Rotation, Revolution and The Answer

“Sy, I’m startin’ to think you got nothin’. Al and me, we ask what’s pushing the Moon away from us and you give us angular momentum and energy transfers. C’mon, stop dancin’ around and tell us the answer.”

“Yeah, Sy, gravity pulls things together, right, so how come the Moon doesn’t fall right onto us?”

“Not dancing, Vinnie, just laying some groundwork for you. Newton answered Al’s question — the Moon is falling towards us, but it’s going so fast it overshoots. That’s where momentum comes in, Vinnie. Newton showed that a ball shot from a cannon files further depending on how much momentum it gets from the initial kick. If you give it enough momentum, and set your cannon high enough that the ball doesn’t hit trees or mountains, the ball falls beyond the planet and keeps on falling forever in an elliptical orbit.”

“Forever until it hits the cannon.”

“hahaha, Al. Anyway, the ball achieves orbit by converting its linear momentum to angular momentum with the help of gravity. The angular momentum pretty much defines the orbit. In Newton’s gravity‑determined universe, momentum and position together let you predict everything.”

“Linear and angular momentum work the same way?”

“Mostly. There’s only one kind of linear momentum — straight ahead — but there are two kinds of angular momentum — rotation and revolution.”

“Aw geez, there’s another pair of words I can never keep straight.”

“You and lots of people, Vinnie. They’re synonyms unless you’re talking technicalese. In Physics and Astronomy, rotation with the O gyrates around an object’s own center, like a top or a planet rotating on its axis. Revolution with the E gyrates around some external location, like the planet revolving around its sun. Does that help?”

“Cool, that may come in handy. So Newton’s cannon ball got its umm, revolution angular momentum from linear momentum so where does rotation angular momentum come from?”

“Subtle question, Vinnie, but they’re actually all just momentum. Fair warning, I’m going to avoid a few issues that’d get us too far into the relativity weeds. Let’s just say that momentum is one of those conserved quantities. You can transfer momentum from one object to another and convert between forms of momentum, but you can’t create momentum in an isolated system.”

“That sounds a lot like energy, Sy.”

“You’re right, Al, the two are closely related. Newton thought that momentum was THE conserved quantity and all motion depended on it. His arch‑enemy Leibniz said THE conserved quantity was kinetic energy, which he called vis viva. That disagreement was just one battle in the Newton‑Leibniz war. It took science 200 years to understand the momentum/kinetic energy/potential energy triad.”

“Wait, Sy, I’ve seen NASA steer a rocketship and give it a whole different momentum. I don’t see no conservation.”

“You missed an important word, Vinnie — isolated. Momentum calculations apply to mechanical systems — no inputs of mass or non‑mechanical energy. Chemical or nuclear fuels break that rule and get you into a different game.”

“Ah-hahh, so if the Earth and Moon are isolated…”

“Exactly, and you’re way ahead of me. Like we said, no significant net forces coming from the Sun or Jupiter, so no change to our angular momentum.”

“Hey, wait, guys. Solar power. I know we’ve got a ton of sunlight coming in every day.”

“Not relevant, Al. Even though sunlight heats the Earth, mass and momentum aren’t affected by temperature. Anyhow, we’re finally at the point where I can answer your question.”

“About time.”

“Hush. OK, here’s the chain. Earth rotates beneath the Moon and gets its insides stirred up by the Moon’s gravity. The stirring is kinetic energy extracted from the energy of the Earth‑Moon system. The Moon’s revolution or the Earth’s rotation or both must slow down. Remember the M=m·r·c/t equation for angular momentum? The Earth‑Moon system is isolated so the angular momentum M can’t change but the angular velocity c/t goes down. Something’s got to compensate. The system’s mass m doesn’t change. The only thing that can increase is distance r. There’s your answer, guys — conservation of angular momentum forces the Moon to drift outward.”

“Long way to the answer.”

“To the Moon and back.”

~~ Rich Olcott

Here’s a Different Angle

“OK, Sy, so there’s a bulge on the Moon’s side of the Earth and the Earth rotates but the bulge doesn’t and that makes the Moon’s orbit just a little bigger and you’ve figured out that the energy it took to lift the Moon raised Earth’s temperature by a gazillionth of a degree, I got all that, but you still haven’t told Al and me how the lifting works.”

“You wouldn’t accept it if I just said, ‘The Moon lifts itself by its bootstraps,’ would you?”

“Not for a minute.”

“And you don’t like equations. <sigh> OK, Al, pass over some of those paper napkins.”

“Aw geez, Sy.”

“You guys asked the question and this’ll take diagrams, Al. Ante up. … Thanks. OK, remember the time Cathleen and I caught Vinnie here at Al’s shop playing with a top?”

“Yeah, and he was spraying paper wads all over the place.”

“I wasn’t either, Al, it was the top sending them out with centri–…, some force I can never remember whether it’s centrifugal or centripetal.”

“Centrifugal, Vinnie, –fugal– like fugitive, outward‑escaping force. It’s one of those ‘depends on how you look at itfictitious forces. From where you were sitting, the wads looked like they were flying outward perpendicular to the top’s circle. From a wad’s point of view, it flew in a straight line tangent to the circle. It’s like we have two languages, Room and Rotor. They describe the same phenomena but from different perspectives.”

“Hey, it’s frames again, ain’t it?”

“Newton’s inertial frames? Sort‑of but not quite. Newton’s First Law only holds in the Room frame — no acceleration, motion is measured by distance, objects at rest stay put. Any other object moves in a straight line unless its momentum is changed by a force. You can tackle a problem by considering momentum and force components along separate X and Y axes. Both X and Y components work the same way — push twice as hard in either direction, get twice the acceleration in that direction. Nice rules that the Rotor frame doesn’t play by.”

“I guess not. The middle’s the only place an object can stay put, right?”

“Exactly, Al. Everything else looks like it’s affected by weird, constantly‑varying forces that’re hard to describe in X‑Y terms.”

“So that breaks Newton’s physics?”

“Of course not. We just have to adapt his F=m·a equation (sorry, Vinnie!) to Rotor conditions. For small movements we wind up with two equations. In the strict radial direction it’s still F=m·a where m is mass like we know it, a is acceleration outward or inward, and F is centrifugal or centripetal, depending. Easy. Perpendicular to ‘radial‘ we’ve got ‘angular.’ Things look different there because in that direction motion’s measured by angle but Newton’s Laws are all about distances — speed is distance per time, acceleration is speed change per time and so forth.”

“So what do you do?”

“Use arc length. Distance along an arc is proportional to the angle, and it’s also proportional to the radius of the arc, so just multiply them together.”

“What, like a 45° bend around a 2-foot radius takes 90 feet? That’s just wrong!”

“No question, Al. You have to measure the angle in the right units. Remember the formula for a circle’s circumference?”

“Sure, it’s 2πr.”

“Which tells you that a full turn’s length is times the radius. We can bridge from angle to arc length using rotational units so that a full turn, 360°, is units. We’ll call that unit a radian. Half a circle is π radians. Your 45° angle in radians is π/4 or about ¾ of a radian. You’d need about (¾)×(2) or 1½ feet of whatever to get 45° along that 2-foot arc. Make sense?”

“Gimme a sec … OK, I’m with you.”

“Great. So if angular distance is radius times angle, then angular momentum which is mass times distance per time becomes mass times radius times angle per time.”

“”Hold on, Sy … so if I double the mass I double the momentum just like always, but if something’s spinning I could also double the angular momentum by doubling the radius or spinning it twice as fast?”

“Couldn’t have put it better myself, Vinnie.”

~~ Rich Olcott

Two Against One, And It’s Not Even Close


On a brisk walk across campus when I hear Vinnie yell from Al’s coffee shop. “Hey! Sy! Me and Al got this argument going you gotta settle.”

“Happy to be a peacemaker, but it’ll cost you a mug of Al’s coffee and a strawberry scone.”

“Coffee’s no charge, Sy, but the scone goes on Vinnie’s tab. What’s your pleasure?”

“It’s morning, Al, time for black mud. What’s the argument, Vinnie?”

“Al read in one of his astronomy magazines that the Moon’s drifting away from us. Is that true, and if it is, how’s it happen? Al thinks Jupiter’s gravity’s lifting it but I think it’s because of Solar winds pushing it. So which is it?”

“Here you go, Sy, straight from the bottom of the pot.”

“Perfect, Al, thanks. Yes, it’s true. The drift rate is about 1¼ nanometers per second, 1½ inches per year. As to your argument, you’re both wrong.”

“Huh?”
 ”Aw, c’mon!”

“Al, let’s put some numbers to your hypothesis. <pulling out Old Reliable and screen‑tapping> I’m going to compare Jupiter’s pull on the Moon to Earth’s when the two planets are closest together. OK?”

“I suppose.”

“Alright. Newton’s Law tells us the pull is proportional to the mass. Jupiter’s mass is about 320 times Earth, which is pretty impressive, right? But the attraction drops with the square of the distance. The Moon is 1¼ lightseconds from Earth. At closest approach, Jupiter is almost 2100 lightseconds away, 1680 times further than the Moon. We need to divide the 320 mass factor by a 1680‑squared distance factor and that makes <key taps> Jupiter’s pull on the Moon is only 0.011 percent of Earth’s. It’ll be <taps> half that when Jupiter’s on the other side of the Sun. Not much competition, eh?”

“Yeah, but a little bit at a time, it adds up.”

“We’re not done yet. The Moon feels the big guy’s pull on both sides of its orbit around Earth. On the side where the Moon’s moving away from Jupiter, you’re right, Jupiter’s gravity slows the Moon down, a little. But on the moving-toward-Jupiter side, the motion’s sped up. Put it all together, Jupiter’s teeny pull cancels itself out over every month’s orbiting.”

“Gotcha, Al. So what about my theory, Sy?”

“Basically the same logic, Vinnie. The Solar wind varies, thanks to the Sun’s variable activity, but satellite measurements put its pressure somewhere around a nanopascal, a nanonewton per square meter. Multiply that by the Moon’s cross‑sectional area and we get <tap, tap> a bit less than ten thousand newtons of force on the Moon. Meanwhile, Newton’s Law says the Earth’s pull on the Moon comes to <tapping>
  G×(Earth’s mass)×(Moon’s mass)/(Earth-Moon distance)²
and that comes to 2×1011 newtons. Earth wins by a 107‑fold landslide. Anyway, the pressure slows the Moon for only half of each month and speeds it up the other half so we’ve got another cancellation going on.”

“So what is it then?”
 ”So what is it then?”

“Tides. Not just ocean tides, rock tides in Earth’s fluid outer mantle. Earth bulges, just a bit, toward the Moon. But Earth also rotates, so the bulge circles the planet every day.”

“Reminds me of the wave in the Interstellar movie, but why don’t we see it?”

“The movie’s wave was hundreds of times higher than ours, Al. It was water, not rock, and the wave‑raiser was a huge black hole close by the planet. The Moon’s tidal pull on Earth produces only a one‑meter variation on a 6,400,000‑meter radius. Not a big deal to us. Of course, it makes a lot of difference to the material that’s being kneaded up and down. There’s a lot of friction in those layers.”

“Friction makes heat, Sy. Rock tides oughta heat up the planet, right?”

“Sure, Vinnie, the process does generate heat. Force times distance equals energy. Raising the Moon by 1¼ nanometers per second against a force of 2×1021 newtons gives us <taping furiously> an energy transfer rate of 4×10‑23 joules per second per kilogram of Earth’s 6×1024‑kilogram mass. It takes about a thousand joules to heat a kilogram of rock by one kelvin so we’re looking at a temperature rise near 10‑27 kelvins per second. Not significant.”

“No blaming climate change on the Moon, huh?”

~~ Rich Olcott

The Top Choice

Al grabs me as I step into his coffee shop. “Sy, ya gotta stop Vinnie, he’s using up paper napkins again, and he’s making a mess!”

Sure enough, there’s Vinnie at his usual table by the door. He’s got a kid’s top, a big one, spinning on a little stand. He’s methodically dropping crumpled-up paper wads onto it and watching them fly off onto the floor. “Hey, Vinnie, what’s the project?”

“Hi, Sy. I’m trying to figure how come these paper balls are doing a circle but when they fly off they always go in a straight line, at least at first. They got going-around momentum, right, so how come they don’t make a spiral like stars in a galaxy?”

Astronomy professor Cathleen’s standing in the scone line. She never misses an opportunity to correct a misconception. “Galaxy stars don’t spray out of the center in a spiral, Vinnie. Like planets going around a star, stars generally follow elliptical orbits around the galactic center. A star that’s between spiral arms now could be buried in one ten million years from now. The spiral arms appear because of how the orbits work. One theory is that the innermost star orbits rotate their ellipse axes more quickly than the outer ones and the spirals form where the ellipses pile up. Other theories have to do with increased star formation or increased gravitational attraction within the pile-up regions. Probably all three contribute to the structures. Anyhow, spirals don’t form from the center outward.”

My cue for some physics. “What happens in a galaxy is controlled by gravity, Vinnie, and gravity doesn’t enter into what you’re doing. Except for all that paper falling onto Al’s floor. There’s no in-plane gravitational or electromagnetic attraction in play when your paper wads leave the toy. Newton would say there’s no force acting to make them follow anything other than straight lines once they break free.”

“What about momentum? They’ve got going-around momentum, right, shouldn’t that keep them moving spirally?”

I haul out Old Reliable for a diagram. “Thing is, your ‘going-around momentum,’ also known as ‘angular momentum,’ doesn’t exist. Calm down, Vinnie, I mean it’s a ‘fictitious force‘ that depends on how you look at it.”

“Is this gonna be frames again?”

“Yup. Frames are one of our most important analytical tools in Physics. Here’s your toy and just for grins I’ve got it going around counterclockwise. That little white circle is one of your paper wads. In the room’s frame that wad in its path is constantly converting linear momentum between the x-direction and the y-direction, right?”

“East-West to North-South and back, yeah, I get that.”

“Such a mess to calculate. Let’s make it easier. Switch to the perspective of a frame locked to the toy. In that frame the wad can move in two directions. It can fly away along the radial direction I’ve called r, or it can ride along sideways in the s-direction.”

“So why hasn’t it flown away?”

“Because you put some spit on it to make it stick — don’t deny it, I saw you. While it’s stuck, does it travel in the r direction?”

“Nope, only in the s direction. Which should make it spiral like I said.”

“I’m not done yet. One of Newton’s major innovations was the idea of infinitesimal changes, also known as little-bits. The s-direction is straight, not curved, but it shifts around little-bit by little-bit as the top rotates. Newton’s Laws say force is required to alter momentum. What force influences the wad’s s-momentum?”

“Umm … that line you’ve marked c.”

“Which is the your spit’s adhesive force between the paper and the top. The wad stays stuck until the spit dries out and no more adhesion so no more c-force. Then what happens?”

“It flies off.”

“In which direction?”

“Huh! In the r-direction.”

“And in a straight line, just like Newton said. What you called ‘going-around momentum’ becomes ‘radial momentum’ and there’s no spiraling, right?”

“I guess you’re right, but I miss spirals.”

Al comes over with a broom. “Now that’s settled, Vinnie, clean up!”

~~ Rich Olcott

  • Thanks for the question, Jen Keeler. Stay tuned.

Conversation of Momentum

Teena bounces out of the sandbox, races over to the playground’s little merry-go-round and shoves it into motion. “Come help turn this, Uncle Sy, I wanna go fast!” She leaps onto the moving wheel and of course she promptly falls off. The good news is that she rolls with the fall like I taught her to do.

“Why can’t I stay on, Uncle Sy?”

“What’s your new favorite word again?”

“Mmmo-MMENN-tumm. But that had to do with swings.”

“Swings and lots of other stuff, including merry-go-rounds and even why you should roll with the fall. Which, by the way, you did very well and I’m glad about that because we don’t want you getting hurt on the playground.”

“Well, it does hurt a little on my elbow, see?”

“Let me look … ah, no bleeding, things only bend where they’re supposed to … I think no damage done but you can ask your Mommie to kiss it if it still hurts when we get home. But you wanted to know why you fell off so let’s go back to the sandbox to figure that out.”

<scamper!> “I beat you here!”

“Of course you did. OK, let’s draw a big arc and pretend that’s looking down on part of the merry-go-round. I’ll add some lines for the spokes and handles. Now I’ll add some dots and arrows to show what I saw from over here. See, the merry-go-round is turning like this curvy arrow shows. You started at this dot and jumped onto this dot which moved along and then you fell off over here. Poor Teena. So you and your momentum mostly went left-to-right.”

“But that’s not what happened, Uncle Sy. Here, I’ll draw it. I jumped on but something tried to push me off and then I did fall off and then I rolled. Poor me. Hey, my arm doesn’t hurt any more!”

“How about that? I’ve often found that thinking about something else makes hurts go away. So what do you think was trying to push you off? I’ll give you a hint with these extra arrows on the arc.”

“That looks like Mr Newton’s new directions, the in-and-out direction and the going-around one. Oh! I fell off along the in-and-out direction! Like I was a planet and the Sun wasn’t holding me in my orbit! Is that what happened, I had out-momentum?”

“Good thinking, Teena. Mr Newton would say that you got that momentum from a force in the out-direction. He’d also say that if you want to stand steady you need all the forces around you to balance each other. What does that tell you about what you need to do to stay on the merry-go-round?”

“I need an in-direction force … Hah, that’s what I did wrong! I jumped on but I didn’t grab the handles.”

“Lesson learned. Good.”

“But what about the rolling?”

“Well, in general when you fall it’s nearly always good to roll the way your body’s spinning and only try to slow it down. People who put out an arm or leg to stop a fall often stress it and and maybe even tear or break something.”

“That’s what you’ve told me. But what made me spin?”

“One of Mr Newton’s basic principles was a rule called ‘Conservation of Momentum.’ It says that you can transfer momentum from one thing to another but you can’t create it or destroy it. There are some important exceptions but it’s a pretty good rule for the cases he studied. Your adventure was one of them. Look back at the picture I drew. You’d built up a lot of going-around momentum from pushing the merry-go-round to get it started. You still had momentum in that direction when you fell off. Sure enough, that’s the direction you rolled.”

“Is that the ‘Conversation of Energy’ thing that you and Mommie were talking about?”

“Conservation. It’s not the same but it’s closely related.”

“Why does it even work?”

“Ah, that’s such a deep question that most physicists don’t even think about it. Like gravity, Mr Newton described what inertia and momentum do, but not how they work. Einstein explained gravity, but I’m not convinced that we understand mass yet.”

~~ Rich Olcott

A Momentous Occasion

<creak> Teena’s enjoying her new-found power in the swings. “Hey, Uncle Sy? <creak> Why doesn’t the Earth fall into the Sun?”

“What in the world got you thinking about that on such a lovely day?”

“The Sun gets in my eyes when I swing forward <creak> and that reminded me of the time we saw the eclipse <creak> and that reminded of how the planets and moons are all floating in space <creak> and the Sun’s gravity’s holding them together but if <creak> the Sun’s pulling on us why don’t we just fall in?” <creak>

“An excellent question, young lady. Isaac Newton thought about it long and hard back when he was inventing Physics.”

“Isaac Newton? Is he the one with all the hair and a long, skinny nose and William Tell shot an arrow off his head?”

“Well, you’ve described his picture, but you’ve mixed up two different stories. William Tell’s apple story was hundreds of years before Newton. Isaac’s apple story had the fruit falling onto his head, not being shot off of it. That apple got him thinking about gravity and how Earth’s gravity pulling on the apple was like the Sun’s gravity pulling on the planets. When he was done explaining planet orbits, he’d also explained how your swing works.”

“My swing works like a planet? No, my swing goes back and forth, but planets go round and round.”

“Jump down and we can draw pictures over there in the sandbox.”

<thump!! scamper!> “I beat you here!”

“Of course you did. OK, what’s your new M-word?”

“Mmmo-MMENN-tummm!”

“Right. Mr Newton’s Law of Inertia is about momentum. It says that things go in a straight line unless something interferes. It’s momentum that keeps your swing going.”

“B-u-u-t, I wasn’t going in a straight line, I was going in part of a circle.”

“Good observing, Teena, that’s exactly right. Mr Newton’s trick was that a really small piece of a circle looks like a straight line. Look here. I’ll draw a circle … and inside it I’ll put a triangle… and between them I’ll put a hexagon — see how it has an extra point halfway between each of the triangle’s points? — and up top I’ll put the top part of whatever has 12 sides. See how the 12-thing’s sides are almost on the circle?”

“Ooo, that’s pretty! Can we do that with a square, too?”

“Sure. Here’s the circle … and the square … and an octagon … and a 16-thing. See, that’s even closer to being a circle.”

“Ha-ha — ‘octagon’ — that’s like ‘octopus’.”

“For good reason. An octopus has eight arms and an octagon has eight sides. ‘Octo-‘ means ‘eight.’ So anyway, Mr Newton realized that his momentum law would apply to something moving along that tiny straight line on a circle. But then he had another idea — you can move in two directions at once so you can have momentum in two directions at once.”

“That’s silly, Uncle Sy. There’s only one of me so I can’t move in two directions at once.”

“Can you move North?”

“Uh-huh.”

“Can you move East?”

“Sure.”

“Can you move Northeast?”

“Oh … does that count as two?”

“It can for some situations, like planets in orbit or you swinging on a swing. You move side-to-side and up-and-down at the same time, right?”

“Uh-huh.”

“When you’re at either end of the trip and as far up as you can get, you stop for that little moment and you have no momentum. When you’re at the bottom, you’ve got a lot of side-to-side momentum across the ground. Anywhere in between, you’ve got up-down momentum and side-to-side momentum. One kind turns into the other and back again.”

“So complicated.”

“Well, it is. Newton simplified things with revised directions — one’s in-or-out from the center, the other’s the going-around angle. Each has its own momentum. The swing’s ropes don’t change length so your in-out momentum is always zero. Your angle-momentum is what keeps you going past your swing’s bottom point. Planets don’t have much in-out momentum, either — they stay about their favorite distance from the Sun.”

“Earth’s angle-momentum is why we don’t fall in?”

“Yep, we’ve got so much that we’re always falling past the Sun.”

~~ Rich Olcott

Gettin’ kinky in space

Things were simpler in the pre-Enlightenment days when we only five planets to keep track of.  But Haley realized that comets could have orbits, Herschel discovered Uranus, and Galle (with Le Verrier’s guidance) found Neptune.  Then a host of other astronomers detected Ceres and a host of other asteroids, and Tombaugh observed Pluto in 1930.whirlpool-44x100-reversed

Astronomers relished the proliferation — every new-found object up there was a new test case for challenging one or another competing theory.

Here’s the currently accepted narrative…  Long ago but quite close-by, there was a cloud of dust in the Milky Way galaxy.  Random motion within it produced a swirl that grew into a vortex dozens of lightyears long.

Consider one dust particle (we’ll call it Isaac) afloat in a slice perpendicular to the vortex.  Assume for the moment that the vortex is perfectly straight, the dust is evenly spread across it, and all particles have the same mass.  Isaac is subject to two influences — gravitational and rotational.

making-a-solar-nebula
A kinked galactic cloud vortex,
out of balance and giving rise
to a solar system.

Gravity pulls Isaac towards towards every other particle in the slice.  Except for very near the slice’s center there are generally more particles (and thus more mass) toward and beyond the center than back toward the edge behind him.  Furthermore, there will generally be as many particles to Isaac’s left as to his right.  Gravity’s net effect is to pull Isaac toward the vortex center.

But the vortex spins.  Isaac and his cohorts have angular momentum, which is like straight-line momentum except you’re rotating about a center.  Both of them are conserved quantities — you can only get rid of either kind of momentum by passing it along to something else.  Angular momentum keeps Isaac rotating within the plane of his slice.

An object’s angular momentum is its linear momentum multiplied by its distance from the center.  If Isaac drifts towards the slice’s center (radial distance decreases), either he speeds up to compensate or he transfers angular momentum to other particles by colliding with them.

But vortices are rarely perfectly straight.  Moreover, the galactic-cloud kind are generally lumpy and composed of different-sized particles.  Suppose our vortex gets kinked by passing a star or a magnetic field or even another vortex.  Between-slice gravity near the kink shifts mass kinkward and unbalances the slices to form a lump (see the diagram).  The lump’s concentrated mass in turn attracts particles from adjacent slices in a viscous cycle (pun intended).

After a while the lumpward drift depletes the whole neighborhood near the kink.  The vortex becomes host to a solar nebula, a concentrated disk of dust whirling about its center because even when you come in from a different slice, you’ve still got your angular momentum.  When gravity smacks together Isaac and a few billion other particles, the whole ball of whacks inherits the angular momentum that each of its stuck-together components had.  Any particle or planetoid that tries to make a break for it up- or down-vortex gets pulled back into the disk by gravity.

That theory does a pretty good job on the conventional Solar System — four rocky Inner Planets, four gas giant Outer Planets, plus that host of asteroids and such, all tightly held in the Plane of The Ecliptic.

How then to explain out-of-plane objects like Pluto and Eris, not to mention long-period comets with orbits at all angles?outer-orbits-1

We now know that the Solar System holds more than we used to believe.  Who’s in is still “objects whose motion is dominated by the Sun’s gravitational field,” but the Sun’s net spreads far further than we’d thought.  Astronomers now hypothesize that after its creation in the vortex, the Sun accumulated an Oort cloud — a 100-billion-mile spherical shell containing a trillion objects, pebbles to planet-sized.

At the shell’s average distance from the Sun (see how tiny Neptune’s path is in the diagram) Solar gravity is a millionth of its strength at Earth’s orbit.  The gravity of a passing star or even a conjunction of our own gas giants is enough to start an Oort-cloud object on an inward journey.

These trans-Neptunian objects are small and hard to see, but they’re revolutionizing planetary astronomy.

~~ Rich Olcott

Smoke and a mirror

Etna jellyfish pairGrammie always grimaced when Grampie lit up one of his cigars inside the house.  We kids grinned though because he’d soon be blowing smoke rings for us.  Great fun to try poking a finger into the center, but we quickly learned that the ring itself vanished if we touched it.

My grandfather can’t take credit for the smoke ring on the left — it was “blown” by Mt Etna.  Looks very like the jellyfish on the right, doesn’t it?  When I see two such similar structures, I always wonder if the resemblance comes from the same physics phenomenon.

This one does — the physics area is Fluid Dynamics, and the phenomenon is a vortex ring. We need to get a little technical and abstract here: to a physicist a fluid is anything that’s composed of particles that don’t have a fixed spatial relationship to each other. Liquid water is a fluid, of course (its molecules can slide past each other) and so is air.  The sun’s ionized protons and electrons comprise a fluid, and so can a mob of people and so can vehicle traffic (if it’s moving at all).  You can use Fluid Dynamics to analyze motion when the individual particles are numerous and small relative to the volume in question.

Ring x-section
Adapted from a NOAA page

You get a vortex whenever you have two distinct fluids in contact but moving at sufficiently different velocities.  (Remember that “velocity” includes both speed and direction.)  When Grampie let out that little puff of air (with some smoke in it), his fast-moving breath collided with the still air around him.  When the still air didn’t get out of the way, his breath curled back toward him.  The smoke collected in the dark gray areas in this diagram.

That curl is the essence of vorticity and turbulence.  The general underlying rule is “faster curls toward slower,” just like that skater video in my previous post.  Suppose fluid is flowing through a pipe.  Layers next to the outside surface move slowly whereas the bulk material near the center moves quickly.  If the bulk is going fast enough, the speed difference will generate many little whorls against the circumference, converting pump energy to turbulence and heat.  The plant operator might complain about “back pressure” because the fluid isn’t flowing as rapidly as expected from the applied pressure.

But Grampie didn’t puff into a pipe (he’s a cigar man, right?), he puffed into the open air.  Those curls weren’t just at the top and bottom of his breath, they formed a complete circle all around his mouth.  If his puff didn’t come out perfectly straight, the smoke had a twist to it and circulated along that circle, the way Etna’s ring seems to be doing (note the words In and Out buried in the diagram’s gray blobs).  When a vortex closes its loop like that, you’ve got a vortex ring.

A vortex ring is a peculiar beast because it seems to have a life of its own, independent of the surrounding medium.  Grampie’s little puff of vortical air usually retained its integrity and carried its smoke particles for several feet before energy loss or little fingers broke up the circulation.

To show just how special vortex rings are, consider the jellyfish.  Until I ran across this article, I’d thought that jellyfish used jet propulsion like octopuses and squids do — squirt water out one way to move the other way.  Not the case.  Jellyfish do something much more sophisticated, something that makes them possibly “the most energy-efficient animals in the world.”

jellyfish vortices

Thanks to a very nice piece of biophysics detective work (read the paper, it’s cool, no equations), we now know that a jellyfish doesn’t just squirt.  Rather, it relaxes its single ring of muscle tissue to open wide.  That motion pulls in a pre-existing vortex ring that pushes against the bell.  On the power stroke, the jellyfish contracts its bell to push water out (OK, that’s a squirt) and create another vortex ring rolling in the opposite direction.  In effect, the jellyfish continually builds and climbs a ladder of vortex rings.

Vortex rings are encapsulated angular momentum, potentially in play at any size in any medium.

~~ Rich Olcott