you travel. Going north, you swerve eastward; going south you swerve westward, always to the right. But what about the in‑betweens? What if I’m going east or west? Does the force just go away?”

“Of course not, Cal, but it mutates. Mind you, the rules you quoted only apply in Earth’s northern hemisphere. If you’re south of the Equator they go the other direction. Anyway, the northbound and southbound cases everybody writes about are the simplest to describe. You might be surprised how it varies across all the compass points separating them.” <pulling another image up on her tablet> “Here’s a chart I did for my class.”

“Whoa, that’s complicated.”

“Let me break it down for you. The circles around the outside represent different travel orientations — north’s at the top, then northeast to its left, directly east at the three-o’clock position, and so on. The brown arrows point to the corresponding direction. They’re all the same length to imply equal travel speed because why not.”

“Southbound’s at the bottom, just like on a map, right?”

“Right. Now, the blue arrow in a circle shows the relative Coriolis force experienced by an object traveling in that circle’s direction. See how the leftward force falls off from full‑strength if you’re northbound, to 70% if you’re going northeast, so zero for eastbound motion.”

“I’ll take your word for the 70%, but yeah, that’s what the picture shows. Wait, right after you turn the corner from east to south that blue arrow flips like the rule says.”

“It’s not like there’s a big toggle switch somewhere. If you’re going a little bit north of due east, there’s just a little bit of east‑pushing Coriolis; drive just a little bit south of due east there’s just a little bit of west‑pushing Coriolis. Build a Coriolis swerve‑meter. Swivel it all around the compass. It’ll show peak force when pointed north or south. The force smoothly fades away through zero, grows to a peak in the other direction, fades away, then re‑grows as you come back full circle.”

“So that’s what the pink and green disks are about, huh? Strong to fade‑away east both sides in the top half, strong to fade‑away west in the south?”

“You’ve got it.”

“What’s the red and blue stuff about then?”

“Re‑think the picture to 3‑D. Visualize each of those circles as a sphere. The thin black arrows are x‑y‑z pointers coming out from the sphere’s center. Can you see that?”

“The arrows coming out an angle, that’s like coming out of the screen?”

“Mm‑hm. Suppose you’re driving straight east in a vehicle that doesn’t care about gravity. What would happen?”

“Heh‑heh‑heh, lift‑off!”

“Exactly. It’s not centrifugal force, technically, but the Coriolis Effect’s equation establishes a trade‑off between Coriolis acting horizontally and a centrifuge‑like sibling acting vertically. Both sibs act to increase or decrease an object’s effective inertia depending on the object’s direction of motion relative to Earth’s rotation. The vertical component strengthens as the horizontal component weakens and vice‑versa.”

“The vertical one is the tubes coming out?”

“Yes, that’s what those are about. Long tubes in the diagram indicate high relative strength, short tubes signify weaker intensity, which is why the northbound and southbound spheres don’t have any tubes at all.” <grins> “Sy would appreciate my color choices.”

“I don’t get the joke.”

“Over there on the left side, the vertical component is upward, towards us. If a star’s coming towards its spectrum is shifted to shorter wavelengths, bluer than it it were standing still. No surprise, we call that a blue shift. Being an astronomer, I made those tubes blue‑ish.”

“I suppose the right side has red tubes because the vertical component pushes down when you’re westbound?”

“You broke the code, Cal. Red‑shifted stars are flying away from us. I’m being careful here — the red tubes don’t represent a true centripetal force. There’s no pushing and the effect doesn’t depend on distance from the rotation axis. But it makes a westbound truck act a bit like the road’s coming up to meet it.”

~ Rich Olcott

The Winds of Change

On By rolcottIn Astronomy: Planetary Science, Physics: Waves, Uncategorized1 Comment

“You said that so careful, Cathleen.”

“What that was that, Cal?”

“When you said those blue donuts in your diagram could be Earth’s equivalent to Jupiter’s brown bands. Why not the white zones, too?”

“Because Earth has a much better analog for the white zones. Juno‘s observations showed us Jupiter’s white zones floating a hundred or more kilometers above the brown stuff.”

“We don’t have that much room, do we?”

“Nowhere near. Our clouds and weather stay inside the troposphere, mostly less than a dozen kilometers up. Inside that shell, though, similar dynamics may apply.” <scribbling on her tablet> “Here’s a grossly oversimplified sketch.”

After an image by Kaidor, lic. under CC A-SA 3.0

“White frosting on the donuts?”

“Winds, Cal, not frosting, though they are cold. Think of each blue donut as a conveyor belt transporting air between warm and cold regions. The arrows reflect separate lower‑level and upper‑level wind regimes. What happens up at 60°N?”

“That’s actually a ring, right, goes all around the planet up there? I see two lower‑level conveyor belt donuts dumping at the same meridian — stuff’s gonna pile up over the ring unless the upper‑level parts move it out fast enough.”

“They do, mostly, during each hemisphere’s Summer. Winter’s another matter. The lower‑level conveyors are more sensitive to surface conditions than their upper‑level partners; seasonal surface condition changes affect the dump/clear balance. Wind speed’s driven by density difference; cold winter air is denser than summer air, even in the Arctic. Typical wintertime lower‑level polar cell transport dumps more air into that convergence than the upper‑level mechanism can sweep away.”

“So it piles up, like I said. Just sits there, I bet.”

“It might if the Earth weren’t rotating. That dense air acts to lift lighter air coming in from the South—”

“I know! Coriolis in action! The lighter southern air gets into the upper level first and it’s already turning to the east so it kicks that white cylinder into going east, too. Except it’s a ring.”

“It’s a continuous process so getting there first doesn’t count. But yes, eastward momentum from lighter southern air is the dominant influence that speeds the polar jet stream’s winds on their way, 200 kilometers/hour or more.”

“Whoa, that ‘polar jet stream’ phrase just sunk in. I keep hearing the weather guy talking about how the polar jet stream brings down the cold.”

“That’s like saying robins bring the springtime. The warm/cold front’s established by the balance between cold’s centrifugal force, heat’s poleward momentum and Coriolis twisting everything to the right. The jet stream just rides the back of the front. To my mind, it’s more accurate to say that the cold brings down the polar jet.”

“Cart before the horse.”

“Mm-hm. Remember I said that diagram is a gross simplification. One of the simplifications was to localize the stream at 60°N. Here’s a slightly less gross simplification. That ‘ring’ isn’t circular, it ranges more-or-less regularly between 60° and 45° in a nice pattern.”

“The crinkly circle looks like a coffee grinder part. So the cold just slides down that jet from Greenland to Europe.”

“Um, no. Weather doesn’t travel along the streams and the waves aren’t locked in place. The whole structure rotates eastward. Carl‑Gustaf Rossby discovered that, which is why it’s called a Rossby wave. Rossby was an early pioneer in atmospheric physics; his group’s weather predictions help decide World War II. Anyway, even Rossby waves are simplifications.”

“How much more unsimple can it be?”

“Much more. This idealized sketch shows how things might settle down under stable conditions. Conditions are rarely stable, especially now that global warming is upsetting the apple cart. The polar land areas are warming up the most, which means the polar cell’s outbound air currents are weaker and patchier than they used to be.”

“So the warm air masses can punch up closer to the poles like Summertime. Big deal.”

“Very big. Amplify the Rossby wave beyond a certain point, distortions create vortex cascades inside the peaks — the structure goes chaotic. Cold air leaks out past the warm air, like for this horrible early May snowstorm we’re getting.”

“Global warming causes cold air leaks. How about that?”

~ Rich Olcott

Belts And Zones

On By rolcottIn Astronomy: Planetary Science, Chemistry, Physics: Newton and Gravity, UncategorizedLeave a comment

“This cold-brew latte concoction — good choice, Cal. Thanks.”

“You’re welcome, Cathleen. Sounded like it’d fit your mood. Hey, Sy’s latitude racetracks got me wondering. Do Jupiter’s stripes follow the same pattern?”

“The ‘racetracks’ exist, sort of, but they’re a very small part of a very complicated picture. Jupiter’s belts and zones are each wider than Earth. Maybe half an Earth‑width deep, too. That’s just a small fraction of Jupiter’s fluid interior. A grand arena for a host of dueling pseudo‑forces.”

“Lotsa ways for winds to work, then.”

“Indeed. Ferocious drafts everywhere, up, down and sideways. Water in all its forms is a major weather driver here on Earth. Jupiter has water, too, in multiple forms acting at multiple atmospheric levels. It also has ammonia, sulfides, phosphines, tholins, hydrocarbons, a potpourri of chemicals flavoring its hydrogen and helium. Ammonia has gas/liquid and liquid/solid transitions like water does but they happen at their own temperatures and pressures. Jupiter’s white zones are mostly ammonia ice floating a couple hundred kilometers above its brown belts of ammonium sulfides and tholins. We’re still learning about how the planet’s complicated ammonia‑sulfides system works. Compared to Jupiter, Earth’s atmosphere is a kid’s toy.”

Earth’s landmasses in natural colors.
Image by Daniel R Strebe, licensed under CC A-SA 3.0

“Earth’s a lot smaller, for sure. Do we have belts and zones?”

“Oh, yes. You’ve seen evidence for them on a world map, but maybe you haven’t noticed it.” <pulls up an image on her tablet> “All those deserts stretching across low latitudes north and south of the forested Equator and below the boreal forests. Pretty distinctive pattern, right?”

“How about that? My astronomy magazines carry photos from Chile’s waterless Atacama observatories all the time. I’ve never connected those with the Australian outback or Namibia’s desert. All at the same level, aren’t they? And the Sahara’s tan blotch goes all the way east to the Gobi and matches northern Mexico and USA’s high plains on the other side. The green areas must get all the water that the deserts don’t. How does that square with your vapor‑ice water pump theory?”

“Sideways, actually. I don’t claim that molecules evaporating near the Equator make it all the way to an ice sheet in a single pass. The heat energy does, eventually, but the molecules get waylaid by the Coriolis force. That’s where the racetracks come in. I can’t do better than this graphic. Each of those flattened blue ovals is a slice through an air‑mass donut that dominates its latitude range.”

Earth’s atmospheric circulation patterns
After an image by Kaidor, lic. under CC A-SA 3.0

“That third‑down donut pretty much covers the Sahara. Is that why it’s dry?”

“It’s a big part of the reason, but you’re way ahead of me. Look at the colored arrows inside that donut’s slice on the right. Why do they point where they do?”

“Well, we’re hottest at the Equator. Hot air rises which is why the red arrow goes up. We said rising air over the ocean carries evaporated water with it, right, which the grey arrow will drop close by as the Earth spins eastward. That’s why the Equator’s got the forest. How’m I doin’?”

“Just fine. How about the yellow and orange arrows?”

“Um, the yellow’s colliding with the next donut north so it’s gotta go down?”

“There’s more to it than that. The air up high gets chilled which makes it more dense. That’s the major reason it descends. When it gets down to ground level, though, how much water does it hold?”

“Not much, ’cause it rained out over the Equator’s forests. The orange arrow’s gonna be thirsty so it’ll pick up more water sweeping over the ocean.”

“But what if it sweeps over land?”

“Ah‑hah. It’ll suck the land dry and THAT’s why the Sahara is where it is.”

“Right. Now, those black arrows over the same cell…?”

“Northbound twisting to the right — that’s Coriolis in action. The gray arrow up top must skew eastward. By the rules, the southbound orange arrow at sea level skews west. Hey, that’s those white‑arrow trade winds. Cool.”

“Those blue donuts could be Earth’s version of Jupiter’s brown belts.”

~ Rich Olcott

Tropical beach with palm trees next to icy polar region with glaciers.

The Big Water Pump

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, UncategorizedLeave a comment

“Springtime! Could you make me a lilac latte, Cal?”

“Maybe if I left out the coffee, Cathleen. Lilac’s too delicate to stand up to coffee’s punch. How about a cold brew of light roast? I just made a batch. Plenty of caffeine in there, not too much intensity and you can imagine the flowery part.”

“I’ll have that, and a lemon scone, please.”

“Here you go, fresh from the filter. Hey, you sure lit a fire under Sy. He’s done a whole string of posts about Coriolois Effects.”

“Tsk, Cal, the scientist’s name was Coriolis. I’m not surprised there’s been multiple posts — the same pseudo‑force shows up in many ways.”

“Pseudo‑force?”

<looks around> “Good, Sy’s not here. He’d talk our ears off about inertial frames. My quick answer from a planet scientist perspective is that real forces are the ones that make things happen in systems where everything’s moving in straight lines at a steady pace.”

“Like on a pool table?”

“Mm-hm. You can generally make good predictions on systems like that, which is how pool sharks make their money. But if part of the system is accelerating in some way, maybe it’s rotating, you’ve got two choices for predicting how the system will behave. The hard way is to calculate each individual component’s motion in a single coordinate system using just the real forces. The easier way is to group components that have a common acceleration. Pick a convenient group to serve as your base subsystem. Define another subsystem for the components that all have the same acceleration relative to the first subsystem and so on. Then you pretend a pseudo‑force drives the interactions between your subsystems.”

“Like Earth and our Moon make a subsystem ’cause they orbit the Sun together and you said rotation’s a kind of acceleration. The pseudo‑force is centrifugal, fighting against the Sun’s gravity to keep Earth’s subsystem in orbit!”

“I love it when that kind of connection‑making happens in my classroom. Thank you, Cal.”

“You’re welcome. So your subsystems are what Sy calls frames?”

“Pretty much. Skipping some technical caveats, that’s the idea. When I think about atmosphere dynamics, I could try to calculate the planet’s whole atmosphere as an incredibly messy collection of atoms. I prefer to think of the Earth as a subsystem hosting some number of air mass subsystems, all embedded in the Universe system. The Universe enforces straight‑line inertia and the Earth adds rotational acceleration but the air masses are constrained to the planet’s spherical geometry. The Coriolis pseudo‑force summarizes all three effects. The calculation’s still messy, but it’s a lot more manageable. And then there’s water.”

“Water?”

“The piston that drives the climate. Water molecules are small so they move easily through the atmosphere. The important thing is, they’re good at transporting heat energy.”

“How’s that? They’d be the same temperature as everything else.”

“Temperature doesn’t always measure energy. Water molecules like to hold onto other water molecules. It takes energy to get them apart. When they get back together, the energy’s released so it’s like the freed‑up molecules store heat energy. In solid water, every molecule is locked into position. Melting a given mass of water amounts to breaking those locks. The liquid mass at freezing temperature contains more energy than the ice did. When liquid water evaporates, the gas contains even more energy, because the molecules can roam even more freely. Visualize a bucket of water someplace warm.”

“A Hawai’ian beach.”

“That bucketful absorbs heat energy as it evaporates, cooling the Pacific Ocean. Winds sweep up the gas and carry it north to the Arctic where it freezes. In the process it warms the ice cap by giving up its liquid‑to‑gas heat and also its solid‑to‑liquid heat. Water’s two active phase transitions make it a far more efficient heat transporter than dry air alone.”

“One bucket’s teeny in the ocean, though.”

“Multiply that by gazillions. We have gigatons of surface water. The evaporate/freeze/melt process cycles as the icecaps degrade, continuously acting to moderate Earth’s temperature differences. If Earth were dry, the gradient would be far steeper. Thermal gradients drive air movement. A dry Earth’s extreme temperature discrepancies would generate permanent gale‑force winds towards the poles.”

~ Rich Olcott

Atmospheric Jiu-jitsu

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, UncategorizedLeave a comment

A gorgeous early Spring day for a walk by the lake — blue sky, air just the right side of crisp, trees showing their young green leaves, geese goosily paddling around. As I pass the park bench I hear a familiar voice. “Hello, Mr Moire.”

“Morning, Walt. It’s been a while. What do your people want to know about now?”

“We’ve been reading your series of posts about the Coriolis Effect. You have masses of air pushing each other around, you have pendulums twisting about, and you have objects flying weird orbits around latitudes instead of the planet’s center. Which is the real Effect?”

“All three.”

“They’re so different. How can all three be right?”

“Knowing something of your interests, I can think of another Coriolis application will help clarify the connection. How do you steer an old‑fashioned artillery shell?”

“You don’t, you aim it.” <His eyes are looking inward.> “Those old howitzers, you traverse to the target’s coordinates, set the elevation for the distance and your munitions and whatever your barrel’s still good for, load ‘er up, let ‘er rip and wait for the forward observer to tell you how to adjust.”

“No correction for the Earth turning west‑to‑east beneath the shell’s trajectory?”

“No need. Inside a max 10‑mile range, the artillery, target and shell all share the same initial eastward vector. Windage and temperature inversions are more of a problem than Coriolis forces. That’s where judgement, feedback and reload speed come in.”

“Now stand that up against a cruise missile.”

“Very different situation. With cannons, all the propulsion happens at the start. That’s why they call it ballistic. Cruise missiles have an extended boost phase, maybe more than one, so they can do in‑flight steering. On the other hand, range is hundreds of miles or more so you do need to figure in relative easting.”

“And the easting correction takes power, right?”

“Of course.”

“From the missile’s point of view, that power goes to counteract the Coriolis force pushing it off‑course. You don’t see it from the ground but the missile does. Clearer now?”

“Give me a minute.” <sketches on his notepad> “Okay, counteracting attempt to deflect course — got it. Hmm, a pendulum’s even simpler, because it’s not trying to keep in sync with the Earth’s rotation. No forces in play crosswise to the swing plane so it can maintain orientation relative to the Universe. To museum visitors it looks like something’s twisting, but it’s us doing the moving. The air masses, though … forces are in play with that one.”

“It’s always important to keep track of who’s doing what to whom. That system has four distinct frames of reference: the Earth, a moving air mass, the air mass it collides with, and the Universe.”

“The Universe?”

“Sets the stage for Newton’s First Law, about conservation of linear momentum. Say there’s an air mass hovering over Dallas, latitude 30° north. Relative to the Earth it’s stationary, but relative to the Sun and the rest of the Universe it has an eastward vector clocking 1450 km/hour. Now suppose that mass moves north relative to the Earth.”

“But there’s already an airmass taking up space there, say in Manitoba. There’ll be a collision, northbound momentum against Manitoban inertia.”

“Here’s where Coriolis gets into the game. Manitoba may have zero motion relative to Earth, but Manitoba and its air mass are also moving eastward relative to the Universe. Manitoba’s speed is slower than Dallas’ but it’s not zero. Manitoba’s momentum deflects the Dallas mass into an even more easterly vector.”

“You’re saying that Coriolis plays jiu‑jitsu with the atmosphere.”

“I wouldn’t have come up with that interpretation, but it’s reasonable.”

“What about the weird orbits?”

“Not really orbits, more like equilibrium bands. The concept comes from the theoretical notion that every latitude along a meridian has a natural equilibrium speed where air pressure balances other forces. The bands would be parallel circles around the globe except for geography and transient disturbances. Dallas’ 1450‑km/h number was an example. If you exceed your local natural speed, centrifugal force moves you towards the Equator; if you’re a slowpoke, you’re shoved towards the nearest pole. Real weather’s more complicated.”

“Everything’s always more complicated.”

~ Rich Olcott

The Polar Expression

On By rolcottIn Astronomy: Planetary Science, Physics: Newton and Gravity, Uncategorized2 Comments

“Good afternoon, Mr … Moire, yes?”

“The same. Can I help you?”

“Yes. I am Tomas Frashko. I am new to this University. I could not help overhearing—”

“The whole neighborhood couldn’t help overhearing.”

“Mmm, yes. My sympathy. But I have some questions, if you have a moment.”

“My coffee mug’s not empty yet. Please sit down. I’ll help if I can.”

“Thank you. I have often seen the Coriolis Effect explained as an atmospheric effect — northbound air with high‑speed low‑latitude momentum deflected eastward by slower‑moving air already at higher latitudes. The last part of your recent post goes to some trouble to avoid that explanation. Why is that?”

“Because the Effect doesn’t only play with the atmosphere. It drives gyre currents in the oceans and probably the magma flows deep inside Earth’s mantle.”

“So fluids, not just air. But it is still a matter of fluid with a velocity in one direction being diverted by fluid with a different velocity. Also, these cases are planet‑scale effects operating over large distances. Surely systems at small scale do not experience a measurable amount of Coriolis force.”

“But they do. Museum Foucault pendulums swing on a scale measured in meters. There’s dozens of them on display all over the world, they act just as Coriolis’ ideas predicted, and the host institutions go to a great deal of trouble to ensure the steady swinging isn’t disturbed by rushing air.”

“Ah, yes. I have seen the pendulum exhibit in our museum in the city where I grew up. A hypnotic thing, swinging back and forth on its wire, each swing a little closer to knocking down a pin … finally! Then slowly turning direction to knock down another one. The museum docent said the plane of the pendulum’s swing pivots to demonstrate Earth’s rotation, but then she mentioned that the full circle takes more than a day to complete. She couldn’t explain why.”

“If it were swinging from a point above the North or South Pole it would be a one-day completion, 15 arcseconds per second.. Scientists tried mounting one at the South Pole and that’s exactly what they determined. The poles are the only points on Earth’s surface where the the pendulum’s inertial frame matches Earth’s so it looks like the Earth is simply turning beneath the pendulum. On the other hand, along the Equator the Coriolis force doesn’t affect a pendulum’s motion at all.”

“Not at all?”

“Nope. Centrifugal force, a little bit, but not Coriolis force.”

“Does the one become the other?”

“Oh no, they’re quite different. Centrifugal force represents competition between dissimilarly rotating frames; Coriolis force represents their coupling. If you’re riding on a merry‑go‑round—”

“A what?”

“Mm, you’d probably call it a carousel.”

“Ah. Yes, go on.”

“If you’re riding on a carousel, your straight‑line inertia in the fairgrounds frame tries to drive you forward. To stay in position on the rotating carousel, you fight that outward inertial impetus by holding onto something. In the ride’s rotating frame, that looks like you’re exerting centripetal force to counterbalance a centrifugal force that the fairgrounds frame doesn’t see.”

“Yes, yes, but how does that differ from Coriolis force?”

Cycle time = 24 hours / Sin(latitude)

“Centrifugal force depends on an object’s distance from the center of rotation. Coriolis force doesn’t care about that. It rises with the sine of the angle between the object’s vector and the axis of rotation. On a sphere the relevant angle is the latitude. A northbound object, could be a pendulum bob, arrives at the North Pole traveling perpendicular to the Earth’s axis. Perpendicular angles have the maximum sine, 1.0. The Coriolis coupling is strongest there and that’s why a pendulum’s reference frame is locked to the Earth’s 24‑hour period. At the equator a northbound object moves parallel to the polar axis. Parallel lines have zero angle with zero sine so the Coriolis coupling’s zero. A pendulum’s plane of motion at the equator stays where it started, infinite precession completion time.”

“And in‑between?”

“In between. A pendulum’s cycle would run 27.7 hours in Helsinki, more than 60 hours at the Tropic of Cancer.”

“Small coupling, not much swerving.”

~ Rich Olcott

  • Thanks to Ric Werme for his thoughtful comments and suggestions.

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