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?”

Adopted from image by Immanuel Giel, CC BY-SA 3.0

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

Traces of Disparity

Cathleen’s an experienced teacher — she knows when off-topic class discussion is a good thing, and when to get back to the lesson plan. “My challenge question remains — why isn’t Earth’s atmosphere some average of the Mars and Venus ones? Thanks to Jeremy and Newt and Lenore we have reason to expect the planets to resemble each other, but in fact their atmospheres don’t. Maria, tell us what you’ve found about how Earth compares with the others.”

“Yes, Profesora. I found numbers for many of the gasses on each planet and put them into this chart. One thing Earth is right in the middle, most things not.”

“That’s a complicated chart. Read it out to us.”

“Of course. I had to make the vertical scales logarithmic to get the big numbers and small numbers on the same chart. First is the pressure which is the black dotted line. Venus pressure at the surface is nearly 100 times ours but Mars pressure is a bit less than 1/100th of ours. Does that count as Earth being in the middle?”

“That’d be a geometric average. It could be significant, we’ll see. Go on.”

“The gas that is almost the same everywhere is helium, the grey diamonds. That surprised me, because I thought the giant planets got all of that.”

Al’s been listening in. Nothing else going on in his coffee shop, I guess. “I’ll bet most of that helium came from radioactive rocks, not from space. Alpha particles, right, Cathleen?”

Cathleen takes unexpected interruptions in stride. “Bad bet, Al. Uranium and other heavy elements do emit alphas which pick up electrons to become helium atoms. You probably remembered Cleve and Langlet, who first isolated helium from uranium ore. However, the major source of atmospheric alphas is the solar wind. Solar wind interception and atmosphere mass are both proportional to planetary surface area so a constant concentration like this is reasonable. Continue, Maria.”

“The major gasses follow a pattern — about the same fractions on Venus and Mars but much higher or lower than on Earth. Look at carbon dioxide, nitrogen, even oxygen.”

Astronomer-in-training Jim has been doing some mental arithmetic. “Our atmosphere is 100 times denser than on Mars, and Venus is another factor of 100 beyond that. That’s a factor of 104 between them — for every molecule of CO2 on Mars there’s 10,000 on Venus. Oh, but Venus has four times Mars’ surface area so make that 40,000.”

“Good points, both of you. Jim’s approximation leads into something we can learn from Maria’s trace gas numbers. Why do you suppose the concentration of SO2 is about the same for Earth and Mars but 100 times higher on Venus, but the reverse is true for argon? Where do they each come from?”

Jeremy finally has something he can contribute. “Volcanoes! They told us in Geology class that most of our SO2 comes from volcanoes. Before the Industrial Revolution, I mean, when we started burning high-sulfur coal and fuel oils and made things worse. Venus has to be the same. Except for the industry, of course.”

“Probably correct, Jeremy. From radar mapping of Venus we know that it has over 150 large volcanoes. We don’t know how many of them are active, but the Venus Express spacecraft sent back evidence of active vulcanism. In fact, Venus’ SO2 score would probably be even higher if much of its production didn’t oxidize to SO3. That combines with water to form the clouds of sulfuric acid that hide the planet’s surface and reflect sunlight so brightly.”

Maria’s hand is up again. “I don’t understand argon’s purple diamonds, profesora. I know it’s one of the inert gasses so it doesn’t have much chemistry and can’t react into a mineral like CO2 and SO2 can. Shouldn’t argon be about the same on all three planets, like helium?”

“Mm-hm, argon does have a simple chemistry, but its radiochemistry isn’t so simple. Nearly 100% of natural argon is the argon-40 isotope created by radioactive decay of potassium-40. Potassium is tied up in the rocks, so the atmospheric load of argon-40 depends on rocky surface erosion. Not much erosion, not much argon.”

Al’s on tenterhooks. “All this is nice, but you still haven’t said why Earth’s atmosphere is so different.”

~~ Rich Olcott

The Still of The Night

Lenore raises her hand. “Maybe it’s my Chemistry background, but to me that protosolar disk model for the early Solar System looks like a distillation process. You heat up a mixture in the pot and then run the resulting vapors through a multi-stage condenser. Different components of the mixture collect at different points in the condenser depending on the local temperature or maybe something about the condenser’s surface. I got some fun correlations from data I dug up related to that idea.”

“Interesting perspective, Lenore You’re got the floor.”

“Thanks, Professor. Like Newt said, hydrogen and helium atoms are so light that even a low-energy photon or solar wind particle can give them a healthy kick away from the Sun and they wind up orbiting where the gas planets grew up. But there was more sorting than that. Check out this chart.”

“What’re the bubbles?”

“Each bubble represents one planet. I’ve scaled the bubble to show what fraction of the planet is its nickel-iron core. Mercury, for instance, is two-thirds core; the other third is its silicate crust and that’s why its overall density is up there between iron and silicates. Then you go through Venus and Earth, all apparently in the zone where gravity’s inward pull on heavy dust particles is balanced by the solar wind’s intense outward push. From the chart I’d say that outbound metallic and rocky materials are mostly gone by the asteroid belt. Big Jupiter grabs most of the the hydrogen and helium; its little brothers get the leavings. Mars looks like it’s right on the edge of the depletion zone — the numbers suggest that its core, if it has one, is only 12% of its mass.”

Jeremy’s ears prick up. “If it has one?”

“Yeah, the sources I checked couldn’t say for sure whether or not it does. That’s part of why we sent the Insight lander up there. Its seismic data should help decide the matter. With such a small iron content the planet could conceivably have cooled like silicate raisin bread. It might have isolated pockets of iron here and there instead of gathered in at the center.”

“Weird. So the giant planets are all — wait, what’s Saturn doing with a density below water’s?”

“You noticed that. Theoretically, if you could put Saturn on a really big pool of water in a gravity field it’d float.”

Meanwhile, astrophysicist-in-training Newt Barnes has been inspecting the chart. “Uranus and Neptune don’t fit the pattern, Lenore. If it’s just a matter of ‘hydrogen flees farthest,’ then those two ought to be as light as Saturn, maybe lighter.”

“Yeah, that bothered me, too. Uranus and Neptune are giant planets like Jupiter and Saturn, but they’re not ‘gas giants,’ they’re ‘ice giants.’ All four of them seem to have a junky nickel-iron-silicate core, maybe 1-to-10 times Earth’s mass, but aside from that the gas giants are mainly elemental hydrogen and helium whereas Uranus and Neptune are mostly compounds of oxygen, nitrogen and carbon with hydrogen.”

“How’d all those light atoms get so far out beyond the big guys?”

“Not a clue. Can you help, Professor?”

Cathleen draws ellipses on Al’s whiteboard. “Maybe they did, maybe they didn’t — the jury’s still out. We’re used to our nice neat modern Solar System where almost everything follows nearly circular orbits. It took a while to evolve there starting from the chaotic protosolar disk. Many of the early planetesimals probably had narrow elliptical orbits if they had an orbit at all, considering how often they collided with each other. Astromechanics modelers have burned years of computer time trying to account for what we know of the planets, asteroids, comets and the Kuiper and Oort formations we’ve barely begun to learn about. Some popular ‘Jumping Jupiter‘ models show Jupiter and Saturn migrating in towards the Sun and out again, playing hob with Uranus, Neptune and maybe a third ice giant before that one was ejected from the system altogether. It’s entirely possible that the ice giants grew up Sunward of the hydrogen-rich gas giants. We just don’t know.”

“That’s a challenge.”

“Yes, and my challenge question remains — why isn’t Earth’s atmosphere some average of the Mars and Venus ones?”

~~ Rich Olcott

Should These Three Be Alike?

“What’s all the hubbub in the back room, Al? I’m a little early for my afternoon coffee break and your shop’s usually pretty quiet about now.”

“It’s Cathleen’s Astronomy class, Sy. The department double-booked their seminar room so she asked to use my space until it’s straightened out.”

“Think I’ll eavesdrop.” I slide in just as she’s getting started.

“OK, folks, settle. Last class I challenged you with a question. Venus and Mars both have atmospheres that are dominated by carbon dioxide with a little bit of nitrogen. Earth is right in between them. How come its atmosphere is so different? I gave each of you a piece of that to research. Jeremy, you had the null question. Should we expect Earth’s atmosphere to be about the same as the other two?”

Venus coudtops image by Damia Bouic
JAXA / ISAS / DARTS / Damia Bouic

“I think so, ma’am, on the basis of the protosolar nebula hypothesis. The –“

“Wait a minute, Jeremy. Sy, I saw you sneak in. Jeremy, explain that term to him.”

“Yes’m. Uh, a nebula is a cloud of gas and dust out in space. It could be what got shot out of an exploding star or it could be just a twist in a stream of stuff drifting through the Galaxy. If the twist kinks up, gravity pulls the material on either side of the kink towards the middle and you get a rotating disk. Most of what’s in the disk falls towards its center. The accumulated mass at the center lights up to be a star. Meanwhile, what’s left in the disk keeps most of the original angular momentum but it doesn’t whirl smoothly. There’s going to be local vortices and they attract more stuff and grow up to be planets. That’s what we think happens, anyway.”

“Good summary. So what does that mean for Mars, Venus and the Earth?”

“Their orbits are pretty close together, relative to the disk’s radius, so they ought to have encountered about the same mixture of heavy particles and light ones while they were getting up to size. The light ones would be gas atoms, mostly hydrogen and helium. Half the other atoms are oxygen and they’d react to produce oxides — water, carbon monoxide, grains of silica and iron oxide. And oxygen and nitrogen molecules, of course.”

“Of course. Was gravity the only actor in play there?”

“No-o-o, once the star lit up its photons and solar wind would have pushed against gravity.”

“So three actors. Would photons and solar wind have the same effect? Anybody?”

Silence, until astrophysicist-in-training Newt Barnes speaks up. “No, they’d have different effects. The solar wind is heavy artillery — electrons, protons, alpha particles. They’ll transfer momentum to anything they hit, but they’re more likely to hit a large particle like a dust grain than a small one like an atom. On average, the big particles would be pushed away more.”

“And the photons?”

“A photon is selective — it can only transfer momentum to an atom or molecule that can absorb exactly the photon’s energy. But each kind of atom has its own set of emission and absorption energies. Most light emitted by transitions within hydrogen atoms won’t be absorbed by anything but another hydrogen atom. Same thing for helium. The Sun’s virtually all hydrogen and helium. The photons they emit would move just those disk atoms and leave the heavier stuff in place.”

“That’s only part of the photon story.”

“Oh? Oh, yeah. The Sun’s continuous spectrum. The Sun is hot. Heat jiggles whole ions. Those moving charges produce electromagnetic waves just like charge moving within an atom, but heat-generated waves can have any wavelength and interact with anything. They can bake dust particles and decompose compounds that contain volatile atoms. Then those atoms get swept away in the general rush.”

“Which has the greater effect, solar wind or photons?”

“Hard to say without doing the numbers, but I’d bet on the photons. The metal-and-silicate terrestrial planets are close to the Sun, but the mostly-hydrogen giants are further out.”

“All that said, Jeremy, what’s your conclusion?”

“It sure looks like Earth’s atmosphere should be intermediate between Mars and Venus. How come it’s not?”

~~ Rich Olcott

Maybe even smaller?

There’s a sofa in my office. Sometimes it’s used to seat some clients for a consultation, sometimes I use it for a nap. This evening Anne and I are sitting on it, close together, after a meal of Eddie’s Pizza d’amore.

“I’ve been thinking, Sy. I don’t want to use my grow-shrink superpower very much.”

“Fine with me, I like the size you are. Why’d you decide that?”

“I remember Alice saying, ‘Three inches is such a wretched height to be.’ She was thinking about what her cat would do to her at that height. I’m thinking about what an amoeba might do to me if I were down to bacteria-size and I wouldn’t be able to see it coming because I’d be too small to see light. It would be even messier further down.”

“Well, mess is the point of quantum mechanics — all we get is the averages because it’s all chaos at the quantum level. Bohr would say we can’t even talk about what’s down there, but you’d be in the thick of it.”

She shudders delicately, leans in tighter. <long, very friendly pause> “Where’d that weird number come from, Sy?”

“What weird number?”

“Ten-to-the-minus-thirty-fifth. You mentioned it as a possible bottom to the size range.”

Now you’re asking?”

“I’ve got this new superpower, I need to think about stuff.  Besides, we’ve finished the pizza.”

<sigh> “This conversation reminds me of our elephant adventure.  Oh well.  Umm. It may have started on a cold, wet afternoon. You know, when your head’s just not up to real work so you grab a scratchpad and start doodling? I’ll bet Max Planck was in that state when he started fiddling with universal constants, like the speed of light and his own personal contribution ħ, the quantum of action.”

“He could change their values?”

“No, of course not. But he could combine them in different ways to see what came out. Being a proper physicist he’d make sure the units always came out right. I’m not sure which unit-system he worked in so I’ll just stick with SI units, OK?”

“Why should I argue?”

“No good reason to. So… c is a velocity so its units are meters per second. Planck’s constant ħ is energy times time, which you can write either as joule-seconds or kilogram-meter² per second. He couldn’t just add the numbers together because the units are different. However, he could divide the one by the other so the per-seconds canceled out. That gave him kilogram-meters, which wasn’t particularly interesting. The important step was the next one.”

“Don’t keep me in suspense.”

“He threw Newton’s gravitational constant G into the mix. Its units are meter³ per kilogram per second². ‘Ach, vut a mess,’ he thought, ‘but maybe now ve getting somevere. If I multiply ħ by G the kilograms cancel out und I get meter5 per second³. Now … Ah! Divide by c³ vich is equal to multiplying by second³/meter³ to cancel out all the seconds and ve are left mit chust meter² vich I can take the square root uff. Wunderbar, it is simply a length! How ’bout that?‘”

“Surely he didn’t think ‘how ’bout that?‘”

“Maybe the German equivalent. Anyway, doodling like that is one of the ways researchers get inspirations. This one was so good that (Għ/c³)=1.6×10-35 meter is now known as the Planck length. That’s where your ten-to-the-minus-thirty-fifth comes from.”

“That’s pretty small. But is it really the bottom?”

“Almost certainly not, for a couple of different reasons. First, although the Planck formula looks like a fundamental limit, it’s not. In the same report Planck re-juggled his constants to define the Planck mass (ħc/G)=2.2×10-8 kilograms or 22 micrograms. Grains of sand weight less than that. If Planck’s mass isn’t a limit, Planck’s length probably isn’t either. Before you ask, the other reason has to do with relativity and this is not the time for that.”

“Mmm … so if space is quantized, which is where we started, the little bits probably aren’t Planck-sized?”

“Who knows? But my guess is, no, probably much smaller.”

“So I wouldn’t accidentally go out altogether like a candle then. That’s comforting to know.”

My turn to shudder. <another long, friendly pause>.

~~Rich Olcott

Small, yes, but how small?

Another quiet summer afternoon in the office. As I’m finishing up some paperwork I hear a fizzing sound I’d not heard in a while. “Hello, Anne, welcome back. Where’ve you been?”

Her white satin looks a bit speckled somehow but her voice still sounds like molten silver. “I’m not sure, Sy. That’s what I’ve come to you about.”

“Tell me about it.”

“Well, after we figured out that I can sort of ‘push’ myself across time and probability variation I realized that the different ‘pushes’ felt like different directions, kind of. When I go backward and forward in time it feels a little like falling backward or forward. Not really, but that’s the best way I can describe it. Moving to a different probability is a little like going left or right. So I wondered, what about up and down?”

“And I gather you tried that.”

“Sure, why not? What good’s a superpower if you don’t know what you can do with it? When I ‘push’ just a little upward thIS HAPPENS.”

“Whoa, watch out for the ceiling fan! Shrink back down again before you break the furniture or something.”

“Oh, I won’t, I’ve learned to be careful when I resize. Good thing I was outside and all by myself the first time I tried it. Took some practice to control how how much my size changes by how light or heavy I ‘pushed’.”

“I think I can see where this is going.”

“Mm-hm, it’s good to know what the limits are, right? I’ve got a pretty good idea of what would happen if I got huge. What I want to know is, what’ll I be getting into if I try ‘pushing’ down as hard as I can?”

“Kinda depends on how far down you go. I’m assuming your retinas scale their sensitivity with your size. When you get bigger do green things look blue and yellow things look green and so forth?”

“Yeah, orange juice had this weird yellow color. Tasted OK, though.”

“Right. So when you get smaller the colors you perceive will shift the other way, to shorter wavelengths — at first, yellow things will look red, blue things will look yellow and you’ll see ultraviolet as blue. When you get a thousand times smaller than normal, most things will look black because there’s not much X-ray illumination unless you’re close to a badly-shielded Crookes tube.”

“Good thing this ‘push’ ability also gave me some kind of extra feel-sense that’s not sight. Sometimes when I try to ‘push’ it ‘feels’ blocked until I move around a little. After the ‘push’ I see a wall or something I would have jumped into.”

“That’s a relief. I was wondering how you’d navigate when you’re a million times smaller than normal, at the single-cell level, or a million times smaller than that when you’d be atom-sized.”

“Then what comes?”

“Mmm… one more factor of a thousand would get you down to about the size of an atomic nucleus, but below that things get real fuzzy. It’s hard to get experimental data in the sub-nuclear size range because any photon with a wavelength that short is essentially an extremely-high-energy gamma ray, better at blowing nuclei apart than measuring them. Theory says you’d encounter nuclei as roiling balls of protons and neutrons, but each of those is a trio of quarks which may or may not be composed of even smaller things.”

“Is that the end of small?”

“Maybe not. Some physicists think space is quantized at scales near 10—35 meter. If they’re wrong then there’s no end.”

“Quantized?”

Quantized means something is measured out in whole numbers. Electric charge is quantized, for instance, because you can have one electron, two electrons, and so on, but you can’t have 1½ electrons. Some physicists think it’s possible that space itself is quantized. The basic idea is to somehow label each point in space with its own set of whole numbers.  There’d be no vacant space between points, just like there’s no whole number between two adjacent whole numbers.”

“So how small can I get?”

“Darned if I know.”

~~ Rich Olcott

Thanks to Jerry Mirelli for his thoughts that inspired this post and the next.

Fly High, Silver Bird

“TANSTAAFL!” Vinnie’s still unhappy with spacecraft that aren’t rocket-powered. “There Ain’t No Such Thing As A Free Lunch!”

“Ah, good, you’ve read Heinlein. So what’s your problem with Lightsail 2?”

“It can’t work, Sy. Mostly it can’t work. Sails operate fine where there’s air and wind, but there’s none of that in space, just solar wind which if I remember right is just barely not a vacuum.”

Astronomer-in-training Jim speaks up. “You’re right about that, Vinnie. The solar wind’s fast, on the order of a million miles per hour, but it’s only about 10-14 atmospheres. That thin, it’s probably not a significant power source for your sailcraft, Al.”

“I keep telling you folks, it’s not wind-powered, it’s light-powered. There’s oodles of sunlight photons out there!”

“Sure, Al, but photons got zero mass. No mass, no momentum, right?”

Plane-polarized electromagnetic wave in motion
Plane-polarized electromagnetic wave
Electric (E) field is red
Magnetic (B) field is blue
(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)

My cue to enter. “Not right, Vinnie. Experimental demonstrations going back more than a century show light exerting pressure. That implies non-zero momentum. On the theory side … you remember when we talked about light waves and the right-hand rule?”

“That was a long time ago, Sy. Remind me.”

“… Ah, I still have the diagram on Old Reliable. See here? The light wave is coming out of the screen and its electric field moves electrons vertically. Meanwhile, the magnetic field perpendicular to the electric field twists moving charges to scoot them along a helical path. So there’s your momentum, in the interaction between the two fields. The wave’s combined action delivers force to whatever it hits, giving it momentum in the wave’s direction of travel. No photons in this picture.”

Astrophysicist-in-training Newt Barnes dives in. “When you think photons and electrons, Vinnie, think Einstein. His Nobel prize was for his explanation of the photoelectric effect. Think about some really high-speed particle flying through space. I’m watching it from Earth and you’re watching it from a spaceship moving along with it so we’ve each got our own frame of reference.”

“Frames, awright! Sy and me, we’ve talked about them a lot. When you say ‘high-speed’ you’re talking near light-speed, right?”

“Of course, because that’s when relativity gets significant. If we each measure the particle’s speed, do we get the same answer?”

“Nope, because you on Earth would see me and the particle moving through compressed space and dilated time so the speed I’d measure would be more than the speed you’d measure.”

“Mm-hm. And using ENewton=mv² you’d assign it a larger energy than I would. We need a relativistic version of Newton’s formula. Einstein said that rest mass is what it is, independent of the observer’s frame, and we should calculate energy from EEinstein²=(pc)²+(mc²)², where p is the momentum. If the momentum is zero because the velocity is zero, we get the familiar EEinstein=mc² equation.”

“I see where you’re going, Newt. If you got no mass OR energy then you got nothing at all. But if something’s got zero mass but non-zero energy like a photon does, then it’s got to have momentum from p=EEinstein/c.”

“You got it, Vinnie. So either way you look at it, wave or particle, light carries momentum and can power Lightsail 2.”

Lightsail 2 flying over Earth, against a yellow background
Adapted from image by Josh Spradling / The Planetary Society

“Question is, can sunlight give it enough momentum to get anywhere?”

“Now you’re getting quantitative. Sy, start up Old Reliable again.”

“OK, Newt, now what?”

“How much power can Lightsail 2 harvest from the Sun? That’ll be the solar constant in joules per second per square meter, times the sail’s area, 32 square meters, times a 90% efficiency factor.”

“Got it — 39.2 kilojoules per second.”

“That’s the supply, now for the demand. Lightsail 2 masses 5 kilograms and starts at 720 kilometers up. Ask Old Reliable to use the standard circular orbit equations to see how long it would take to harvest enough energy to raise the craft to another orbit 200 kilometers higher.”

“Combining potential and kinetic energies, I get 3.85 megajoules between orbits. That’s only 98 seconds-worth. I’m ignoring atmospheric drag and such, but net-net, Lightsail 2‘s got joules to burn.”

“Case closed, Vinnie.”

~~ Rich Olcott

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

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