Tag: Cal’s Coffee

Cause, Effect And Time

On By rolcottIn Physics: Black Holes and Relativity, Uncategorized5 Comments

We’re still at Vinnie’s table by the door of Al’s coffee shop. “Long as we’re talking about black holes, Sy, I read in one of my astronomy magazines that an Event Horizon traps information the same way it traps light. I understand how gravity makes escape velocity for photons go beyond lightspeed, but how does that trap information?”

“Well, to start with, Al, you understand wrong. The whole idea of escape velocity applies to massive objects like rockets that feel the force of gravity. Going up they trade kinetic energy for potential energy; given enough kinetic energy they escape. Photons have zero mass — the only way gravity influences them is by bending the spacetime they fly through.”

“Does the bending also affect information or is that something else?”

Minkowski’s spacetime diagram…

“Fair question, but it’ll take some background to answer it. Good thing I’ve got Old Reliable and my graphics files along. Let’s start with this one. Vinnie’s seen a lot of spacetime graphs like this, Al, but I don’t think you have. Time runs upward, distance runs sideward, okay? Naming a specific time and location specifies an event, just like a calendar entry. Draw a line between two events; the slope is the speed you have to go to get from one to the other.”

“Just the distance, you’re not worrying about direction?”

“Good question. You’re thinking space is 3D and this picture shows only one space dimension. Einstein’s spacetime equations take account of all four dimensions mixing together, which is one reason they’re so hard to solve except in special cases. For where we’re going, distance will be enough, okay?”

“Not gonna argue.”

… compartmentalized by Einstein’s speed limit …

“Now we roll in Einstein’s speed limit. Relativity says that nothing can go faster than light. On a Minkowski diagram like this we draw the lightspeed slope at a 45″ angle. Any physical motion has a slope more vertical than that.”

“Huh?”

“See, Al, you’re going one second per second along time, right? If you’re not making much progress distance‑wise, you don’t do much on Sy’s sideways axis. You move mostly up.”

“Exactly, Vinnie. The bottom and top sections are called ‘timelike‘ because, well, they’re mostly like time.”

“Are the other two sections spacelike?”

“Absolutely. You can’t get from ‘Here & Now‘ to the ‘Too far to see‘ event without going faster than light. Einstein said that’s a no‑no. Suppose that event’s a nova, ‘Now‘ but far away. Astronomers will have to just wait until the nova’s light reaches them at ‘Here‘ but at a later ‘Now.’ Okay, Vinnie, here’s a graphic you haven’t seen yet.”

… and re-interpreted in terms of causality.

“Looks pretty much the same, except for that arrow. What’s cause and effect got to do with time?”

“I don’t want to get into the metaphysical weeds here. There’s a gazillion theories about time — the Universe is expanding and that drives time; entropy always increases and that drives time; time is an emergent property of the underlying structure of the Universe, whatever that means. From an atomic, molecular, mechanical physics point of view, time is the result of causes driving effects. Causes always come first. Your finger bleeds after you cut it, not before. Cause‑effect runs along the time axis. Einstein showed us that cause‑effect can’t travel any faster than lightspeed.”

“That’s a new one. How’d he figure that?”

“Objects move objects to make things happen. They can’t move faster than lightspeed because of the relativity factor.”

“What if the objects are already touching?”

“Your hand and that cup are both made of atoms and it’s really their electric fields that touch. Shifting fields are limited by lightspeed, too.”

“So you’re saying that cause-effect is timelike.”

“Got it in one. Einstein would say causality is not only timelike, but exactly along the time axis. That’s one big reason he was so uncomfortable about action at a distance — a cause ‘Here‘ having an effect ‘There‘ with zero time elapsed would be a horizontal line, pure spacelike, on Minkowski’s graph. Einstein invented the principle of entanglement as a counterexample, thinking it impossible. He’d probably be shocked and distressed to see that today we have experimental proof of entanglement.”

~~ Rich Olcott

Holes in A Hole?

On By rolcottIn Physics: Black Holes and Relativity, UncategorizedLeave a comment

Mid-afternoon coffee break time so I head over to Al’s coffee shop. Vinnie’s at his usual table by the door, fiddling with some spilled coffee on the table top. I notice he’s pulled some of it into a ring around a central blob. He looks at it for a moment. His mental gears whirl then he looks up at me. “Hey Sy! Can you have a black hole inside another black hole?”

“That’s an interesting question. Quick answer is, ‘No.’ Longer answer is, ‘Sort of, maybe, but not the way you’re thinking.’ You good with that, Vinnie?”

“You know me better than that, Sy. Pull up a chair and give.”

I wave at Al, who brings me a mug of my usual black mud. “Thanks, Al. You heard Vinnie’s question?”

“Everyone on campus did, Sy. Why the wishy-washy?”

“Depends on your definition of black hole.”

Sky-watcher Al is quick with a response. “It’s a star that collapsed denser than a neutron star.”

Vinne knows me and black holes better than that. “It’s someplace where gravity’s so strong that nothing can get out, not even light.”

“Both right, as far as they go, but neither goes deep enough for Vinnie’s question.”

“You got a better one, I suppose?”

“I do, Vinnie. My definitition is that a black hole is a region of spacetime with such intense gravitation that it wraps an Event Horizon around itself. Al’s collapsed star is one way to create one, but that probably doesn’t account for the Event Horizons around supermassive black holes lurking in galactic cores. Your ‘nothing escapes‘ doesn’t say anything about conditions inside.”

“Thought we couldn’t know what happens inside.”

“Mostly correct, which is why your question is as problematical as you knew it was. Best I can do is lay out possibilities, okay? First possibility is that the outer black hole forms around a pre-existing inner one.”

“Can they do that?”

“In principle. What makes a black hole is having enough mass gathered in close proximity. Suppose you have a black hole floating our there in space, call it Fred, and a neutron star comes sidling by. If the two bodies approach closely enough, the total amount of mass could be large enough to generate a second Event Horizon shell enclosing both of them. How long that’d last is another matter.”

“The outer shell’d go away?”

“No chance of that. Once the shell’s created, the mass is in there and the star is doomed … unless the star’s closest approach matches Fred’s ISCO. That’s Innermost Stable Circular Orbit, about three times Fred’s Event Horizon’s half-diameter if Fred’s not rotating. Then the two bodies might go into orbit around their common center of gravity.”

“How’s rotation come into this?”

“If the mass is spinning, then you’ve got a Kerr black hole, frame-dragging and an ISCO each along and against the spin direction. Oh, wait, I forgot about tidal effects.”

“Like spaghettification, right.”

“Like that but it could be worse. Depending on how tightly neutronium holds itself together, which we don’t know, that close approach might be inside the Roche limit. Fred’s gravity gradient might simply shred the star to grow the black hole’s accretion disk.”

“Grim. You said there’s other possibilities?”

“Sorta like the first one, but suppose the total mass comes from two existing black holes, like the collision that LIGO picked up accidentally back in 2014. Suppose each one is aimed just outside the other’s ISCO. Roche fragmentation wouldn’t happen, I think, because each body’s contents are protected inside its own personal Event Horizon. Uhh … darn, that scheme won’t work and neither will the other one.”

“Why not?”
 ”Why not?”

“Because the diameter of an Event Horizon is proportional to the enclosed mass. The outer horizon’s diameter for the case with two black holes would be exactly the sum of the diameters of the embedded holes. If they’re at ISCO distances apart they’re can’t be close enough to form the outer horizon. For the same reason, I don’t think a neutron star could get close enough, either.”

“No hole in a hole, huh?”

“I’m afraid not.”

~~ Rich Olcott

  • Thanks to Alex and Xander, who asked the question.

A Match Game

On By rolcottIn Chemistry, UncategorizedLeave a comment

<chirp chirp> “Lab C-324, Susan Kim speaking.”

<hoarsely> “Hi Susan, it’s Sy. Fair warning. The at‑home test I just ran says I’ve got Covid. I’ve had all four shots but it looks like some new variant dodged in anyway. We had coffee together at Al’s yesterday so I wanted to warn you. Better stock up on cough medicine and such.”

“Ooh. Thanks, Sy, sorry to hear that. If it’s any consolation, you’re not alone. About half the lab’s empty today because of Covid. I’m just waiting for this last extraction to complete and then I’m outta here myself. There’s chicken soup going in the slow‑cooker at home.”

“Ah, yes, a Jewish mother’s universal remedy.”

“Korean mothers, too, Sy, except we use more garlic. Chicken soup’s a standard all over the world — soothing, easy on the stomach and loaded with protein.”

“While you’re in wait mode, maybe you could explain something to me.”

“I can try. What is it?”

“How do these tests work? I swabbed my nose, swirled the yuck with the liquid in the little vial and put three drops into the ‘sample port‘ window. In the next few minutes fluid crept across the display window next to the port and I saw dark bars at the T and C markers. What’s that all about?”

“Miracles of modern immunochemistry, Sy, stuff we wouldn’t have been able to execute fifty years ago. What do you know about antibodies?”

“Not much. I’ve read a little about immunology but I always get the antibodies confused with the antigens and then my understanding goes south.”

“Ignore the ‘anti‘ parts — an antigen is usually a part of something from outside that generates an immune response. As part of the response, cells in your body build antibodies, targeted proteins that stick to specific antigens. Each unique antibody is produced by just a few of your cells. When you’re under a disease attack, your antibodies that match the attacker’s antigens lock onto the attacker to signal your defender cells what needs chewing up. About half‑a‑dozen Nobel Prizes went to researchers who figured out how to get a lab‑grown cell to react to a given antigen and then how to clone enough copies of that cell to make industrial quantities of the corresponding antibody. You follow?”

“So far, so good.”

“One more layer of detail. All antibodies are medium-sized proteins with the same structure like a letter Y. There’s a unique targeting bit at the end of each upper arm. An antigen can be anything — a fragment of protein or carbohydrate, a fatty acid, even some minerals.”

“Wait. If a protein can be an antigen, does that mean that an antibody can be an antigen, too?”

“Indeed, that’s the key for your test kit’s operation. The case holds a strip of porous plastic like filter paper that’s been treated with two narrow colorless stripes and a dot. The T stripe contains immobilized antibody for some fragment of the virus. The C stripe contains immobilized antibody antibody.”

“Hold on — an antibody that targets another antibody like maybe the bottom of the Y?”

“Exactly. That’s the control indicator. The dot holds virus antibodies that can move and they’re linked to tiny particles of gold. Each gold particle is way too small to see, but a bunch of them gathered together looks red‑brown. Okay, you put a few drops of yuckified liquid on top of the dot and the mixture migrates along the porous material. You tell me what happens.”

“Wait, what’s in that liquid?”

“It’s standard pH-buffered saline, keeps the proteins healthy.”

“Hmm. Alright, the dot’s gold‑labeled virus antibody grabs virus in my yuck and swims downstream. The T stripe’s virus antibody snags the virus‑antigen combination particles and I see red‑brown there. Or not, if there’s no virus. Meanwhile, the creeping liquid sweeps other gold‑labeled antibodies, virus‑bound or not, until they hit the C stripe and turn it red‑brown if things are working right. Uhhh, how much gold are we talking about?”

“Colloidal gold particles are typically balls maybe 50 nanometers across. Stripe area’s about 1 mm2, times 50 nanometers, density 19.32 kg/m3, gold’s $55 per gram today … about 5 microcents worth.”

~~ Rich Olcott

Shadow Plays

On By rolcottIn Astronomy: Techniques, UncategorizedLeave a comment

“A strawberry scone and my usual black, Al.”

“Sure thing, Sy, comin– Hiya, Cathleen, see my new poster? Event Horizon Telescope pictures of the two big‑guy black holes we’ve actually seen so far. Those white-hot blobs buried in those red rings. Ain’t it a beaut? What’ll you have?”

“They’re certainly wonderful graphics, Al. I’ll have a caramel latte, please, with a plain scone.” I’m waiting for it, because Cathleen never passes up a teachable moment. Sure enough — “Of course, neither one actually looks like that or represents what you think. Those images were created from radio waves, not visible light or even infrared. The yellows and whites don’t represent heat, and that darkness in the middle isn’t the black hole.”

“Whoa, don’t harsh Al’s happy, Cathleen. Maybe just go at it a step at a time?”

<sigh> “You’re right, Sy. Sorry, Al, I just get frustrated when press‑agent science gets in the way of the real stuff which is already interesting on its own. For instance, I haven’t seen anything in the pop‑sci press about the EHT people using the same 2017 data to produce both images, even though the two objects are almost 90° apart in the sky. I think about our optical telescopes and the huge high-tech motors it takes to point them in the right direction. These guys just re-work their data and they’re good for another round.”

“It’s a cute trick, alright, Cathleen, steering a distributed telescope with arithmetic.”

“OK, you guys are over my head — distributed telescope?”

“The EHT Collaboration works with eight radio telescopes scattered across the world. The signal from any point in the sky has a different time offset at each telescope depending on the angle to the point. If you know the baseline between each pair of scopes and you’ve got really good clocks keeping track of time at each location, when you combine the data from all eight locations it’s just arithmetic to pick out matching signals at the right set of offsets for any point of origin.”

“A lot of arithmetic, Cathleen.”

“I’ll give you that, Sy. Al, it took the researchers and some hefty compute facilities two years to boil down the data for the M87 monster. In principle, when they wanted to inspect the Milky Way’s beast all they had to do was run through the same data selecting for signal matches at the offsets pointing to Sgr A*. Awesome tech, huh?”

“Awesome, yeah, but if the colors aren’t heat, what are they?”

“Electron density, mostly. Your red‑and‑yellow Jupiter poster over there is like most heat maps. Researchers figure a pixel’s temperature by comparing data from multiple wavelengths with the Planck curve or some other calibrated standard. These images, though, came from a single wavelength, 1.3 millimeters. Light at shorter wavelengths can’t get past the dust, longer wavelengths can’t give us the image resolution. Millimeters waves are in the radio part of the spectrum — too low‑energy to detect moving charge inside atoms or between molecule components. The only thing that can give off those photons is free‑floating electrons. The brightest pixels have the most electrons.”

“So the hole isn’t the black hole?”

“Depends on your definition, I suppose. Everyone visualizes that black sphere, the event horizon, when they think ‘black hole.’ That’s not what the dark patches are. By my definition, though, a ‘black hole‘ is the whole package — central mass, event horizon, ergosphere if it’s spinning, a jet maybe and everything else that’s associated with the mass. It’s as much a collection of processes as a thing. Anyhow, the bright stuff in these images does come from accretion disks.”

“The dark patch is the disk’s inside edge?”

“Nope, it’s the shadow of the photon sphere. Before you ask, that’s a light‑trapping shell 1½ times the horizon’s diameter. Depending on its angle of approach, a photon that touches the sphere either spirals inward, orbits forever, or swerves outward. Going straight doesn’t happen. The shadow memorializes Earth‑bound photons that bounced away from us.”

“I guess my happy’s back, Cathleen, but it’s different.”

“You’re welcome, Al. Now how about the coffee and scones we asked for?”

~~ Rich Olcott

Credit: Event Horizon Telescope Collaboration
Image: Lia Medeiros, ISA, EHTC

When The Stars Are Aligned Right

On By rolcottIn Astronomy: Techniques, James Webb Space Telescope, Physics: Light and Relativity, UncategorizedLeave a comment

Cathleen and I are chatting when Vinnie bursts into the coffee shop waving a newspaper. “New news, guys, they’ve just announced Hubble spotted the farthest‑away star. How about that? Think what JWST will be able to do!”

Cathleen raises an eyebrow. “Sounds like press release science. What else do they say?”

“Not a whole lot. Lessee… These guys went through old Hubble data and found a piece of an Einstein ring which I don’t know what that is and partway along the ring is a star and somehow they figured out it’s 50 times heavier than the Sun and 12 billion years old and it’s the farthest star they’ve ever seen and that’s why NASA’s all excited.”

“Do you believe all that?”

“Maybe the NASA PR people do?”

“Maybe. I just read the technical paper behind that announcement. The authors themselves aren’t absolutely sure. The paper’s loaded with supporting evidence and ‘how we did it‘ details but it’s also loaded with caveats. The text includes a string of alternative explanations for their observations, winding up with a typical ‘we await further evidence from JWST‘ statement. Reads a lot more like real science. Besides, we’ve already seen more distant stars but they’re all jumbled together inside their very distant galaxies.”

“Unpack it for me. Start with what’s an Einstein ring?”

“It’s a gravitational lensing effect. Sy, does Old Reliable still have a copy of that graphic you did about gravitational lensing?”

“That was years ago. Let me check… Uh‑huh, here it is.”

“Thanks. Vinnie, you know how a prism changes light’s direction.”

“Sy and me, we talked about how a prism bends light when light crosses from air to glass or the other way ’cause of the different speed it goes in each material. Uhh, if I remember right the light bends toward the slower speed, and you get more bend with shorter wavelengths.”

“Bingo, Vinnie. Gravitational lensing also bends light, but the resemblance ends there. The light’s just going through empty space, not different media. What varies is the shape of spacetime itself. Say an object approaches a heavy mass. Because of relativity the space it moves through appears compressed and its time is dilated. Compressed distance divided by dilated time means reduced velocity. Parts of a spread‑out lightwave closest to the mass slow down more than parts further way so the whole wave bends toward the heavy mass. Okay?”

“Hold on. Umm, so in your picture light coming towards us from that galaxy doesn’t get blocked by that black thingy, the light bends around it on both sides and focuses in on us?”

“Exactly. Now carry it further. The diagram cuts a flat 2D slice along round 3D spatial reality. Those yellow lines really are cones. Three‑sixty degrees around the black blob, the galaxy’s light bends by the same amount towards the line between us and the blob. Your Einstein ring is a cut across the cone, assuming that the galaxy, the blob and Earth are all exactly on the same straight line. If the galaxy’s off‑center the picture isn’t as pretty — you only get part of a ring, like those red arcs in Sy’s diagram.”

“A galactic rainbow. That ought to be awesome!”

“Well it would be, but there’s another difference between prisms and blobs. Rainbows happen because prisms and raindrops bend short‑wavelength colors more than longer ones, like you said. Gravitational lensing doesn’t care about wavelength. Wavelengths do shift as light traverses a gravitational well but the outbound red shift cancels the inbound blue shift.. Where gravity generates an Einstein ring, all wavelengths bend through the same angle. Which is a good thing for bleeding‑edge astronomy researchers.”

“Why’s that, Cathleen?”

“If the effect were wavelength‑dependent we’d have aberration, the astronomer’s nemesis. Images would be smeared out. As it is, all the photons from a point hit the same spot on the sensor and we’ve got something to see.”

“Tell him about amplification, Cathleen.”

“Good point, Sy. Each galactic star emits light in every direction. In effect, the blob collects light over its entire surface area and concentrates that light along the focal line. We get the brightest image when the stars are aligned right.”

~~ Rich Olcott

Now And Then And There

On By rolcottIn Cosmology, James Webb Space Telescope, Physics: Light and Relativity, UncategorizedLeave a comment

Still at our table in Al’s otherwise empty coffee shop. We’re leading up to how Physics scrambled ‘Now‘ when a bell dings behind the counter. Al dashes over there. Meanwhile, Cathleen scribbles on a paper napkin with her colored pencils. She adds two red lines just as Al comes back with a plate of scones. “Here, Sy, if you’re going to talk Minkowski space this might be useful.”

“Hah, you’re right, Cathleen, this is perfect. Thanks, Al, I’ll have a strawberry one. Mmm, I love ’em fresh like this. OK, guys, take a look at Cathleen’s graphy artwork.”

“So? It’s the tile floor here.”

“Not even close, Mr Feder. Check the labels. The up‑and‑down label is ‘Time’ with later as higher. The diagram covers the period we’ve been sitting here. ‘Now‘ moves up, ‘Here’ goes side‑to‑side. ‘Table‘ and ‘Oven‘, different points in space, are two parallel lines. They’re lines because they both exist during this time period. They’re vertical because neither one moves from its relative spatial position. Okay?”

“Go on, Moire.”
  ”Makes sense to me, Sy.”

“Good. ‘Bell‘ marks an event, a specific point in spacetime. In this case it’s the moment when we here at the table heard the bell. I said ‘spacetime‘ because we’re treating space and time as a combined thing. Okay?”

“Go on, Moire.”
  ”Makes sense to me, Sy.”

“So then Al went to the oven and came back to the table. He traveled a distance, took some time to do that. Distance divided by time equals velocity. ‘Table‘ has zero velocity and its line is vertical. Al’s line would tilt down more if he went faster, okay?”

“Mmmm, got it, Sy.”
  ”Cute how you draw the come-back label backwards, lady. Go on, Moire.”

“I do my best, Mr Feder.”

“Fine, you’ve got the basic ideas. Now imagine all around us there’s graph paper like this — except there’s no paper and it’s a 4‑dimensional grid to account for motion in three spatial dimensions while time proceeds. Al left and returned to the same space point so his spacetime interval is just the time difference. If two events differ in time AND place there’s special arithmetic for calculating the interval.”

“So where’s that get us, Moire?”

“It got 18th and 19th Century Physics very far, indeed. Newton and everyone after him made great progress using math based on a nice stable rectangular space grid crossed with an orderly time line. Then Lorentz and Poincaré and Einstein came along.”

“Who’s Poincaré?”

“The foremost mathematician of nineteenth Century France. A mine safety engineer most days and a wide‑ranging thinker the rest of the time — did bleeding‑edge work in many branches of physics and math, even invented a few branches of his own. He put Lorentz’s relativity work on a firm mathematical footing, set the spacetime and gravity stage for Minkowsky and Einstein. All that and a long list of academic and governmental appointments but somehow he found the time to have four kids.”

Simultaneity Animation by “Acdx”
licensed under Creative Commons Attribution-Share Alike 4.0 International.

“A ball of fire, huh? So what’d he do to Newton’s jungle gym?”

“Turned its steel rod framework into jello. Remember how Cathleen’s Minkowski diagram connected slope with velocity? Einstein showed how Lorentz’s relativity factor sets a speed limit for our Universe. On the diagram, that’d be a minimum slope. Going vertical is okay, that’s standing still in space. Going horizontal isn’t, because that’d be instantaneous travel. This animation tells the ‘Now‘ story better than words can.”

“Whah?”
  ”Whah?”

“We’re looking down on three space travelers and three events. Speeds below lightspeed are within the gray hourglass shape. The white line perpendicular to each traveler’s time line is their personal ‘Now‘. The travelers go at different velocities relative to us so their slopes and ‘Now‘ lines are different. From our point of view, time goes straight up. One traveler is sitting still relative to us so its timeline is marked ‘v=0‘ and parallels ours. We and the v=0 traveler see events A, B and C happening simultaneously. The other travelers don’t agree. ‘Simultaneous‘ is an illusion.”

~~ Rich Olcott

Hyperbolic plane image by Murdock Grewar,
licensed under Creative Commons Attribution-Share Alike 4.0 International.

Lord Rayleigh Resolves

On By rolcottIn Astronomy: Techniques, James Webb Space Telescope, Space Travel, UncategorizedLeave a comment

Mr Feder just doesn’t quit. “But why did they make JWST so big? We’re getting perfectly good pictures from Hubble and it’s what, a third the size?”

Al’s brought over a fresh pot and he’s refilling our coffee mugs. “Chalk it up to good old ‘because we can.’ Rockets are bigger than in Hubble‘s day, robots can do more remote stuff by themselves, it all lets us make a bigger scope.”

Cathleen smiles. “There’s more to it than that, Al. It’s really about catching photons. You’re nearly correct, Mr Feder, the diameter ratio is 2.7. But photons aren’t captured by a line across the primary mirror, they’re captured by the mirror’s entire area. The important JSWT:Hubble ratio is between their areas. JWST beats Hubble there by a factor of 7.3. For a given source and the same time interval, we’d expect JWST to be that much more sensitive than Hubble.”

“Well,” I break in, “except that the two use photon detectors that are sensitive to different energy ranges. The two scopes often won’t even be looking at the same kinds of object. Hubble‘s specialized for visible and UV light. It’s easy to design detectors for that range because electrons in solid‑state devices respond readily to the high‑energy photons. The infrared light photons that JWST‘s designed for don’t have enough energy to kick electrons around the same way. Not really a fair comparison, although everything I’ve read says that JWST‘s sensitivity will be way up there.”

Mr Feder is derisive. “‘Way up there.’ Har, har, de-har. I suppose you’re proud of that.”

“Not really, it just happened. But Cathleen, I’m surprised that you as an astronomer didn’t bring up the other reason the designers went big for JWST.”

“True, but it’s more technical. You’re thinking of resolution and Rayleigh’s diffraction limit, aren’t you?”

“Bingo. Except Rayleigh derived that limit from the Airy disk.”

“Disks in the air? We got UFOs now? What’re you guys talking about?”

Portrait of Sir George Airy
licensed under the Creative Commons
Attribution 4.0 International license.

“No UFOs, Mr Feder, I’ll try to be non‑technical. Except for the big close objects like the Sun and its planets, telescopes show heavenly bodies as circular disks accompanied by faint rings. In the early 1800s an astronomer named George Airy proved that the patterns are an illusion produced by the telescope. His math showed that even the best possible apparatus will force lightwaves from any small distant light source to converge to a ringed circular disk, not a point. The disk’s size depends on the ratio between the light’s wavelength and the diameter of the telescope’s light‑gathering aperture. How am I doing, Al?”

“Fine so far.”

“Good. Rayleigh took that one step further. Suppose you’re looking at two stars that are very close together in the sky. You’d expect to see two Airy patterns. However, if the innermost ring from one star overlaps the other star’s disk, you can’t resolve the two images. That’s the basis for Rayleigh’s resolvability criterion — the angle between the star images, measured in arc‑seconds, has to be at least 252000 times the wavelength divided by the diameter.”

After a diagram by cmglee
licensed under the Creative Commons
Attribution 3.0 International license.

“But blue light’s got a shorter wavelength than red light. Doesn’t that say that my scope can resolve close-together blue stars better than red stars?”

“Sure does, except stars don’t emit just one color. In visible light the disk and rings are all rimmed with reddish and bluish fuzz. The principle works just fine when you’re looking at a single wavelength. That gets me to the answer to Mr Feder’s question. It’s buried in this really elegant diagram I just happen to have on my laptop. Going across we’ve got the theoretical minimum angle for resolving two stars. Going up we’ve got aperture diameters, running from the pupil of your eye up to radio telescope coalitions that span continents. The colored diagonal bands are different parts of the electromagnetic spectrum. The red bars mark each scope’s sensor wavelength range. Turns out JWST‘s size compared to Hubble almost exactly compensates for the longer wavelengths it reports on.”

~~ Rich Olcott

Attitude Adjustment

On By rolcottIn Astronomy: Techniques, James Webb Space Telescope, Space Travel, UncategorizedLeave a comment

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

It’s A Trap!

On By rolcottIn Astronomy: Planetary Science, Physics: Light and Relativity, UncategorizedLeave a comment

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

On By rolcottIn Astronomy: Planetary Science, Chemistry, Uncategorized3 Comments

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