Attitude Adjustment

Mr Feder has a snarky grin on his face and a far‑away look in his eye. “Got another one. James Webb Space Telescope flies in this big circle crosswise to the Sun‑Earth line, right? But the Earth doesn’t stand still, it goes around the Sun, right? The circle keeps JWST the same distance from the Sun in maybe January, but it’ll fly towards the Sun three months later and get flung out of position.” <grabs a paper napkin> “Lemme show you. Like this and … like this.”

“Sorry, Mr Feder, that’s not how either JWST or L2 works. The satellite’s on a 6-month orbit around L2 — spiraling, not flinging. Your thinking would be correct for a solid gyroscope but it doesn’t apply to how JWST keeps station around L2. Show him, Sy.”

“Gimme a sec with Old Reliable, Cathleen.” <tapping> “OK, here’s an animation over a few months. What happens to JWST goes back to why L2 is a special point. The five Lagrange points are all about balance. Near L2 JWST will feel gravitational pulls towards the Sun and the Earth, but their combined attraction is opposed by the centrifugal force acting to move the satellite further out. L2 is where the three balance out radially. But JWST and anything else near the extended Sun‑Earth line are affected by an additional blended force pointing toward the line itself. If you’re close to it, sideways gravitational forces from the Sun and the Earth combine to attract you back towards the line where the sideways forces balance out. Doesn’t matter whether you’re north or south, spinward or widdershins, you’ll be drawn back to the line.”

Al’s on refill patrol, eavesdropping a little of course. He gets to our table, puts down the coffee pot and pulls up a chair. “You’re talking about the JWST. Can someone answer a question for me?”

“We can try.”
 ”What’s the question?”
  Mr Feder, not being the guy asking the question, pooches out his lower lip.

“OK, how do they get it to point in the right direction and stay there? My little backyard telescope gives me fits just centering on some star. That’s while the tripod’s standing on good, solid Earth. JWST‘s out there standing on nothing.”

JWST‘s Attitude Control System has a whole set of functions to do that. It monitors JWST‘s current orientation. It accepts targeting orders for where to point the scope. It computes scope and satellite rotations to get from here to there. Then it revises as necessary in case the first‑draft rotations would swing JWST‘s cold side into the sunlight. It picks a convenient guide star from its million‑star catalog. Finally, ACS commands its attitude control motors to swing everything into the new position. Every few milliseconds it checks the guide star’s image in a separate sensor and issues tweak commands to keep the scope in proper orientation.”

“I get the sequence, Sy, but it doesn’t answer the how. They can’t use rockets for all that maneuvering or they’d run out of fuel real fast.”

“Not to mention cluttering up the view field with exhaust gases.”

“Good point, Cathleen. You’re right, Al, they don’t use rockets, they use reaction wheels, mostly.”

“Uh-oh, didn’t broken reaction wheels kill Kepler and a few other missions?”

“That sounds familiar, Mr Feder. What’s a reaction wheel, Sy, and don’t they put JWST in jeopardy?”

 Gyroscope, image by Lucas Vieira

“A reaction wheel is a massive doughnut that can spin at high speed, like a classical gyroscope but not on gimbals.”

“Hey, Moire, what’s a gimbal?”

“It’s a rotating frame with two pivots for something else that rotates. Two or three gimbals at mutual right angles let what’s inside orient independent of what’s outside. The difference between a classical gyroscope and a reaction wheel is that the gyroscope’s pivots rotate freely but the reaction wheel’s axis is fixed to a structure. Operationally, the difference is that you use a gyroscope’s angular inertia to detect change of orientation but you push against a reaction wheel’s angular inertia to create a change of orientation.”

“What about the jeopardy?”

Kepler‘s failing wheels used metal bearings. JWST‘s are hardened ceramic.”

<whew>

~~ Rich Olcott

Pinks In Space

Mr Feder, of Fort Lee NJ, is outraged. “A pretty pink parasol? NASA spent taxpayer dollars to decorate the James Webb Space Telescope with froufrou like that?”

Astronomer Cathleen stays cool. “Certainly not, Mr Feder. This is no effete Victorian‑era parasol. It’s a big, muscular ‘defender against the Sun,’ which is what the word means when you break it down — para‑sol. Long and wide as a tennis court. Its job is to fight off the Sun’s radiation and keep JWST‘s cold side hundreds of degrees colder than the Sunfacing side. Five layers of highstrength Kapton film, the same kind that helped protect New Horizons against freezing and micrometeorites on its way to Pluto and beyond. Each layer carries a thin coat of aluminum, looks like a space blanket or those Mylar mirror balloons but this is a different kind of plastic.”

“Sounds like a lot of trouble for insulation. Why not just go with firebrick backed up with cinder blocks? That’s what my cousin used for her pottery kiln.”

I cut in, because Physics. “Two reasons, Mr Feder. First one is mass. Did you help your cousin build her kiln?”

“Nah, bad back, can’t do heavy lifting.”

“There you go. On a space mission, every gram and cubic centimeter costs big bucks. On a benefit/cost scale of 1 to 10, cinder blocks rate at, oh, about ½. But the more important reason is that cinder blocks don’t really address the problem.”

“They keep the heat in that kiln real good.”

“Sure they do, but on JWST‘s hot side the problem is getting rid of heat, not holding onto it. That’s the second reason your blocks fail the suitability test. Sunlight at JWST ‘s orbit will be powerful enough to heat the satellite by hundreds of degrees, your choice of Fahrenheit or centigrade. That’s a lot of heat energy to expel. Convection is a good way to shed heat but there’s no air in space so that’s not an option. Conduction isn’t either, because the only place to conduct the heat to is exactly where we don’t want it — the scope’s dish and instrument packages. Cinder blocks don’t conduct heat as well as metals do, but they do it a lot better than vacuum does.”

“So that leaves what, radiating it away?”

“Exactly.”

“Aluminum on the plastic makes it a good radiator, huh?”

“Sort of. The combo’s a good reflector, which is one kind of radiating.”

“So what’s the problem?”

“It’s not a perfect reflector. The challenge is 250 kilowatts of sunlight. Each layer blocks 99.9% but that still lets 0.1% through to heat up what’s behind it. The parasol has radiate away virtually all the incoming energy. That’s why there’s five layers and they’re not touching so they can’t conduct heat to each other.”

“Wait, they can still radiate to each other. Heat bounces back and forth like between two mirrors, builds up until the whole thing bursts into flames. Dumb design.”

“No flames, despite what the Space Wars movies show, because there’s no oxygen in space to support combustion. Besides, the designers were a lot smarter than that. The mirrors are at an angle to each other, just inches apart near the center, feet apart at the edges. Heat in the form of infrared light does indeed bounce between each pair of layers but it always bounces at an angle aimed outwards. The parasol’s edges will probably shine pretty brightly in the IR, but only from the sides and out of the telescope’s field of view.”

“OK, I can understand the aluminum shiny, but why make it pink?”

“That’s a thin extra coat of a doped silicon preparation, just on the outermost two layers. It’s not so good at reflection but when it heats up it’s good at emitting infrared. Just another way to radiate.”

“But it’s pink?”

“The molecules happen to be that color.”

“Why’s it dopey?”

“Doped, not dopey. Pure silicon is an electrical insulator. Mixing in the right amount of the right other atoms makes the coating a conductor so it can bleed off charge coming in on the solar wind.”

“Geez, they musta thought of everything.”

“They tried hard to.”

~~ Rich Olcott

Yardsticks

“Hi, Cathleen, meet Mr Richard Feder, of Fort Lee NJ. He’s got a question that’s more in your Astronomy bailiwick than mine. Have a strawberry scone.”

“Mmm, still warm from Al’s oven. Thanks, Sy. Hello and what’s your question, Mr Feder?”

“Hiya. So if the James Webb Space Telescope is gonna be a million miles behind the Moon, won’t the Moon block its signals to us?”

“Oh dear, he said ‘miles.’ Sy, you’d better get out Old Reliable to look up numbers and do unit conversions. Mr Feder, I don’t think in miles.”

“Huh? What do you use instead, like paces or something?”

“Depends on what objects I’m considering and why I’m thinking about them. There are so many useful ratios out there it’s often easier to use ratios than huge numbers one can’t wrap one’s head around. Jupiter’s radius, for instance, is eleven times Earth’s, and the Sun is ten times wider still. Diameter and circumference follow the same ratios, of course. Square those ratios for relative surface area, cube them for relative volume. Who needs miles or kilometers?”

“Those numbers right, Moire?”

“Mmm … 6371 kilometers or 3959 miles for Earth, 71492 kilometers or 42441 miles for Jupiter, 695700 kilometers or 432300 miles for the Sun. The Jupiter/Earth ratio’s 11.2, the Sun/Jupiter ratio’s 9.73. The lady knows what she’s talking about.”

“Here’s a few fun factoids. The Moon’s distance is 10 times Earth’s Equator which is 100 times the International Space Station’s altitude. For that matter, if you wrapped a string around Earth’s Equator, it’d be just long enough to reach up to a GPS satellite and back. But all those are near‑Earth measurements where it makes sense to think in miles or kilometers. That’s too cumbersome for the bigger picture.”

“What else you got?”

“Within the Solar System I generally use one or the other of two convenient yardsticks. They measure the same distances, of course, but they have different applications. One is the nominal radius of Earth’s orbit, about 150 million kilometers.’

“That’s 93 million miles, Mr Feder.”

“I knew that one, Moire.”

“Anyway, we call that distance an Astronomical Unit. It’s handy for locating bodies relative to the Sun. Parker Solar Probe has gotten within a tenth of an AU of the Sun, for instance, and Neptune’s about 30 AU out. The Oort Cloud begins near 2000 AU and may extend a hundred times as far.”

“I ain’t even gonna ask what the Oort‐thing is, but I’m glad it’s a long way away.”

“We think it’s where long‑period comets come from.”

“Far away is good then. So what’s your other yardstick?”

“Lightspeed.”

“186 thousand miles per second, Mr Feder.”

“Yeah, yeah.”

“It’s also 300 thousand kilometers per second, and one light‑second per second, and one light‑year per year. Within the Solar System my benchmarks are that Earth is 500 light-seconds from the Sun, and Pluto was 4½ light-hours away from us when New Horizons sent back those marvelous images. The Sun’s nearest star system, Alpha Centauri, is 4⅓ light‑years away, and when you compare hours to years that gives you an idea of how small we are on the interstellar scale.”

“Cathleen, when you mentioned New Horizons that reminded me of the JWST. We’ve gotten off the track from Mr Feder’s question. Why isn’t the Moon going to block those signals?”

“Because it’ll never be in the way.” <sketching on a paper napkin> “There’s a bunch of moving parts here so hold on. The Earth orbits the Sun and the Moon orbits the Earth once a month, right? The L2 point doesn’t orbit the Earth. It orbits the Sun, staying exactly behind Earth so yeah, once a month the Moon could maybe get between Earth and L2. But JWST won’t be at L2, it’ll be in a wide orbit around that point and mostly perpendicular to the orbits of the Earth and Moon.”

“How wide?”

“It’ll vary depending on what they need, but it’s big enough to keep the spacecraft’s solar panels in the sunlight.”

“Solar panels? I thought the IR sensors needed cold cold cold.”

“They do. JWST protects its cold side with a hot side featuring a pretty pink Kapton parasol.”

~~ Rich Olcott

Prime Contenders

Between COVID and the post‑holiday wind‑down, things are slow. Vinnie and I are playing cards on my office side table, except my only deck is missing the heart face cards (long story) so we’re just trying to edge‑stack them. It’s not going well. “Geez, Sy, these towers collapse so quick, it’s boring. What else you got around here?”

“Well, before you arrived I was chasing prime numbers on Old Reliable for a New Year piece. Did you know, for instance, there we’re smack in the middle of a decade-long prime year dearth?”

“Prime year dearth?”

Prime as in not divisible by any number other than itself and one, dearth as in no year’s name being a prime number since 2017 and the next one isn’t until 2027. In the forty‑four years leading up to 2017 we averaged one prime per 5½ years. On the other hand, after 2029 (also a prime year, by the way) there’s fifty‑two years with only five primes.””

“Is there some rule for how many to expect?”

“Sort of. I sampled a series of hundred‑number ranges on up to a billion. The percentage of primes fell off as the numbers got larger, settled in at about 6%.”

“Makes sense — you got a bigger number, you got more little numbers that might divide into it.”

“Mm-hm. Something weird happens around ten million, though. The percentage drops down to only 2% but then it goes right back up to around 6% and stays there. I tried different scan resolutions but couldn’t locate any single especially long non‑prime string. The mathematicians have carried the research a lot further than my little experiment. The Prime Number Theorem gives a general curve that’s good ‘for sufficiently large numbers,’ but a million is a small number on their scale. As a physicist I’m a bit frustrated because the Theorem says, ‘This is the way it is‘ but it doesn’t give a reason. Although there probably isn’t a reason, any more than there’s a reason for 2017 being a prime to begin with.”

“I know what you mean. My car’s Owner Manual is the same way. Uhh… as I recall, you had a post a while ago about primes and 3’s and 7’s.”

“That was for New Year 2016, to be exact. Yeah, I found a collection of primes like 3337 and 733333 that have a string of 3’s or 7’s fronted and trailed by 3’s or 7’s. It wasn’t a bad bet. No primes (except 2 and 5) can have 0, 2, 4, 5, 6 or 8 as a trailing digit, right?”

“Lemme think for a minute. … Right.”

“That list didn’t include scrambled combinations like 37737, so what I did this year was to use Old Reliable to construct a big list of all possible 3’s‑and‑7’s numbers between 3 and a billion.”

“That’s a lot of numbers.”

“Not so many, actually, only about 1000. I told Old Reliable not to sample numbers that have any non‑3‑or‑7 digit buried in them somewhere. That’s a lot of pass‑overs.”

“That’s a lot of checking and skipping.”

“I used a short cut. It’s easy to build a list of all possible numbers with a certain number of binary digits — just count in binary. The three‑digit binary numbers, for instance, give you every zero‑one combination between 000 is zero and 111 is seven. Then I converted all the zeroes to 3’s and all the ones to 7’s and got every 3’s‑and‑7’s number between a hundred and a thousand with no interlopers. As a bonus that method organizes the overall list by powers of ten, like 333 to 777 in a sublist, 3333 to 7777 in another and so on. I counted the primes in each sublist and charted all the sublist percentages in the same graph as the hundred‑number sampling. Pretty much the same curve, but no dip near 10 million. For the heck of it I played the same game with 1’s and 9’s. Same behavior. Oh well.”

“So that’s how you keep yourself occupied on a slow day, huh? I got a New Year prediction for you.”

“What’s that?”

“I’m gonna bring you a couple fresh decks of playing cards.”

~~ Rich Olcott

Save The Whales? Burn Turpentine

“OK, Sy, I’ve told you the oil, wax and spermaceti story from my chemistry viewpoint. What got you reading up on whales?”

“A client asked a question that had me going down a rabbit hole that turned into a wormhole leading to a whole bunch of Biology and some Economics. Good thing I enjoy learning random facts.”

“OK, I’ll bite. What was the question?”

“Alright, Susan, see how you do with this. We need our eyes to be round so they can rotate in their sockets and still focus images on their retinas. They can hold that spherical shape against atmospheric pressure because they’re filled with watery stuff and they have a pump‑and‑drain mechanism inside that maintains a slight positive internal pressure. Whales dive down to where water pressures are a hundred atmospheres or more, enough to squeeze their lungs shut. They must use their vision sense down there because their retinal rod cells, the low‑light receptors, are sensitive to blue light. That’s what you’d need for hunting where the water above you filters out all the longer wavelengths. So why doesn’t the pressure down there crumple their eyeballs?”

“Oh, Sy, that’s easy. Water’s among the least compressible molecular liquids we know of. It takes an immense amount of pressure to reduce its volume even by 1%. Hunting-ground pressure isn’t nearly high enough to sabotage water‑filled eyeballs.”

“D’oh! So simple. And here I am, reading a dissection report on a sperm whale’s eyeball. Which, by the way, is about 22 times heavier than a human’s.”

“That’s where your wormhole led you?”

“No, actually, it led me to a econo-political argument about why kerosene got big in the 1860s.”

“Say what? I thought kerosene came in because sperm whales were getting hard to find.”

“That’s the story Big Oil likes. Apparently free-market enthusiasts have been lauding the petroleum industry as heroes dashing in with kerosene to save the whales and by the way, prospering completely independent of any government actions. Turns out History doesn’t support either claim. Ever hear of Camphine?”

“Nope.”

“Camphine saved the whales but then sank with nary a trace. I got most of the story from a PBS blog but pieced that together with a Wikipedia article and a bunch of old government statistics.. I charted the numbers and came up with some interesting correlations. Are you at your computer so I can email it to you?”

“Sure.”

“On its way.”

“Ooo, complicated. Care to read it to me?”

“Of course. Fun fact — fats from toothed whales are generally waxier than fat from baleen whales. Sperm whales just happen to be at the far end of that trend. Anyway, I concentrated on the sperm whale data. The red line is the total amount of spermaceti obtained from whales taken by US craft in each year,”

“Five million gallons in 1842? That’s ten thousand whales!”

“Mm-hm. The red line drops sharply after those peak years despite the whalers floating a bigger fleet — that’s the black line. The hunters found diminishing returns because the harvest just wasn’t sustainable. But people still wanted their spermaceti candles — the green line shows the price continued to rise until the mid‑1850s. Not only inside the US — the blue line shows exports rising because foreign whalers couldn’t supply demand from their own markets.”

“Bad prospects. What happened in the yellow part of the chart?”

“Competition from a new product called Camphine, a.k.a. ‘burning oil.’ In the mid‑1830s a guy in Maine and a couple of New Yorkers started making liquid substitutes for spermaceti. The products were mixtures of turpentine, grain alcohol and a little camphor for aroma. You needed a special lamp to burn it but you got a flame that rivaled sperm candles for brightness and color purity. Sold like gang‑busters, up to 200 million gallons per year, but the Civil War killed it off.”

“How?”

“Federal embargoes on Southern pine forest turpentine, Federal taxes on alcohol. Kerosene and the Pennsylvania oil wells in 1859 rode in decades late to save the whales. Camphine was helping but government trade and tax policies cut it off at the pass.”

~~ Rich Olcott

Candle, Candle, Burning Bright

<chirp, chirp> “Moire here.”

“Hi, Sy, it’s Susan Kim. I did a little research after our chat. The whale oil story isn’t quite what we’re told.”

“Funny, I’ve been reading up on whales, too. So what’s your chemical discovery?”

“What do we get from a fire, Sy?”

“Light, heat and leftovers.”

“Mm-hm, and back in 18th Century America, there was plenty of wood and coal for heat. Light was the problem. I can’t imagine young Abe Lincoln reading by the flickering light of his fireplace — he must have had excellent eyesight. If you wanted a mostly steady light you burned some kind of fat, either wax candles or oil lamps.”

“Wait, aren’t fat and wax and oil three different things?”

“Not to a chemist. Fat’s the broadest category, covers molecules and mixtures with chains of ‑CH2‑ groups that don’t dissolve in water. Maybe the chains include a few oxygen atoms but the molecules are basically hydrocarbons. Way before we knew about molecules, though, we started classifying fats by whether or not the material is solid at room temperature. Waxes are solid, oils are liquid. You’re thinking about waxy‑looking coconut oil, aren’t you?”

“Well….”

“Coconuts grow where rooms are warm so we call it an oil, OK? I think it’s fun that you can look at a molecular structure and kind of predict whether the stuff will be waxy or oily.”

“How do you do that?”

“Mmm… It helps to know that a long chain of ‑CH2‑ groups tends to be straight‑ish but if there’s an ‑O‑ link in the chain the molecule can bend and even rotate there. Also, you get a kink in the chain wherever there’s a –CH=CH– double bond. We call that a point of unsaturation.”

“Ah, there’s a word I recognize, from foodie conversations. Saturated, unsaturated, polyunsaturated — that’s about double bonds?”

“Yup. So what does your physicist intuition make of all that?”

“I’d say the linear saturated molecules ought to pack together better than the bendy unsaturated ones. Better packing means lower entropy, probably one of those solid waxes. The more unsaturation or more ‑O‑ links, the more likely something’s an oil. How’d I do?”

“Spot on, Sy. Now carry it a step further. Think of a –CH2– chain as a long methane. How do suppose the waxes and oils compare for burning?”

“Ooo, now that’s interesting. O2 has much better access to fuel molecules if they’re in the gas phase so a good burn would be a two‑step process — first vaporization and then oxidation. Oils are already liquid so they’d go gaseous more readily than an orderly solid wax of the same molecular weight. Unless there’s something about the –O– links that ties molecules together…”

“Some kinds have hydrogen-bond bridging but most of them don’t.”

“OK. Then hmm… Are the double-bond kinks more vulnerable to oxygen attack?”

“They are, indeed, which is why going rancid is a major issue with the polyunsaturated kinds.”

“Oxidized hydrocarbon fragments can be stinky, huh? Then I’d guess that oil flames tend to be smellier than wax flames. And molecules we smell aren’t getting completely oxidized so the flame would probably be smokier, too. And sootier. Under the same conditions, of course.”

“Uh-huh. Would you be surprised if I told you that flames from waxes tend to be hotter than the ones from oils?”

“From my experience, not surprised. Beeswax candlelight is brighter and whiter than the yellow‑orange light I saw when the frying oil caught fire. Heat glow changes red to orange to yellow to white as the source gets hotter. Why would the waxes burn hotter?”

“I haven’t seen any studies on it. I like to visualize those straight chains as candles burning from the ends and staying alight longer than short oil fragments can, but that’s a guess. Ironic that a hydrogen flame is just a faint blue, even though it’s a lot hotter than any hydrocarbon flame. Carbon’s the key to flamelight. Anyway, the slaughter started when we learned a mature sperm whale’s head holds 500 gallons of waxy spermaceti that burns even brighter than beeswax.”

~~ Rich Olcott

  • Whale image adapted from a photo by Gabriel Barathieu CC BY SA 2.0

The Venetian Blind Problem

Susan Kim gives me the side‑eye. “Sy, I get real suspicious when someone shows me a graph with no axis markings. I’ve seen that ploy used too often by people pushing a bias — you don’t know what happens offstage either side and you don’t know whether an effect was large or small. Your animated chart was very impressive, how that big methane infrared absorption peak just happens to fill in the space between CO2 and H2O peaks. But how wide is the chart compared to the whole spectrum? Did you cherry‑pick a region that just happens to make your point?”

“Susan, how could you accuse me of such underhanded tactics? But I confess — you’re right, sort of. <more tapping on Old Reliable’s keyboard> The animation only covered the near‑IR wavelengths from 1.0 to 5.0 micrometers. Here’s the whole strip from 0.2 micrometers in the near UV, out to 70 micrometers in the far IR. Among other things, it explains the James Webb Space Telescope, right, Al?”

Spectrum of Earth’s atmosphere. Adapted
under the Creative Commons 3.0 license
from Robert Wohde’s work
with the HITRAN2004 spectroscopic database,

“I know the Webb’s set up for IR astronomy from space, Sy. Wait, does this graph say there’s too much water vapor blocking the galaxy’s IR and that’s why they’re putting the scope like millions of miles away out there?”

“Not quite. The mission designers’ problem was the Sun’s heat, not Earth’s water vapor. The solution was to use Earth itself to shield the device from the Sun’s IR emissions. The plan is to orbit the Webb around the Earth‑Sun L2 point, about a million miles further out along the Sun‑Earth line. Earth’s atmosphere being only 60 miles thick, most of it, the Webb will be quite safe from our water molecules. No, our steamy atmosphere’s only a problem for Earth‑based observatories that have to peer through a Venetian blind with a few missing slats at very specific wavelengths.”

“Don’t forget, guys, the water spectrum is a barrier in both directions. Wavelengths the astronomers want to look at can’t get in, but also Earth’s heat radiation at those wavelengths can’t get out. Our heat balance depends on the right amount of IR energy making it out through where those missing slats are. That’s where Sy’s chart comes in — it identifies the wavelengths under threat by trace gases that aren’t so trace any more.”

“And we’re back to your point, Susan. We have to look at the whole spectrum. I heard one pitch by a fossil fuel defender who based his whole argument on the 2.8‑micrometer CO2 peak. ‘It’s totally buried by water’s absorption,‘ he claimed. ‘Can’t possibly do us any further damage.’ True, so far as it goes, but he carefully ignored CO2‘s other absorption wavelengths. Pseudoscience charlatan, ought to be ashamed of himself. Methane’s not as strong an absorber as CO2, but its peaks are mostly in the right places to do us wrong. Worse, both gas concentrations are going up — CO2 is 1½ times what it was in Newton’s day, and methane is 2½ times higher.”

“Funny how they both go up together. I thought the CO2 thing was about humanity burning fossil fuels but you said methane operations came late to that game.”

“Right on both counts, Al. Researchers are still debating why methane’s risen so bad but I think they’re zeroing in on cow gas — belches and farts. By and large, industry has made the world’s population richer over the past two centuries. People who used to subsist on a grain diet can now afford to buy meat so we’ve expanded our herds. Better off is good, but there’s an environmental cost.”

Al gets a far-away look. “Both those gases have carbon in them, right? How about we burn methane without the carbon in, just straight hydrogen?”

Susan gets excited. “Several groups in our lab are working on exactly that possibility, Al. The 2H2+O2→2H2O reaction yields 30% more energy per oxygen atom than burning methane. We just need to figure out how to use hydrogen economically.”

~~ Rich Olcott

It’s A Trap!

Late morning, no-one else in his coffee shop so Al pulls up a chair. “OK, Susan, so coal’s a mess for ash and air pollution but also each carbon from coal gives us less energy than a carbon from methane. So why the muttering against switching to natural gas?”

“Big-ticket reasons, Al. One, natural gas isn’t pure methane. Mostly methane, sure, but depending on the source you get a whole collection of other things in the mix — heavier hydrocarbons like propane and butane, stinky sulfides and amines, even helium and mercury. Gas from a well has to be purified before you’d want it piped to your house.”

“Piped. Oh, yeah, pipelines. Probably a lot more efficient than coal transport but I see how they get problems, too.”

“Indeed they do. Pipelines break and leak and some idiots even use them for target practice. The worst kind of waste.”

“Yeah, when the oil gets out and ruins the land or someone’s water supply.”

“That’s bad locally, all right, but it’s when methane leaks out that the global damage starts.”

“Global?”

“Mm-hm, because methane’s a gas and mixes in with the rest of the atmosphere. If a pipeline or a truck or anything springs a leak in, say, Chicago, the methane molecules can go anywhere.”

“So?”

“So a couple of things. A decade in the atmosphere oxidizes most methane molecules to, guess what, CO2, the same problematic CO2 we get from burning coal. But before it degrades, methane’s an even bigger heat‑trapper than CO2 is.”

“Whaddaya mean, heat‑trapper?”

“Do you want to take this, Sy? It’s more Physics than Chemistry and besides, my mocha latte’s getting cold.”

“Hmm, there’s a bunch of moving parts in this. Al, you owe Susan a warm-up while I think.”

“Here ya go, Susan.”

“Thanks, Al. I’ll get you guys started. Why did my coffee get cold?”

“Good one, Susan. Al, it’s a universal principle — left to itself, energy spreads out. Heat finds ways to travel from a concentrated, high‑temperature source to low‑temperature absorbers. The exceptions occur when some extra process expends energy to pump heat in the other direction. So, that coffee naturally lost heat to the table by conduction, to the air by convection and to the general environment by radiation. The only thing that can stop those processes is perfect insulation. That’s the thing about the atmosphere.”

“Whoa, that’s a jump or three too fast.”

“OK, let’s follow a sunbeam aimed in the Earth’s direction. Its photons carry a wide range of energies, ultraviolet down to far infrared. On the way in, a UV photon hits an atmospheric ozone molecule and gets absorbed. No more UV photon but now the molecule is in an excited state. It calms down by joggling its neighbor molecules, that’s heat transfer, and maybe emitting a longer wavelength photon or two. Ozone filters out incoming UV and in the process spreads out the photon’s concentrated energy. What’s left in the sunbeam is visible and infrared light that gets down to us. You with me?”

“Makes sense so far.”

“Good. Next stage is that the visible and IR light heat the Earth, which then re-radiates the energy as infrared light mostly at longer wavelengths. The problem is that not all the IR gets out. Water molecules absorb some wavelengths in that range. Every absorption event means more heat distribution into the atmosphere when the molecule relaxes. Ocean evaporation maintains a huge number of IR‑blocking water molecules in the atmosphere.”

“I heard that ‘some‘ weasel‑word. Other wavelengths still make it through, right?”

I unholster Old Reliable, tap a few keys. “Here’s water’s absorption pattern in the mid‑to‑far‑infrared. A high peak means absorption centered at that wavelength. This is scaled per molecule per unit area, so double the molecules gives you double the absorption.”

Spectrum profiles from M. Etminan, et al., doi:10.1002/2016GL071930

“Lots of blank space between the peaks, though.”

“Which is where CO2 and methane get into the game. It’s like putting green and blue filters in front of a red one. With enough of those insulating molecules up there there’s no blank space and lots of imbalance from trapped heat.”

“Methane’s worse.”

“Lots worse.”

~~ Rich Olcott

Going from Worse to Bad

Al delivers coffees to our table, then pauses. “Why methane?”

Susan Kim looks up from her mocha latte. “Sorry?”

“Why all the fuss about methane all of a sudden? I thought carbon dioxide was the baddie. Everybody’s switching from coal to natural gas which they say is just methane and now that’s a bad thing, too. I’m confused. You’re a chemist, unconfuse me.”

“You’re right, there’s mixed message out there. Here’s the bottom line. Methane’s bad, but coal’s a worse bad.”

“OK, but why?”

“Pass me a paper napkin so I can write down the chemical reactions. When we look at them in detail there’s all kinds of complicated reaction paths, but the overall processes are pretty simple. The burnable part of coal is carbon. In an efficient coal‑fired process what happens is
  C + O2 → CO2 + energy.
The C is carbon, of course and O2 is an oxygen molecule, two atoms linked together. Carbon atoms weigh 12 and each oxygen atoms weighs 16, so 12 grams of carbon produces 12+(2×16)=44 grams of CO2. Scaling up, 12 tons of carbon produces 44 tons of CO2 and so on. The energy scales up, too. and that’s what heats the boilers that make the steam that spins the turbines that make electricity.”

“I heard a couple of weasel words but go on to methane.”

“You caught them, eh? They’re important weasels and we’ll get to them. OK, methane is CH4 and its overall burn equation is
  CH4 + 2O2 → CO2 + 2H2O + energy.
Oxidizing those hydrogens releases about twice as much energy per carbon as the coal reaction does.”

“Already I see one big advantage for methane — more bang per CO2. So about those weasels…”

“Right. Well, coal isn’t just pure burnable carbon. It’s 350‑million‑year‑old trees and ferns and animal carcasses and swamp muck and mineral sediments, all pressure‑baked together. There’s sulfur and nitrogen in there, mixed in with nasty elements like mercury and arsenic.”

“The extras go up the smokestack along with the CO2, huh? Bad, for sure.”

“The good news is that coal-burning power plants are under the gun to clean up those emissions. The bad news is that effective mitigation technologies themselves cost energy. That lowers the net yield. But the inefficiency gets worse. Think coal trains.”

“Yeah, half the time I get held up on the way home by one of those hundred‑car strings, either full-up heading to the power plant or empties going back for another load.”

“Mm-hm. Transporting coal takes energy, and so does mining it and crushing it and pre‑treating to get rid of dirt and then taking care of the ashes. Even less net energy output per ton of smokestack CO2, even worse inefficiency. See why coal’s on its way out?”

“I guess all that didn’t matter when it was cheap to dig up and there wasn’t much competition.”

“You put your finger on it, Al. Coal got its foot in the door with steam engines 300 years ago when about the only other things you could burn were wood and whale oil. Crude oil got big in the mid‑1800s but it had to be refined and that made it expensive. Cheap natural gas wasn’t really a thing until fracking came along 50 years ago, but that brought a different set of issues.”

“Yeah, I’ve seen videos of people lighting their kitchen sink water on fire. And wasn’t there an earthquake thing in Oklahoma?”

“That was an interesting situation. Oklahoma’s in the middle of the continent, not a place you’d expect earthquakes, but they began experiencing flurries of shallow ones in 2011. The fracking process starts with water pumped at high pressure into gas-bearing strata to loosen things up. People suspected fracking was connected to the earthquakes. It was, but only indirectly. When fracked gas comes out of a well, water does, too. The rig operators pump that expelled water down old oil wells. Among other things, the state’s Corporation Commission is in charge of their hydrocarbon production. When the Commission ordered a 60% cut in the waste‑water down‑pumping, the earthquake rate dropped by 90%. Sometimes regulations are good things, huh?”

~~ Rich Olcott

Hyperbolas But Not Hyperbole

Minus? Where did that come from?”

<Gentle reader — If that question looks unfamiliar, please read the preceding post before this one.>

Jim’s still at the Open Mic. “A clever application of hyperbolic geometry.” Now several of Jeremy’s groupies are looking upset. “OK, I’ll step back a bit. Jeremy, suppose your telescope captures a side view of a 1000‑meter spaceship but it’s moving at 99% of lightspeed relative to you. The Lorentz factor for that velocity is 7.09. What will its length look like to you?”

“Lorentz contracts lengths so the ship’s kilometer appears to be shorter by that 7.09 factor so from here it’d look about … 140 meters long.”

“Nice, How about the clocks on that spaceship?”

“I’d see their seconds appear to lengthen by that same 7.09 factor.”

“So if I multiplied the space contraction by the time dilation to get a spacetime hypervolume—”

“You’d get what you would have gotten with the spaceship standing still. The contraction and dilation factors cancel out.”

“How about if the spaceship went even faster, say 99.999% of lightspeed?”

“The Lorentz factor gets bigger but the arithmetic for contraction and dilation still cancels. The hypervolume you defined is always gonna be just the product of the ship’s rest length and rest clock rate.”

His groupies go “Oooo.”

One of the groupies pipes up. “Wait, the product of x and y is a constant — that’s a hyperbola!”

“Bingo. Do you remember any other equations associated with hyperbolas?”

“Umm… Yes, x2–y2 equals a constant. That’s the same shape as the other one, of course, just rotated down so it cuts the x-axis vertically.”

Jeremy goes “Oooo.”

Jim draws hyperbolas and a circle on the whiteboard. That sets thoughts popping out all through the crowd. Maybe‑an‑Art‑major blurts into the general rumble. “Oh, ‘plus‘ locks x and y inside the constant so you get a circle boundary, but ‘minus‘ lets x get as big as it wants so long as y lags behind!”

Another conversation – “Wait, can xy=constant and x2–y2=constant both be right?”
  ”Sure, they’re different constants. Both equations are true where the red and blue lines cross.”

A physics student gets quizzical. “Jim, was this Minkowski’s idea, or Einstein’s?”

“That’s a darned good question, Paul. Minkowski was sole author of the paper that introduced spacetime and defined the interval, but he published it a year after Einstein’s 1905 Special Relativity paper highlighted the Lorentz transformations. I haven’t researched the history, but my money would be on Einstein intuitively connecting constant hypervolumes to hyperbolic geometry. He’d probably check his ideas with his mentor Minkowski, who was on the same trail but graciously framed his detailed write‑up to be in support of Einstein’s work.”

One of the astronomy students sniffs. “Wait, different observers see the same s2=(ct)2d2 interval between two events? I suppose there’s algebra to prove that.”

“There is.”

“That’s all very nice in a geometric sort of way, but what does s2 mean and why should we care whether or not it’s constant?”

“Fair questions, Vera. Mmm … you probably care that intervals set limits on what astronomers see. Here’s a Minkowski map of the Universe. We’re in the center because naturally. Time runs upwards, space runs outwards and if you can imagine that as a hypersphere, go for it. Light can’t get to us from the gray areas. The red lines, they’re really a hypercone, mark where s2=0.”

From the back of the room — “A zero interval?”

“Sure. A zero interval means that the distance between two events exactly equals lightspeed times light’s travel time between those events. Which means if you’re surfing a lightwave between two events, you’re on an interval with zero measure. Let’s label Vera’s telescope session tonight as event A and her target event is B. If the A–B interval’s ct difference is greater then its d difference then she can see Bif the event is in our past but not beyond the Cosmic Microwave Background. But if a Dominion fleet battle is approaching us through subspace from that black dot, we’ll have no possible warning before they’re on us.”

Everyone goes “Oooo.”

~~ Rich Olcott