# Disentangling 3-D Plaid

Our lake-side jog has slowed to a walk and suddenly Mr Feder swerves off the path to thud onto a park bench. “I’m beat.”

Meanwhile, heavy footsteps from behind on the gravel path and a familiar voice. “Hey, Sy, you guys talking physics?”

“Well, we were, Vinnie. Waves, to be exact, but Feder’s faded and anyway his walk wasn’t fast enough to warm me up.”

“I’ll pace you. What’d I miss?”

“Not a whole lot. So many different kinds of waves but physicists have abstracted them down to a common theme — a pattern that moves through space.”

“Haw — flying plaid.”

“That image would work if each fiber color carried specific values of energy and momentum and the cross-fibers somehow add together and there’s lots of waves coming from all different directions so it’s 3-D.”

“Sounds complicated.”

“As complicated as the sound from a symphony.”

“I prefer dixieland.”

“Same principle. Trumpet, trombone, clarinet, banjo — many layers of harmony but you can choose to tune in on just one line. That’s a clue to how physicists un-complicate waves.”

“How so?”

“Back in the early 19th century, Fourier showed that you can think about any continuous variation stream, no matter how complicated, in terms of a sum of very simple variations called sine waves. You’ve seen pictures of a sine wave — just a series of Ss laid on their sides and linked together head-to-tail.”

“Your basic wiggly line.”

“Mm-hm, except these wiggles are perfectly regular — evenly spaced peaks, all with the same height. The regularity is why sine waves are so popular. Show a physicist something that looks even vaguely periodic and they’ll immediately start thinking sine wave frequencies. Pythagoras did that for sound waves 2500 years ago.”

“Nah, he couldn’t have — he died long before Fourier.”

“Good point. Pythagoras didn’t know about sine waves, but he did figure out how sounds relate to spatial frequencies. Pluck a longer bowstring, get a lower note. Pinch the middle of a vibrating string. The strongest remaining vibration in the string sounds like the note from a string that’s half as long. Pythagoras worked out length relationships for the whole musical scale.”

“You said ‘spacial frequency’ like there’s some other kind.”

“There is, though they’re closely related. Your ear doesn’t sense the space frequency, the distance between peaks. You sense the time between peaks, the time frequency, which is the space frequency, peaks per meter, times how fast the wave travels, meters per second. See how the units work out?”

“Cute. Does that space frequency/time frequency pair-up work for all kinds of waves?”

“Mostly. It doesn’t work for standing waves. Their energy’s trapped between reflectors or some other way and they just march in place. Their time frequency is zero peaks per second whatever their peaks per meter space frequency may be. Interesting effects can happen if the wave velocity changes, say if the wave path crosses from air to water or if there’s drastic temperature changes along the path.”

“Hah! Mirages! Wait, that’s light getting deflected after bouncing off a hot surface into cool air. Does sound do mirages, too?”

“Sure. Our hearing’s not sharp enough to notice sonic deflection by thermal layering in air, but it’s a well-known issue for sonar specialists. Echoes from oceanic cold/warm interfaces play hob with sonar echolocation. I’ll bet dolphins play games with it when the cold layer’s close enough to the surface.”

“Those guys will find fun in anything. <pause> So Pythagoras figured sound frequencies playing with a bow. Who did it for light?”

“Who else? Newton, though he didn’t realize it. In his day people thought that light was colorless, that color was a property of objects. Newton used the rainbow images from prisms to show that color belonged to light. But he was a particle guy. He maintained that every color was a different kind of particle. His ideas held sway for over 150 years until Fresnel convinced the science community that lightwaves are a thing and their frequencies determine their color. Among other things Fresnel came up with the math that explained some phenomena that Newton had just handwaved past.”

“Fresnel was more colorful than Newton?”

“Uh-uh. Compared to Newton, Fresnel was pastel.”

~~ Rich Olcott

# Wave As You Go By

A winter day, a bit nippy and windy enough to raise scattered whitecaps on the park lake. Apparently neither the geese nor Mr Richard Feder (of Fort Lee, NJ) enjoy that — the geese are standing on the shore and he’s huddled down on a bench as I pass. “Hey Moire, I gotta question.”

“Mr Feder. I’m trying to keep warm. If you want answers you’ll have to jog along.”

“Oh, alright <oof>. OK, watching those waves got me thinking. They keep going because the wind pushes on ’em, right? So what pushes on sound waves and light waves? If something pushes hard enough on a sound wave does it speed up enough to be a light wave?”

“So many questions. Are you sure you’ve got enough wind?”

“Ha, ha. I’ve been working out a little.”

“We’ll see. Well, first, nothing needs to push on a wave once it’s started. They travel on their own momentum.”

“Then why do these waves die away when the wind stops?”

“You’ve got two things going on there, on different time scales. When the wind stops blowing it stops making new waves. Actually, winds rarely stop all at once, they taper off. It looks like waves are dying away but really you just see smaller and smaller waves. Inside a single wave, though, friction takes its toll.”

“Friction? Waves rub against each other? That’s not what’s going on here — they keep their distance unless different groups run crosswise and then they all just keep going.”

“Not friction between waves, friction within a wave. There’s a lot of turbulence inside a water wave — the wind piles up surface molecules on one side, gravity and surface tension move the other side’s molecules downward, and the ones inside are pulled in every direction. All that helter-skelter motion randomizes the wave’s momentum and converts the wave’s energy to heat. When that’s gone, the wave’s gone.”

“So how’s sound different from that?”

“Lots of ways. To begin with, wind and gravity move molecules up and down perpendicular to the wave’s direction of travel. Sound waves aren’t affected by gravity. They move molecules back and forth parallel to the wave’s direction.”

“But they still die out, right? Turn to heat and all that?”

“Absolutely, Mr Feder. How fast a wave dies out depends on what heat-conversion processes are in play. In a water wave gravity and surface tension work together to smooth things out. Neither’s active in sound waves. The only way a sound wave can lose energy is through random collisions between molecules that aren’t in sync with the wave. Could be the wave hits a mushy object or maybe it just gets buried in other waves.”

“Like at a football game, when everyone’s shouting but all you hear is the roar.”

“Pretty good example, Mr Feder.”

“So how’s a light wave different?”

“Light waves don’t even need molecules. The electromagnetic field near a particle is the net effect of all the attractions and repulsions it feels from all other charged particles everywhere in the Universe. When some charged particle somewhere moves, that changes the field. The change is transmitted throughout the field as a wave traveling at the speed of light.”

“What makes it die away?”

“It doesn’t. On a dark, clear night your eyes can see stars a quintillion miles away. Astronomers with their instruments can detect objects millions of times further away.”

“No smoothing out? How come?”

“That’s a very deep question, Mr Feder, one that really bothered Einstein. You’d think a photon’s wave would get fainter the further it spreads. In fact, it delivers all its energy to the first charged particle it can interact with, no matter how far it had traveled. Weird, huh?”

“Weird, all right. So we got these three very different things — they start different, they push different, they got different speeds, they die different, but we call them all waves. Why’s that?”

“They’re all waves because they’re all patterns that transmit energy and momentum across space. Physicists have found general rules that apply to the patterns, whatever the wave type. Equations that work for one kind work for many others, too.”

“And gravitational waves.”

~~ Rich Olcott

# A Mole’s Tale

Chilly days are always good for a family trip to the science museum. Sis is interested in the newly unearthed dinosaur bones, but Teena streaks for the Space Sciences gallery. “Look, Uncle Sy, it’s a Mars rover. No, wait — it doesn’t have wheels — it’s a lander!”

A nearby museum docent catches that. “Good observing, young lady. You’re right, it’s NASA’s Insight lander. It touched down on Mars last Thanksgiving Day. While you were having turkey and dressing, we were having a party over here.”

“Is this the real one? How’d you get it back?”

“No, it’s just a model, but it’s full-size, 19½ feet across. We’re never going to get the real one back — those little bitty landing rockets you see around the electronics compartment are too small to get it off the planet.”

“Tronics compartment? You mean the pretty gold box underneath the flat part? Why’d they make it gold?”

“That gold is just the outside layer of a dozen layers of Mylar insulation. It helped to keep the computers in there cool during the super-hot minutes when the lander was coming down through Mars atmosphere. The insulation also keeps the electronics warm during the cold martian night. A thin gold coating on the outermost layer reflects the bad part of sunlight that would crumble the Mylar.”

“Computers like Mommie’s laptop? I don’t see any screens.”

“They don’t need any. No-one’s on Mars to look at them. The instructions all come in from Earth by radio.”

Sis is getting into it. “Look, Sweetie, the platform in the middle’s about the same size as our kitchen table.”

“Yeah, but it’s got butterfly wings. A flying kitchen table, whee!”

“Those wings are solar panels. They turn sunlight into the electricity Insight needs to run things and keep warm. They make enough power for three households here on Earth.”

“What’s the cake box about?”

“Cake box?”

“Yeah, down there on the floor.”

“Ah. That’s for … have you ever experienced an earthquake?”

“Yes! Suddenly all the dishes in the cupboard went BANG! It was weird but then everything was fine.”

“I’m glad. OK, an earthquake is when vibrations travel through the Earth. Vibrations can happen on Mars, too, but they’re called…”

“Marsquakes! Ha, that’s funny!”

“Mm-hm. Well, that ‘cake box’ is something called a seismometer. It’s an extremely sensitive microphone that listens for even the faintest vibrations. When scientists were testing the real seismometer in Boulder, Colorado it recorded a steady pulse … pulse … pulse … that they finally traced back to ocean waves striking the coast of California, 1200 miles away. Insight took it to Mars and now it’s listening for marsquakes. It’s already heard a couple dozen. They’ve given the scientists lots of new information about Mars’ crust and insides.”

“Like an X-ray?”

“Just like that. We’ll be able to tell if the planet’s middle is molten–“

“Hot lava! Hot lava!”

“Maybe. Earth has a lot of underground lava, but we think that Mars has cooled off and possibly doesn’t have any. That other device on the ground is supposed to help find out.”

“It looks like The Little Engine That Could.”

“It does, a little, but this one maybe can’t. We’re still waiting to see. That chimney-looking part held The Mole, a big hollow spike with something like a thermometer at its pointy tip. Inside The Mole there’s a hammer arrangement. The idea was that the hammer would bang The Mole 15 feet into the ground so we could take the planet’s temperature.”

“Did the banging work?”

“It started to, but The Mole got stuck only a foot down. The engineers have been working and working, trying different ways to get it down where we want it but so far it’s still stuck.”

“Aww, poor Mole.”

“Yes. But there’s another neat instrument up on the platform. Here, I’ll shine my laser pointer at it. See the grey thingy?”

“Uh-huh.”

“That’s a weather station for temperature and wind. You can check its readings on the internet. Here, my phone’s browser’s already set to mars.nasa.gov/insight/weather. Can you read the high and low temperatures?”

“Way below zero! Wow, Mars is chilly! I’d need a nice, warm spacesuit there.”

“For sure.”

~~ Rich Olcott

# A Wheel in A Wheel

The conversation’s gotten a little dry so I carry our mugs over to Al’s coffee tap for refills. Vinnie’s closest so he gets the first one. “Thanks, Sy. So you say that a black hole has all these other things on the outside — the photon sphere and that weird belt if it’s rotating and the accretion disk and the jets which is what I asked about in the first place.”

Astrophysicist-in-training Newt Barnes gets the second mug. “My point, Vinnie, is they all act together. You can’t look at just one thing. Thanks, Sy. You know, you should’ve paid more attention to the ergosphere.”

“Ergosphere?”

“Yeah, Vinnie, that pumpkin-shaped layer Sy described — actually, more a pumpkin shell. The event horizon and photon sphere take up space inside of it and the accretion disk’s inner edge grazes its equator. The pumpkin is fatter for a more rapidly rotating black hole, but its boundary still dips down to meet the event horizon at the rotational poles. Diagrams usually show it just sitting there but that’s not quite true.”

“It wobbles?”

“No, the shape stays in place, locked to the event horizon just like the diagrams show. What’s inside it, though, is moving like mad. That’s what we’d see from a far-away frame, anyhow.”

Frames again, I knew it. The pumpkin’s got frames?”

“With extreme-gravity situations it’s always frames, Vinnie. The core’s gravity pulls in particles from the accumulation disk. They think they’re going straight. From an outsider’s perspective everything swerves spinwise at the ergosphere’s boundary. Even if a high-speed particle had been aimed in the other direction, it’s going spinwise once it’s inside the ergosphere.”

“Who’s making it do that?”

“Frame-dragging on steroids. We’ve known for a century that gravity from any massive body compresses the local space. ‘Kilometers are shorter near a black hole,’ as the saying goes. If the body is rotating, that counts too, at least locally — space itself joins the spin. NASA’s Gravity B probe detected micromicrodegree-level frame rotation around Earth. The ergosphere, though, has space is twisted so far that the direction of time points spinwise in the same way that it points inwards within the event horizon. Everything has to travel along time’s arrow, no argument.”

“You said ‘local‘ twice there. How far does this spread?”

“Ah, that’s an important question. The answer’s ‘Not as far as you think.’ Everything scales with the event horizon’s diameter and that scales with the mass. If the Sun were a non-rotating black hole, for instance, its event horizon would be only about 6 kilometers across, less than 4 miles. Its photon sphere would be 4.5 kilometers out from the center and the inner edge of its accretion disk would be a bit beyond that. Space compression dies out pretty quick on the astronomical scale — only a millionth of the way out to the orbit of Mercury the effect’s down to just 3% of its strength at the photosphere.”

“How about if it’s rotating?”

“The frame-dragging effect dies out even faster, with the cube of the distance. At the same one-millionth of Mercury’s orbit, the twist-in-space factor is 0.03% of what it is at the photosphere. At planet-orbit distances spin’s a non-player. However, in the theory I’m researching, spin’s influence may go much further.”

“Why’s that?”

“Seen from an outside frame, what’s inside the ergosphere rotates really fast. Remember that stuff coming in from the accretion disk’s particle grinder? It ought to be pretty thoroughly ionized, just a plasma of negative electrons and positive particles like protons and atomic nuclei. The electrons are thousands of times lighter than the positive stuff. Maybe the electrons settle into a different orbit from the positive particles.”

“Further in or further out?”

“Dunno, I’m still calculating. Either way, from the outside it’d look like two oppositely-charged disks, spinning in the same direction. We’ve known since Ørsted that magnetism comes from a rotating charge. Seems to me the ergosphere’s contents would generate two layers of magnetism with opposite polarities. I think what keeps the jets confined so tightly is a pair of concentric cylindrical magnetic fields extruded from the ergosphere. But it’s going to take a lot of math to see if the idea holds water.”

“Or jets.”

~~ Rich Olcott

# The Jet and The Plane

“OK, Sy, I get your point about a black hole being more than a mystical event horizon hiding whatever’s inside it. I’ll give you it’s a structure with a trapped-light shell and a pumpkin-donut belt around that –“

“… if it’s rotating, Vinnie…”

“– if it’s rotating, but what does all that have to do with those huge jets coming out of the poles instead of the equator where they belong?”

Suddenly Newt Barnes, astrophysicist in training, is standing by our table. “You guys are talking my research topic, just the hottest thing in astrophysics these days. Those jets were the subject of over a thousand papers last year. Mind if I sit in?”

“Of course not.” “We’re all ears.”

“Well, there’s a couple more layers to peel before we can make a maybe connection. Vinnie, what’s the weirdest thing about those jets?”

“Like I said, they’re huge — millions of lightyears long.”

“True, but other structures are huge, too — galaxy superclusters, for instance. The real weirdness is how narrow the jets are — less than a degree wide, and they’ve maintained that tight geometry while they’ve grown for millions of years. We still don’t know what’s in a jet. If it’s a beam of charged particles you’d think they’d repel each other and spread out almost immediately. If the particles are uncharged they’d bang into each other and into the prevailing interstellar medium. Random collisions would spread the beam out maybe a little slower than a charged-particle beam but still. A photon beam would be more stable but you’d need a really good collimating mechanism at the jet’s base to get the waves all marching so precisely.”

“What’s left, dark matter?”

“Almost certainly not. Many jets emit huge quantities of electromagnetic radiation at all frequencies from radio up through X-rays and beyond. Dark matter doesn’t do electromagnetism. No, jets are somehow created from normal stuff. The question is, how is it kept under such tight control?”

“The other question is, where’s all that stuff coming from if nothing can escape outta the event horizon?”

“Ah, that has to do with yet another part of the structure — the accretion disk.”

“What they got that orange picture of, right? Big ring like Saturn’s.”

“Well, similar shape, but different origin, different composition and very different dynamics. Saturn’s rings are mostly water-ice, built up from the debris of ice-moons that collided or were pulled apart by tidal forces. A black hole’s accretion disk is made up of planets, dust particles, atoms, whatever junk was unfortunate enough to be too close when the black hole passed by. Pick any incoming object and call it Freddie. Unless Freddie and the event horizon’s core are on an exact collision course, Freddie gets swept up by the disk.”

“Then what happens?”

“Freddie collides with something already in the disk. Lots of somethings. Each collision does two things. One, Freddie and the something break into smaller pieces. Two, some of Freddie’s gravitational potential energy relative to the core is converted to heat, making the collision debris package hotter than Freddie and the something were to begin with. After a while, Freddie gets ground down to atoms or smaller and they’re all really hot, radiating intensely just like Planck and Einstein said they would.”

“So we got a ring like Saturn’s, like I said.”

“Only sort of. Saturn has half-a-dozen distinct rings. They shine by reflected sunlight, the middle ring is brightest and broadest, and the innermost ring is dark and skinny. Our only direct accretion disk image so far is a one blurry view, but the object shines with its own light and in theory the disk isn’t segmented. There should be just one ring and it’d be brightest at a sharp inner edge.”

“Why’s that?”

“The light’s produced by hot particles. Heat generation’s most intense where the gravity well is steepest. That’s nearest the core. For a non-spinning black hole the threshold is one-sixth of the horizon’s diameter. If Freddie gets knocked the slightest bit closer than that it’s doomed to fall the rest of the way in. The edge is closer-in if the hole’s rotating but then Freddie has an interesting time. Relatively.”

“Gonna be frames again, right?”

“Yeah.”

~~ Rich Olcott

# Beyond The Shadow of A…?

“Alright, Vinnie, what’s the rest of it?”

“The rest of what, Sy?”

“You wouldn’t have hauled that kid’s toy into Al’s shop here just to play spitballs with it. You’re building up to something and what is it?”

“My black hole hobby, Sy. The things’re just a few miles wide but pack more mass than the Sun. A couple of my magazines say they give off jets top and bottom because of how they spin. That just don’t fit. The stuff ought to come straight out to the sides like the paper wads did.”

“Well, umm… Ah. You know the planet Saturn.”

“Sure.”

“Are its rings part of the planet?”

“No, of course not, they go around it. I even seen an article about how the rings probably came from a couple of collided moons and how water from the Enceladus moon may be part of the outside ring. Only thing Saturn does for the rings is supply gravity to keep ’em there.”

“But our eyes see planet and rings together as a single dot of light in the sky. As far as the rest of the Solar System cares, Saturn consists of that big cloudy ball of hydrogen and the rings and all 82 of its moons, so far. Once you get a few light-seconds away, the whole collection acts as a simple point-source of gravitational attraction.”

“I see where you’re going. You’re gonna say a black hole’s more than just its event horizon and whatever it’s hiding inside there.”

“Yup. That ‘few miles wide’ — I could make a case that you’re off by trillions. A black hole’s a complicated beast when we look at it close up.”

“How can you look at a thing like that close up?”

“Math, mostly, but the observations are getting better. Have you seen the Event Horizon Telescope’s orange ring picture?”

“You mean the one that Al messed with and posted for Hallowe’en? It’s over there behind his cash register. What’s it about, anyway?”

“It’s an image of M87*, the super-massive black hole at the center of the M87 galaxy. Not the event horizon itself, of course, that’s black. The orange portion actually represents millimeter-radio waves that escape from the accretion disk circling the event horizon. The innermost part of the disk is rotating around the hole at near-lightspeed. The arc at the bottom is brighter because that’s the part coming toward us. The photons get a little extra boost from Special Relativity.”

Frames again?”

“With black holes it’s always frames. You’ll love this. From the shell’s perspective, it spits out the same number of photons per second in every direction. From our perspective, time is stretched on the side rotating away from us so there’s fewer photons per one of our seconds and it’s dimmer. In the same amount of our time the side coming toward us emits more photons so it’s brighter. Neat demonstration, eh?”

“Cute. So the inner black part’s the hole ’cause it can’t give off light, right?”

“Not quite. That’s a shadow. Not a shadow of the event horizon itself, mind you, but of the photon sphere. That’s a shell about 1½ times the width of the event horizon. Any photon that passes exactly tangent to the sphere is doomed to orbit there forever. If the photon’s path is the slightest bit inward from that, the poor particle heads inward towards whatever’s in the center. The remaining photons travel paths that look bent to a distant observer, but the point is that they keep going and eventually someone like us could see them.”

“The shadow and the accretion disk, that’s what the EHT saw?”

“Not exactly.”

“There’s more?”

“Yeah. M87* is a spinning black hole, which is more complicated than one that’s sitting still. Wrapped around the photon sphere there’s an ergosphere, as much as three times wider than the event horizon except it’s pumpkin-shaped. The ergosphere’s widest at the rotational equator, but it closes in to meet the event horizon at the two poles. Anything bigger than a photon that crosses its boundary is condemned to join the spin parade, forever rotating in sync with the object’s spin.”

“When are you gonna get to the jets, Sy?”

~~ Rich Olcott

# Never Chuck Muck at A Duck

Mr Richard Feder of Fort Lee NJ is in terrible shape. Barely halfway into our walk around the park’s lake, he flops onto a bench to catch his breath. The geese look on unsympathetically. “<puff, puff> I got another question, Moire. <wheeze> Why is water wet?”

He’s just trying to make conversation while his heart slows down but I take him up on it. “Depends on what you mean by ‘wet‘ — that’s a slippery word, can be a verb or an adjective or a noun. If you wet something, you’ve got a wet something. If there’s wet weather you go out in the wet. If you live in a wet jurisdiction you can buy liquor if you’re old enough. You can even have wet and dry molecules. Which are you asking about?”

That’s gotten him thinking, always a good sign. “Let’s start with the verb thing. Seems like that’s the key to the others.”

“So we’re asking, ‘Does water wet?‘ The answer is, ‘Sometimes,‘ and that’s where things get interesting. That duck over there, diving for something on the bottom, but when it comes back up again the water rolls off it like –“

“Don’t say it — ‘like water off a duck’s back‘ — yeah, I know, but I’m sweating over here and that ain’t rolling off. Why the difference?”

“Blame it on the Herence twins, Co and Addie.”

“Come again?”

“A little joke, has to do with two aspects of stickiness. Adherence is … you know adhesive tape?”

“Adhe — you playin’ word games, Moire?”

“No, really, adhesive and adherence are both about sticking together things that are chemically different, like skin and tape. Coherence is about stickiness between things that are chemically similar, like sweat and skin.”

“What makes things ‘chemically similar’?”

“Polarity. I don’t want to get into the weeds here –“

“Better not, the ground’s squishy over there.”

“– but there are certain pairs of atoms, like oxygen and hydrogen, where one atom pulls a small amount of electron charge away from the other and you wind up with part of a molecule being plus-ish and another part being minus-ish. That makes the molecule polar. Other pairings, like carbon and hydrogen, are more evenly matched. You don’t get charge separation from them and we call that being non-polar. Charge variation in polar molecules forces them to cluster together positive-to-negative. The electrostatic gang crowds out any nearby non-polar molecules.”

“What’s all that got to do with wetting?”

“Water’s all oxygen and hydrogen and quite polar. Water coheres to itself. If it didn’t you’d get rain-smear instead of raindrops. It also adheres to polar materials like skin and hair and bricks, so raindrops wet them. But it doesn’t adhere to non-polar materials like oil and wax. Duck feathers are oily so they shed water.”

“So that’s why the duck doesn’t get wet!”

“Not unless you throw detergent on him, like they have to do with waterfowl after an oil spill. Detergent molecules have a polar end and a non-polar end so they can bridge the electro divide. Rubbing detergent into a dirty bird’s sludgy oil coating lets water sink into the mess and break it up so you can rinse it off. The problem is that the detergent also washes off the good duck oil. If you let a washed-off duck go swimming too soon after his bath the poor thing will sink. You have to give him time to dry off and replenish his natural feather-oil.”

“Hey, you said ‘wet-and-dry molecules.’ How can they be both?”

“Because they’re really big, thousands of atoms if they’re proteins, even bigger for other kinds of polymers. Anything that large can have patches that are polar and other patches that are oily. In fact, patchwise polarity is critical to how proteins get their 3-D structure and do their jobs. A growing protein strand wobbles around like a spring-toy puzzle until positive bits match up with negative bits and oily meets up with oily. Probably water molecules sneak into the polar parts, too. The configuration’s only locked down when everything fits.”

“So water’s wet because water wets water. Hah!”

~~ Rich Olcott

• Thanks to Museum visitor Jessie for asking this question.

# Eyes on The Size

An excellent Fall day, perfect for a brisk walk around the park’s goose-governed lake. Suddenly there’s a goose-like yawp behind me. “Hey Moire, wait up, I got a question!”

“Afternoon, Mr Feder. What’s your question today?”

“You know how the Moon’s huge just after it gets over the horizon but then it gets small? How do they make it do that?”

“Well, ‘they’ is you, Mr Feder, except that nothing physically changes.”

“Whaddaya mean, I seen it change size every time there’s a full moon.”

“That’s what it looks like, but think it through. We’re here in the Midwest, two hours away from your folks back home in Fort Lee. Back when you lived there, did the Moon ever suddenly grow and then shrink when it was two hours up into the sky?”

“Um, no, just at the horizon. So you’re saying it’s one of them optical delusions?”

“Something like that. Here, I’ve got a video on Old Reliable. See how the disk stays the same size but it looks bigger in comparison to the railroad tracks? Your brain expects the tracks to be parallel lines despite the perspective, right, so it compensates by thinking the Moon must be wider when it’s next to them. In the real world you’ve looking at the Moon past trees or buildings, but the false perspective principle applies whether the horizon’s relatively close or far away.”

“Whaddaya mean, close or far horizon? It’s the edge of how far I can see and that’s always the same.”

“Oh, hardly, Mr Feder. You ever visit the Empire State Building’s observation deck?”

“Sure.”

“How about deep-sea fishing, out of sight of land?”

“Aw, that’s a blast, when you hook one of those big guys and you’re –“

“I’m sure you enjoyed it, but did you look around while you were waiting for a strike?”

“Yeah, nothin’ else to do but yammer and drink beer.”

“Mm-hm. So could you see as far from the boat’s deck as you could from the building’s deck?”

“Hey, you’re right. A lot farther from high up. They say on a clear day you can see 80 miles from the Empire State Building — nowhere near that from the boat, believe me. ‘S why they put those decks up there, I guess. How far up do I gotta be to see the whole world, I wonder.”

“Quick answer is, infinitely far away.”

“Wait, those astronauts got that ‘Blue Marble’ picture from the Moon and it showed the whole day side.”

“Take a closer look someday. It shows Antarctica but essentially nothing north of the 45th parallel. The limit’s set by the points on the planet where lines from your eye just graze the planet’s surface. The astronauts in this LEM, for instance, are about an Earth-radius away. They’d be able to see the Atlantic Ocean and a little bit of Brazil, but neither of the poles and no part of the USA.”

“Gimme a sec … yeah, I see how that works. So that ‘how high up you are‘ thing keeps going all the way out into space. There’s probably some complicated formula for it, right?”

“Not that complicated, just d=(h²+2Rh), where h is your height above the surface and R is the radius of the planet you’re looking at. Plug in the numbers and d gives you your distance to the horizon. For that LEM, for example, h is one Earth radius and R is one radius, so those straight lines are 3=1.73 Earth radii long.”

“How about the line on top of the ocean?”

“That’s a little more complicated.” <more tapping on Old Reliable> “Says here that line stretches exactly one-third of the Earth’s circumference.”

“You can do that with other planets?”

“Sure. Mars, for instance. It has the tallest volcano in the Solar System, Olympus Mons. Depending on where you’re measuring from it’s about 22 kilometers high. I’ll put that into the formula with Mars’ radius, 3389 kilometers, and … OK, if you’re standing on top, your horizon is 387 kilometers away. That’s like looking halfway across France. Mars’ big canyon Vallis Marinaris has 7-kilometer cliffs. There are places where the opposite wall is way beyond the cliff-top’s 96-mile horizon.”

“That beats the Empire State Building.”

~~ Rich Olcott

# Where would you put it all?

Vinnie’s a big guy but he’s good at fading into the background. I hadn’t even noticed him standing in the back corner of Cathleen’s impromptu seminar room until he spoke up. “That’s a great theory, Professor, but I wanna see numbers for it.”

“Which part of it don’t you like, Vinnie?”

“You made it seem so easy for all those little sea thingies to scrub the carbon dioxide out of Earth’s early atmosphere and just leave the nitrogen and oxygen behind. I mean, that’d be a lot of CO2. Where’d they put it all?”

“That’s a reasonable question, Vinnie. Lenore, could you put your Chemistry background to work on it for us?”

“Oh, this’ll be fun, but I don’t want to do it in my head. Mr Moire, could you fire up Old Reliable for the calculations?”

“No problem. OK, what do you want to calculate?”

“Here’s my plan. Rather than work with the number of tons of carbon in the whole atmosphere, I’ll just look at the sky-high column of air sitting on a square meter of Earth’s surface. We’ll figure out how many moles of CO2 would have been in that column back then and then work on how thick a layer of carbon stuff it would make on the surface. Does that sound like a good attack, Professor?”

“Sure, but I see a couple of puzzled looks in the class. You’d better say something about moles first.”

“Hey, I know about moles. Sy and me talked about ’em when he was on that SI kick. They’re like a super dozen, right, Sy?”

“Right, Vinnie. A mole of anything is 6.02×1023 of that thing. Eggs, atoms, gas molecules, even stars if that’d be useful.”

“Back to my plan. First thing is the CO2 was in that column back when. Maria, your chart showed that Venus’ atmospheric pressure is 100 times ours and Mars’ is 1/100 ours and each of them is nearly pure CO2, right? So I’m going to assume that Earth’s atmosphere was what we have now plus a dose of CO2 that’s the geometric mean of Venus and Mars. OK, Professor?”

“That’d be a good starting point, Lenore.”

“Good. Now we need the mass of that CO2, which we can get from the weight of the column, which we can get from the air pressure, which is what?”

Every car buff in the room, in chorus — “14½ pounds per square inch.”

“I need that in kilograms per square meter.”

“Strictly speaking, pressure’s in newtons per square meter. There’s a difference between weight and force, but for this analysis we can ignore that. Keep going, Lenore.”

“Thanks, Professor. Sy?”

“Old Reliable says 10194 kg/m².”

“So we’ve got like ten-thousand kilograms of CO2 in that really tall meter-square column of ancient air. Now divide that by, um, 44 to get the number of moles of CO2. No, wait, then multiply by 1000 because we’ve got kilograms and it’s 44 grams per mole for CO2.”

“232 thousand moles. Still sounds like a lot.”

“I’m not done. Now we take that carbon and turn it into coal which is solid carbon mostly. One mole of carbon from each mole of CO2. Take the 232 thousand moles, multiply by 12 grams, no make that 0.012 kilogram per mole –“

“2786 kilograms”

“Right. Density of coal is about 2 grams per cc or … 2000 kilograms per cubic meter. So. Divide the kilograms by 2000 to get cubic meters.”

“1.39 meters stacked on that square-meter base.”

“About what I guessed it’d be. Vinnie, if Earth once had a carbon-heavy atmosphere log-halfway between Venus and Mars, and if the sea-plankton reduced all its CO2 down to coal, it’d make a layer all over the planet not quite as tall as I am. If it was chalk it’d be thicker because of the additional calcium and oxygen atoms. A petroleum layer would be thicker, too, with the hydrogens and all, but still.”

Jeremy’s nodding vigorously. “Yeah. We’ve dug up some of the coal and oil and put it back into the atmosphere, but there’s mountains of limestone all over the place.”

Cathleen’s gathering up her papers. “Add in the ocean-bottom carbonate ooze that plate tectonics has conveyor-belted down beneath the continents over the eons. Plenty of room, Vinnie, plenty of room.”

~~ Rich Olcott

# The Moon And Chalk

Cathleen’s talking faster near the end of the class. “OK, we’ve seen how Venus, Earth and Mars all formed in the same region of the protosolar disk and have similar overall compositions. We’ve accounted for differences in their trace gasses. So how come Earth’s nitrogen-oxygen atmosphere is so different from the CO2-nitrogen environments on Venus and Mars? Let’s brainstorm — shout out non-atmospheric ways that Earth is unique. I’ll record your list on Al’s whiteboard.”

“Oceans!”

“Plate tectonics!”

“Photosynthesis!”

“Limestone!”

“The Moon!”

“Wombats!” (That suggestion gets a glare from Cathleen. She doesn’t write it down.)

“Goldilocks zone!”

“Magnetic field!”

“People!”

She registers the last one but puts parentheses around it. “This one’s literally a quickie — real-world proof that human activity affects the atmosphere. Since the 1900s gaseous halogen-carbon compounds have seen wide use as refrigerants and solvents. Lab-work shows that these halocarbons catalyze conversion of ozone to molecular oxygen. In the 1970s satellite data showed a steady decrease in the upper-atmosphere ozone that blocks dangerous solar UV light from reaching us on Earth’s surface. A 1987 international pact banned most halocarbon production. Since then we’ve seen upper-level ozone concentrations gradually recovering. That shows that things we do in quantity have an impact.”

“How about carbon dioxide and methane?”

“That’s a whole ‘nother topic we’ll get to some other day. Right now I want to stay on the Mars-Venus-Earth track. Every item on our list has been cited as a possible contributor to Earth’s atmospheric specialness. Which ones link together and how?”

Astronomer-in-training Jim volunteers. “The Moon has to come first. Moon-rock isotope data strongly implies it condensed from debris thrown out by a huge interplanetary collision that ripped away a lot of what was then Earth’s crust. Among other things that explains why the Moon’s density is in the range for silicates — only 60% of Earth’s density — and maybe even why Earth is more dense than Venus. Such a violent event would have boiled off whatever atmosphere we had at the time, so no surprise the atmosphere we have now doesn’t match our neighbors.”

Astrophysicist-in-training Newt Barnes takes it from there. “That could also account for why only Earth has plate tectonics. I ran the numbers once to see how the Moon’s volume matches up with the 70% of Earth’s surface that’s ocean. Assuming meteor impacts grew the Moon by 10% after it formed, I divided 90% of the Moon’s present volume by 70% of Earth’s surface area and got a depth of 28 miles. That’s nicely within the accepted 20-30 mile range for depth of Earth’s continental crust. It sure looks like our continental plates are what’s left of the Earth’s original crust, floating about on top of the metallic magma that Earth held onto.”

Jeremy gets excited. “And the oceans filled up what the continents couldn’t spread over.”

“That’s the general idea.”

Al’s not letting go. “But why does Earth have so much water and why is it the only one of the three with a substantial magnetic field?”

Cathleen breaks in. “The geologists are still arguing about whether Earth’s surface water was delivered by billions of incoming meteorites or was expelled from deep subterranean sources. Everyone agrees, though, that our water is liquid because we’re in the Goldilocks zone. The water didn’t steam away as it probably did on Venus, or freeze below the surface as it may have on Mars. Why the magnetic field? That’s another ‘we’re still arguing‘ issue, but we do know that magnetic fields protect Earth and only Earth from incoming solar wind.”

“So we’re down to photosynthesis and … limestone?”

“Photosynthesis was critical. Somewhere around two billion years ago, Earth’s sea-borne life-forms developed a metabolic pathway that converted CO2 to oxygen. They’ve been running that engine ever since. If Earth ever did have CO2 like Venus has, green things ate most of it. Some of the oxygen went to oxidizing iron but a lot was left over for animals to breathe.”

“But what happened to the carbon? Wouldn’t life’s molecules just become CO2 again?”

“Life captures carbon and buries it. Chalky limestone, for instance — it’s calcium carbonate formed from plankton shells.”

Jim grins. “We owe it all to the Moon.”

~~ Rich Olcott