Sail On, Silver Bird

Big excitement in Al’s coffee shop. “What’s the fuss, Al?”

Lightsail 2, Sy. The Planetary Society’s Sun-powered spacecraft. Ten years of work and some luck and it’s up there, way above Hubble and the ISS, boosting itself higher every day and using no fuel to do it. Is that cool or what?”

“Sun-powered? Like with a huge set of solar panels and an electric engine?”

“No, that’s the thing. It’s got a couple of little panels to power its electronics and all, but propulsion is all direct from the Sun and that doesn’t stop. Steady as she goes, Skipper, Earth to Mars in weeks, not months. Woo-hoo!”

Image by Josh Spradling / The Planetary Society

Never the rah-rah type, Big Vinnie throws shade from his usual table by the door. “It didn’t get there by itself, Al. SpaceX’s Falcon Heavy rocket did the hard work, getting Lightsail 2 and about 20 other thingies up to orbit. Takes a lot of thrust to get out of Earth’s gravity well. Chemical rockets can do that, puny little ion drives and lightsails can’t.”

“Yeah, Vinnie, but those ‘puny’ guys could lead us to a totally different travel strategy.” A voice from the crowd, astrophysicist-in-training Newt Barnes. “Your big brawny rocket has to burn a lot of delta-v just to boost its own fuel. That’s a problem.”

Al looks puzzled. “Delta-v?”

“It’s how you figure rocket propellant, Al. With a car you think about miles per gallon because if you take your foot off the gas you eventually stop. In space you just keep going with whatever momentum you’ve got. What’s important is how much you can change momentum — speed up, slow down, change direction — and that depends on the propellant you’re using and the engine you’re putting it through. All you’ve got is what’s in the tanks.”

Al still looks puzzled. I fill in the connection. “Delta means difference, Al, and v is velocity which covers both speed and direction so delta-v means — “

“Got it, Sy. So Vinnie likes big hardware but bigger makes for harder to get off the ground and Newt’s suggesting there’s a limit somewhere.”

“Yup, it’s gotten to the point that the SpaceX people chase an extra few percent performance by chilling their propellants so they can cram more into the size tanks they use. I don’t know what the limit is but we may be getting close.”

Newt’s back in. “Which is where strategy comes in, Vinnie. Up to now we’re mostly using a ballistic strategy to get to off-Earth destinations, treating the vehicle like a projectile that gets all its momentum at the beginning of the trip. But there’s really three phases to the trip, right? You climb out of a gravity well, you travel to your target, and maybe you make a controlled landing you hope. With the ballistic strategy you burn your fuel in phase one while you’re getting yourself into a transfer orbit. Then you coast on momentum through phase two.”

“You got a better strategy?”

“In some ways, yeah. How about applying continuous acceleration throughout phase two instead of just coasting? The Dawn spacecraft, for example, was rocket-launched out of Earth’s gravity well but used a xenon-ion engine in continuous-burn mode to get to Mars and then on to Vesta and Ceres. Worked just fine.”

“But they’re such low-thrust –“

“Hey, Vinnie, taking a long time to build up speed’s no problem when you’re on a long trip anyway. Dawn‘s motor averaged 1.8 kilometer per second of delta-v — that works out to … about 4,000 miles per hour of increased speed for every hour you keep the motor running. Adds up.”

“OK, I’ll give you the ion motor’s more efficient than a chemical system, but still, you need that xenon reaction mass to get your delta-v. You still gotta boost it up out of the well. All you’re doing with that strategy is extend the limit.”

Al dives back in. “That’s the beauty of Lightsail, guys. No delta-v at all. Just put it up there and light-pressure from the Sun provides the energy. Look, I got this slick video that shows how it works.”

Video courtesy of The Planetary Society.

~~ Rich Olcott

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Red Velvet with Icing

“So Jupiter’s white stripes are huge updrafts of ammonia snow and its dark stripes are weird chemicals we only see when downdrafted ammonia snow evaporates. Fine, but how does that account for my buddy the Great Red Spot? Have another lemon scone.”

“Thanks, Al, don’t mind if I do. Well, those ideas only sort-of account for Spot. The bad news is that they may not have to for much longer.”

“Huh? Why not?”

“Because it seems to be going away.”

“Hey, Sy, don’t mess with me. You know it’s been there for 400 years, why should it go away now?”

“I don’t know anything of the kind. Sure, the early telescope users saw a spot 350 years ago but there’s reason to think that it wasn’t in the same location as your buddy. Then there was a century-long gap when no-one recorded seeing anything special on Jupiter. Without good evidence either way, I think it’s entirely possible we’ve had two different spots. Anyway, the new one has been shrinking for the past 150 years.”

“The big hole must be filling in, then.”

“What hole?”

Juno GRS image, NASA/JPL-Caltech/SwRI/MSSS/Gerald Eichstädt

“The Spot. If the dark-colored stripes are what we see when the bright ammonia ice evaporates, then the Spot’s gotta be a hole.”

“A reasonable conclusion from what we’ve said so far, but the Juno orbiter has given us more information. The Spot actually reaches 500 miles further up than the surrounding cloud tops.”

“But higher-up means colder, right? How come we don’t see the white snow?”

“That higher-is-colder rule does apply within Jupiter’s weather layer, mostly, but the Spot’s different. There seems to be a LOT of heat pouring straight up out of it, enough to warm the overlying atmosphere by several hundred degrees compared to the planetary average. That suppresses the ammonia ice, lifts whatever makes the red color and may even promote chemical reactions to make more.”

“But Sy, even I know heat spreads out. You’ve just described something that acts like a searchlight. How could it work like that?”

“Here’s one hypothesis. You’ve got your sound system here rigged up so the back of the shop is quiet, right? How’d you do that?”

“Oh, I bought a couple of directional speakers. They’re deeper than the regular kind and they’ve got this parabolic shape. I aimed them up here to the front where the traffic is. Work pretty good, don’t they?”

“Yes, indeed, and I’m grateful for that. See, they focus sound energy just like you can focus light. Now, to us the Spot just looks like an oval. But it’s probably the big end of a deep cone, spinning like mad and turning turbulent wind energy into white noise that’s focused out like one of your speakers. Wouldn’t that do the trick?”

“Like a huge trombone. Yeah, I suppose, but what keeps the cone cone-shaped?”

“The same thing that keeps it spinning — it’s trapped between two currents that are zipping along in opposite directions. The Spot’s northern boundary is the fastest westbound windstream on the planet. Its southern boundary is an eastbound windstream. The Spot’s trapped between two bands screaming past each other at the speed of sound.”

“Wow. Sounds violent.”

“Incredibly violent, much more than Earth hurricanes. At a hurricane’s eye-wall the wind speeds generally peak below 200 miles per hour. The Great Red Spot’s outermost winds that we can see are 50 miles per hour faster but those triangular regions just east and west must be far worse. When I think about adding in the updrafts and downdrafts I just shudder.”

“Does that have anything to do with the shrinking you told me about?”

“Almost certainly — we simply don’t have enough data to tell. But the new news is that your buddy’s uncorked a fresh shrinkage mode. Since the mid-1800s it’s been contracting along the east-west line, getting more circular. Now it seems to be flaking, too. Big, continent-size regions break away and mix into the dark belt above it. Meanwhile, the white equatorial zone is getting darker, sort of a yellow-green-orange mix.”

GRS image courtesy of Sharin Ahmad

“Yucky-colored. Does that mean the Spot’s draining into it?”

“Who knows? We certainly don’t. Only time will tell.”

~~ Rich Olcott

Icing on The Brownie

“So what you’re saying, Sy, is that Jupiter’s white stripes are ammonia snow clouds that go way up above a lower layer of brown clouds like the white icing stripes I put on my brownies.”

“That’s what I’m saying, Al.”

“But why stripes? We got white clouds here on Earth and sometimes they’re in layers but they don’t make stripes.”

“Well, actually they do, but you need the long-term picture to see it. Ever notice that Earth’s forests and deserts make stripes?”

“How ’bout that? I guess they do, sorta. How’s that work?”

“It took us five hundred years to figure out the details. Quick summary. Sunlight does its best year-round heating job at the Equator, where the oceans humidify the air. Warm air rises. Rising warm air cools, releases its moisture as rain, and you get a rainforest belt. The cooled, dried air spreads out until it sinks at about the 30th parallels north and south. Dry air sucks moisture out of the land as it returns to the Equator and you get desert belts. Repeat the cycle. More loops like that center around both 60th parallels. The pattern’s not completely uniform because of things like mountain ranges that block some of the flows. Basically, though, as the years accumulate you get stripes.”

“Jupiter does that, too, huh?”

“On steroids. In one way it’s simpler — no underlying continents mess things up. On the other hand, Jupiter’s got more than a hundred times Earth’s surface area so there’s room for more loops. Also, Jupiter’s interior is still shedding a lot of heat, almost as much as the planet gets from the Sun. Here’s a diagram on Old Reliable.”

“So you’re saying that the upward loops push Jupiter’s atmosphere to where it’s colder and those white ammonia snow clouds form. Then the downward loops move the clouds to where it’s warmer and the ammonia evaporates to show us the brown stuff. Makes sense. But what’re those side-to-side arrows about? We got anything like those on Earth?”

“Sort of, a little bit. Remember the Coriolis force?”

“Uhh, that’s what makes hurricanes go round and round, right? Something to do with the Equator running faster than places further north or south?”

“That’s the start of it. The Earth as a whole rotates 360° eastward in 24 hours, but how many miles per hour that is depends on where you are. The Equator’s about 25000 miles long so Quito, Ecuador on the Equator does a bit more than 1000 miles per hour. Forty-five degrees away, the 45th parallels are only 70% as long as that, so Salem, Oregon and Queenstown, New Zealand circle 70% slower in miles per hour. Suppose a balloon from Salem travels south as seen from space. As seen from the Equator, the balloon appears in the northeast rather than straight north. Winds work the way that balloon would. All around the world, winds between 10° and 30° north and south come from an east-ish direction most of the time.”

“What about the winds right at the Equator? You’d think the northerly part and the southerly part would cancel each other out.”

“That’s exactly what happens, Al. We’ve got a more-or-less equatorial belt of thunderstorms from humid air cooling off as it goes straight up, but not much of a prevailing wind in any direction — that’s why the old sea captains called the region ‘the doldrums’.”

“An equator belt like Jupiter’s, eh?”

“Not quite. Jupiter has a lovely white equatorial zone all right, but that one doesn’t stand still. It roars eastward, 300 miles per hour faster than the equator’s own 28000 miles per hour. All Jupiter’s white zones move east at a pretty good clip. Its dark belts sprint westward at their own hundred-mile pace. Then there’s the jet streams that run between neighboring bands, and lots of big and little vortices carried along for the ride. The planet’s way too segmented and violent for Coriolis forces to build up enough to play a part. The scientists have a couple of heavily-simplified models, but nowhere near enough data or computer time to fill them in.”

“Earth’s atmosphere is messy enough, thanks. My brain’s hurting.”

Voyager I video of Jupiter, processed by JPL,
from Wikimedia Commons

~~ Rich Olcott

Lemon, Vanilla, Cinnamon

Al claims that lemon’s a Summertime flavor, which is why his coffee shop’s Scone Flavor of the Month in July is lemon even though it doesn’t go well with his coffee. “Give me one of those lemon scones, Al, and an iced tea. It’s a little warm out there this morning.”

“Sure thing, Sy. Say, what’s the latest science-y thing up in the sky?”

“Oh, there’s a bunch, Al. The Japanese Hayabusa-2 spacecraft collected another sample from asteroid Ryugu. NASA’s gravity-sniffer GRAIL lunar orbiter found evidence for a huge hunk of metallic material five times larger than the Big Island of Hawai’i buried deep under the Moon’s South Pole-Aitken Basin. The Insight Mars lander’s seismometer heard its first Marsquake —“

“Quit yanking my chain, Sy. Anything about Jupiter?”

“Gotcha, Al. I know Jupiter’s your favorite planet. As it happens I do have some Jupiter news for you.”

“The Juno orbiter’s still working, I hope.”

“Sure, sure, far as I know. It’s about to make its 13th close flyby of Jupiter, and NASA administrators have green-lighted the mission to continue until July 2021. Lots of data for the researchers to work on for years. Here’s a clue — what’re the top three things that everyone knows about Jupiter?”

“It’s the biggest planet, of course, and it’s got those stripes and the Great Red Spot. Has the planet gotten smaller somehow?”

“No, but the stripes and the Red Spot are acting weird. Had you heard about that?”

“No, just that the Spot’s huge and red and been there for 400 years.”

“Mmm, we’re not sure about the 400 years. But yes, it’s huge.”

“Four times wider than Earth, right?”

“Hasn’t been that big for a long time. Back in the 1870s telescope technology gave the astronomers that ‘four Earths wide‘ estimate. But the Spot’s shrunk in the last 150 years.”

“A whole lot?”

“Last measurement I saw, it’s just barely over one Earth wide. Seems to have gotten a bit taller, though, and maybe deeper.”

“Taller and deeper? Huh, that’s a new one. I always thought of the Spot as just this big oval ring on Jupiter’s surface.”

“Everyone has that bogus idea of Jupiter as a big smooth sphere with stripes and ovals and swirls painted on it. Don’t forget, we’re looking down at cloud tops, like those satellite pictures we get looking down at a storm system on Earth. From space, one of our hurricanes looks like a spirally disk centered on a dark spot. That dark spot isn’t in the clouds, it’s actually the top of the ocean, miles below the clouds. If you were a Martian working with photos from a telescope on Phobos, you’d be hard-put to figure that out. You need 3-D perspective to get planets right.”

Jupiter image courtesy ESA/Hubble

“Those stripes and stuff aren’t Jupiter’s surface?”

“As far as we can tell, Jupiter doesn’t have a surface. The hydrogen-helium atmosphere just gets denser and denser until it acts like a liquid. There’s a lot of pressure down there. Juno recently gave us evidence for a core that’s a fuzzy mix of stony material and maybe-metallic maybe-solid hydrogen but if that mush is real it’s only 3% of the planet’s mass. Whatever, it’s thousands of miles below what we see. Jupiter’s anything but smooth.”

“Lumps and bumps like this bubbly scone, huh?”

“More organized than that, more like corduroy or a coiled garden hose. The white stripes are hundreds of miles higher-up than the brown stripes so north-to-south it’s like a series of extreme mountain ranges and valleys. The Great Red Spot reaches up maybe 500 miles further.”

“Does that have to do with what they’re made of?”

“It has everything to do with that, we think. You know Earth’s atmosphere has layers, right?”

“Yeah, the stratosphere’s on top, then you got the weather layer where the clouds are.”

“Close enough. Jupiter has all that and more. Thanks to the Galileo probe we know that Jupiter’s ‘weather layer’ has a topmost blue-white cloud layer of ammonia ice particles, a middle red-to-brown layer containing compounds of ammonia and sulfur, and a bottommost white-ish layer of water clouds. The colors we see depend on which layer is exposed where.”

“But why’re they stripey?”

~~ Rich Olcott

The Big Chill

Jeremy gets as far as my office door, then turns back. “Wait, Mr Moire, that was only half my question. OK, I get that when you squeeze on a gas, the outermost molecules pick up kinetic energy from the wall moving in and that heats up the gas because temperature measures average kinetic energy. But what about expansion cooling? Those mist sprayers they set up at the park, they don’t have a moving outer wall but the air around them sure is nice and cool on a hot day.”

“Another classic Jeremy question, so many things packed together — Gas Law, molecular energetics, phase change. One at a time. Gas Law’s not much help, is it?”

“Mmm, guess not. Temperature measures average kinetic energy and the Gas Law equation P·V = n·R·T gives the total kinetic energy for the n amount of gas. Cooling the gas decreases T which should reduce P·V. You can lower the pressure but if the volume expands to compensate you don’t get anywhere. You’ve got to suck energy out of there somehow.”

Illustrations adapted from drawings by Trianna

“The Laws of Thermodynamics say you can’t ‘suck’ heat energy out of anything unless you’ve got a good place to put the heat. The rule is, heat energy travels voluntarily only from warm to cold.”

“But, but, refrigerators and air conditioners do their job! Are they cheating?”

“No, they’re the products of phase change and ingenuity. We need to get down to the molecular level for that. Think back to our helium-filled Mylar balloon, but this time we lower the outside pressure and the plastic moves outward at speed w. Helium atoms hit the membrane at speed v but they’re traveling at only (v-w) when they bounce back into the bulk gas. Each collision reduces the atom’s kinetic energy from ½m·v² down to ½m·(v-w)². Temperature goes down, right?”

“That’s just the backwards of compression heating. The compression energy came from outside, so I suppose the expansion energy goes to the outside?”

“Well done. So there has to be something outside that can accept that heat energy. By the rules of Thermodynamics, that something has to be colder than the balloon.”

“Seriously? Then how do they get those microdegree above absolute zero temperatures in the labs? Do they already have an absolute-zero thingy they can dump the heat to?”

“Nope, they get tricky. Suppose a gas in a researcher’s container has a certain temperature. You can work that back to average molecular speed. Would you expect all the molecules to travel at exactly that speed?”

“No, some of them will go faster and some will go slower.”

“Sure. Now suppose the researcher uses laser technology to remove all the fast-moving molecules but leave the slower ones behind. What happens to the average?”

“Goes down, of course. Oh, I see what they did there. Instead of the membrane transmitting the heat away, ejected molecules carry it away.”

“Yup, and that’s the key to many cooling techniques. Those cooling sprays, for instance, but a question first — which has more kinetic energy, a water droplet or the droplet’s molecules when they’re floating around separately as water vapor?”

“Lessee… the droplet has more mass, wait, the molecules total up to the same mass so that’s not the difference, so it’s droplet velocity squared versus lots of little velocity-squareds … I’ll bet on the droplet.”

“Sorry, trick question. I left out something important — the heat of vaporization. Water molecules hold pretty tight to each other, more tightly in fact than most other molecular substances. You have to give each molecule a kick to get it away from its buddies. That kick comes from other molecules’ kinetic energy, right? Oh, and one more thing — the smaller the droplet, the easier for a molecule to escape.”

“Ah, I see where this is going. The mist sprayer’s teeny droplets evaporate easy. The droplets are at air temperature, so when a molecule breaks free some neighbor’s kinetic energy becomes what you’d expect from air temperature, minus break-free energy. That lowers the average for the nearby air molecules. They slow their neighbors. Everything cools down. So that’s how sprays and refrigerators and such work?”

“That’s the basic principle.”

“Cool.”

~ Rich Olcott

Thanks to Mitch Slevc for the question that led to this post.

The Hot Squeeze

A young man’s knock, eager yet a bit hesitant.

“C’mon in, Jeremy, the door’s open.”

“Hi, Mr Moire. How’s your Summer so far? I got an ‘A’ on that black hole paper, thanks to your help. Do you have time to answer a question now that Spring term’s over?”

“Hi, Jeremy. Pretty good, congratulations, and a little. What’s your question?”

“I don’t understand about the gas laws. You squeeze a gas, you raise its temperature, but temperature’s the average kinetic energy of the molecules which is mass times velocity squared but mass doesn’t change so how does the velocity know how big the volume is? And if you let a gas expand it cools and how does that happen?”

“A classic Jeremy question. Let’s take it a step at a time, big-picture view first. The Gas Law says pressure times volume is proportional to the amount of gas times the temperature, or P·V = n·R·T where n measures the amount of gas and R takes care of proportionality and unit conversions. Suppose a kid gets on an airplane with a balloon. The plane starts at sea level pressure but at cruising altitude they maintain cabins at 3/4 of that. Everything stays at room temperature, so the balloon expands by a third –“

Kid drawing of an airplane with a red balloon
Adapted from a drawing by Xander

“Wait … oh, pressure down by 3/4, volume up by 4/3 because temperature and n and R don’t change. OK, I’m with you. Now what?”

“Now the plane lands at some warm beach resort. We’re back at sea level but the temp has gone from 68°F back home to a basky 95°F. How big is the balloon? I’ll make it easy for you — 68°F is 20°C is 293K and 95°F is 35°C is 308K.”

“Volume goes up by 308/293. That’s a change of 15 in about 300, 5% bigger than back home.”

“Nice estimating. One more stop on the way to the molecular level. Were you in the crowd at Change-me Charlie’s dark matter debate?”

“Yeah, but I didn’t get close to the table.”

“Always a good tactic. So you heard the part about pressure being a measure of energy per unit of enclosed volume. What does that make each side of the Gas Law equation?”

“Umm, P·V is energy per volume, times volume, so it’s the energy inside the balloon. Oh! That’s equal to n·R·T but R‘s a constant and n measures the number of molecules so T = P·V/n·R makes T proportional to average kinetic energy. But I still don’t see why the molecules speed up when you squeeze on them. That just packs the same molecules into a smaller volume.”

“You’re muddling cause and effect. Let’s try to tease them apart. What forces determine the size of the balloon?”

“I guess the balance between the outside pressure pushing in, versus the inside molecules pushing out by banging against the skin. Increasing their temperature means they have more energy so they must bang harder.”

“And that increases the outward pressure and the balloon expands until things get back into balance. Fine, but think about individual molecules, and let’s pretend that we’ve got a perfect gas and a perfect balloon membrane — no leaks and no sticky collisions. A helium-filled Mylar balloon is pretty close to that. When things are in balance, molecules headed outward approach the membrane with some velocity v and bounce back inward with the same velocity v though in a different direction. Their kinetic energy before hitting the membrane is ½m·v²; after the collision the energy’s also ½m·v² so the temperature is stable.”

“But that’s at equilibrium.”

“Right, so let’s increase the outside pressure to squeeze the balloon. The membrane closes in at some speed w. Out-bound molecules approach the membrane with velocity v just as before but the membrane’s speed boosts the bounce. The ‘before’ kinetic energy is still ½m·v² but the ‘after’ value is bigger: ½m·(v+w)². The total and average kinetic energy go up with each collision. The temperature boost comes from the energy we put into the squeezing.”

“So the heating actually happens out at the edges.”

“Yup, the molecules in the middle don’t know about it until hotter molecules collide with them.”

“The last to learn, eh?.”

“Always the case.”

~~ Rich Olcott

Thanks to Mitch Slevc for the question that led to this post.

Seesaw to The Stars

I look around the playground. “Where’s the seesaw, Teena?”

“They took it away. That’s good ’cause I hated that thing!”

“Why’s that, Sweetie?”

“I never could play right on it. Almost never. Sometimes there’d be a kid my size on the other end and that worked OK, but a lot of times a big kid got on the other end and bounced me up in the air. The first time I even fell off and they laughed.”

“Well, I can understand that. I’m sure you’ve been nicer than that to the littler kids.”

“Uh-huh, except for Bratty Brian, but he liked it when I bounced him. He called it ‘going to the Moon’.”

“I can understand that, too. If things go just right you come off your seat and float like an astronaut for a moment. I bet he held onto the handles tight.”

“Yeah, I just wasn’t ready for it the first time.”

“Y’know, there’s another way that Brian’s bounces were like a rocket trip to somewhere. They went through the same phases of acceleration and deceleration.”

“Uncle Sy, you know you’re not allowed to use words like that around me without ‘splaining them.”

“Mmm, they both have to do with changing speed. Suppose you’re standing still. Your speed is zero, right? When you start moving your speed isn’t zero any more and we say you’ve accelerated. When you slow down again we say you’re decelerating. Make sense?”

“So when Bratty Brian gets on the low end of the seesaw he’s zero. When I squinch down at my end he accelerates –“

“Right, that’s like the boost phase of a rocket trip.”

“… And when he’s floating at the very top –“

“Like astronauts when they’re coasting, sort of but not really.”

“… And then they decelerate when they land. Bratty Brian did, too. I guess deceleration is like acceleration backwards. But why such fancy words?”

“No-one paid much attention to acceleration until Mr Newton did. He changed Physics forever when he said that all accelerations involve a force of some kind. That thought led him to the whole idea of gravity as a force. Ever since then, when physicists see something being accelerated they look for the force that caused it and then they look for what generated the force. That’s how we learned about electromagnetism and the forces that hold atoms together and even dark matter which is ultra-mysterious.”

“Ooo, I love mysteries! What did Mr Newton tell us about this one?”

“Nothing, directly, but his laws gave us a clue about what to look for. Tell me what forces were in play during Brian’s ‘moon flight’.”

“Let’s see. He accelerated up and then he accelerated down. I guess while he was on the seesaw seat at the beginning the up-acceleration came from an up-force from his end of the board. And the down-acceleration came from gravity’s force. But the gravity force is there all along, isn’t it?”

“Good point. What made the difference is that your initial force was greater than gravity’s so Brian went up. When your force stopped, gravity’s force was all that mattered so Brian came back down again.”

“So it’s like a tug-of-war, first I won then gravity won.”

“Exactly. Now how about the forces when you were on the merry-go-round?”

“OK. Gravity’s always there so it was pulling down on me. The merry-go-round was pushing up?”

“Absolutely. A lot of people think that’s weird, but whatever we stand on pushes up exactly as hard as gravity pulls us down. Otherwise we’d sink into the ground or fly off into space. What about other forces?”

“Oh, yeah, Mr Newton’s outward force pushed me off until … holding the handles made the inward force to keep me on!”

“Nice job! Now think about a galaxy, millions of stars orbiting around like on a merry-go-round. They feel an outward force like you did, and they feel an inward force from gravity so they all stay together instead of flying apart. But…”

“But?”

“Mr Newton’s rules tell us how much gravity the stars need to stay together. The astronomers tell us that there aren’t enough stars to make that much gravity. Dark matter supplies the extra.”

~~ Rich Olcott

Conversation of Energy

Teena’s next dash is for the slide, the high one, of course. “Ha-ha, Uncle Sy, beat you here. Look at me climbing up and getting potential energy!”

“You certainly did and you certainly are.”

“Now I’m sliding down all kinetic energy, wheee!” <thump, followed by thoughtful pause> “Uncle Sy, I’m all mixed up. You said momentum and energy are like cousins and we can’t create or destroy either one but I just started momentum coming down and then it stopped and where did my kinetic energy go? Did I break Mr Newton’s rule?”

“My goodness, those are good questions. They had physicists stumped for hundreds of years. You didn’t break Mr Newton’s Conservation of Momentum rule, you just did something his rule doesn’t cover. I did say there are important exceptions, remember.”

“Yeah, but you didn’t say what they are.”

“And you want to know, eh? Mmm, one exception is that the objects have to be big enough to see. Really tiny things follow quantum rules that have something like momentum but it’s different. Uhh, another exception is the objects can’t be moving too fast, like near the speed of light. But for us the most important exception is that the rule only applies when all the energy to make things move comes from objects that are already moving.”

“Like my marbles banging into each other on the floor?”

“An excellent example. Mr Newton was starting a new way of doing science. He had to work with very simple systems and and so his rules were very simple. One Sun and one planet, or one or two marbles rolling on a flat floor. His rules were all about forces and momentum, which is a combination of mass and speed. He said the only way to change something’s momentum was to push it with a force. Suppose when you push on a marble it goes a foot in one second and has a certain momentum. If you push it twice as hard it goes two feet in one second and has twice the momentum.”

“What if I’ve got a bigger marble?”

“If you have a marble that’s twice as heavy and you give it the one-foot-per-second speed, it has twice the momentum. Once there’s a certain amount of momentum in one of Mr Newton’s simple systems, that’s that.”

“Oh, that’s why I’ve got to snap my steelie harder than the glass marbles ’cause it’s heavier. Oh!Oh!And when it hits a glass one, that goes faster than the steelie did ’cause it’s lighter but it gets the momentum that the steelie had.”

“Perfect. You Mommie will be so proud of you for that thinking.”

“Yay! So how are momentum and energy cousins?”

“Cous… Oh. What I said was they’re related. Both momentum and kinetic energy depend on both mass and speed, but in different ways. If you double something’s speed you give it twice the momentum but four times the amount of kinetic energy. The thing is, there’s only a few kinds of momentum but there are lots of kinds of energy. Mr Newton’s Conservation of Momentum rule is limited to only certain situations but the Conservation of Energy rule works everywhere.”

“Energy is bigger than momentum?”

“That’s one way of putting it. Let’s say the idea of energy is bigger. You can get electrical energy from generators or batteries, chemical energy from your muscles, gravitational energy from, um, gravity –“

“Atomic energy from atoms, wind energy from the wind, solar energy from the Sun –“

“Cloud energy from clouds –“

“Wait, what?”

“Just kidding. The point is that energy comes in many varieties and they can be converted into one another and the total amount of energy never changes.”

“Then what happened to my kinetic energy coming down the slide? I didn’t give energy to anything else to make it start moving.”

“Didn’t you notice the seat of your pants getting hotter while you were slowing down? Heat is energy, too — atoms and molecules just bouncing around in place. In fact, one of the really good rules is that sooner or later, every kind of energy turns into heat.”

“Big me moving little atoms around?”

“Lots and lots of them.”

~~ Rich Olcott

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