Tag: JWST

To See Beneath The Starlight

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

C‑J casts an image to Al’s video screen. “This is new news, just came out a couple of weeks ago. It’s the lead figure from NASA’s announcement of JWST’s first exoplanet examination. We’re picked this study because the scientists used the transit technique. I’ve added the orange stuff so we can make a point. Each blue dot is one measurement from JWST’s Near‑Infrared Spectrograph while it looked at a star named LHS 457. Even though the telescope is outside Earth’s atmosphere and operating at frigid temperatures, you can see that the numbers scatter. Surely the star’s light isn’t changing that quickly – the dots are about 9 seconds apart – the spread has to come from noise in JWST’s electronics.”

Adapted from image by NASA Credit: NASA, ESA, CSA, L. Hustak (STScI).

“We’re just partway through our statistics class but we know to expect 95% of noise to be within 2 standard deviations either way of the average. With about 400 dots per hour, C‑J drew his lines to put about 10 dots per hour each above and below.”

“Right, Madison, and the point we want to make is how small that range is. Only about 0.04% difference. That’s like one drop in a 2500‑drop titration. Professor Kim’s samples in our Chem lab generally take around 20 milliliters which is about 400 drops.”

“So anyway, look at that dip in the light curve. That’s way out of the noise range. The starlight really did dim, even though it wasn’t by much.”

“By the way, NASA’s press release is a little misleading and in fact missed the point of the research. JWST didn’t find this exoplanet, the TESS satellite system did. JWST looked where TESS said to and yup, there it was. This report was really about what JWST could tell us about the exoplanet’s atmosphere.”

“There’s a bunch of possibilities that the researchers can now eliminate. C‑J, please cast the next slide to the screen. We need to be clear, this isn’t the spectrum that JWST recorded during a transit.”

Adapted from image by NASA (Credit: NASA, ESA, CSA, L. Hustak (STScI)), and Figure 2 in Lustig-Yeager, et al.

“No, that would have been simply the star’s light after some of it was filtered through the planet’s atmosphere. The researchers used a lot of computer time to subtract out the right amount of the star’s own spectrum. This is what’s left — their estimate of the spectrum of the planet’s atmosphere if it has one. I added the orange error bar on each point and for the sake of comparisons I traced in that dotted curve marked ‘Metallicity‘ from the scientists’ paper. The other lines are models for four possible atmospheres.”

“Why orange again? And why are the bars longer to the right of that gap?”

“I like orange. I had to trace the bars for this slide because NASA’s diagram used dark grey that doesn’t show up very well. The dots in the wavelength range beyond 3.8 microns are from a noisier sensor. Professor O’Meara, we need some help here. What’s metallicity and why did the paper’s authors think it’s important?”

“We haven’t touched on that topic in class yet. ‘Metallicity’ is the fraction of a star’s material made up of atoms heavier than hydrogen and helium. A star could have high metallicity either because it was born in a dust cloud loaded with carbons and oxygens, or maybe it’s old and has generated them from its own nuclear reactions. Either way, a planet in a high‑metallicity environment could have an atmosphere packed with molecules like O2, H2O, CH4 and CO2. That doesn’t seem to be the case here, does it?”

“No, ma’am. The measured points don’t have this model’s peaks or valleys. Considering the error bars, the transmission spectrum is pretty much flat. Most of the researchers’ other models also predict peaks that aren’t there. The best models are a tight cloud deck like Venus or Titan, or thin and mostly CO2 like Mars, or no atmosphere at all.”

“Even a null curve tells us more than we knew.”

~~ Rich Olcott

A Needle in A Needlestack

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

“How’d they find that far-away star, Cathleen? Seems like you’d have to know just where to point your telescope.”

“It’s worse than that, Al, first you’ve got to find that telescope, or more precisely, its lens. We can’t simply swing a black hole or galaxy cluster into position for a good look at something interesting. No, we have to discover lensing objects that magnify good stuff beyond them. The good news is that some of those are out there, but the bad news is that the sky is cluttered with far more objects that don’t play the game we want. This research team appears to have hit paydirt but they did it with humungous power shovels and heavy‑duty panning techniques.”

“Impressive metaphor, Cathleen. Could you un‑metaphor it for us?”

“Sure, Sy. The power shovels are Hubble and Spitzer, both of which piled up beaucoodles of data from decades of infrared observing time.”

“I thought Hubble was designed for visible and UV surveillance.”

“It is, mostly, but since 2009 its instrument suite included WFC3, a camera that’s sensitive out to 1700 nanometers and covers a square 2 arcminutes on a side. That’s a lot, by big‑telescope astronomy standards.”

“Wait, arcminutes?”

“That’s right, Mr Feder. We astronomers have trouble with distances but we’re good at measuring angles. The Moon’s about a degree across. One degree is sixty arcminutes, next step down is sixty arcseconds per arcminute. After that we go semi‑metric, milliarcseconds and so forth. One WFC3 pixel records a patch of sky 130 milliarcseconds across. JWST‘s NIRCam instrument has a resolution twice as sharp. Anyway, Hubble‘s 1700‑nanometer limit is plenty good enough to pick up 120‑nanometer hydrogen light that’s been stretched out by a factor of z=2.8. Distance and stretch correlate; the lens that highlighted Earendel and its Sunrise Arc for NASA and Vinnie is that far away.”

“How far away?”

“It’s tricky to answer that. The spectra we see let us measure an object’s z‑factor, which by way of the Doppler effect tells us how fast the object is moving away. Hubble’s constant ties that to distance, sort of. My convenient rule of thumb is that an object whose z is near 2 is running away at 80% of lightspeed and on the average is about 55 trillion lightyears from us but don’t quote me because relativity complicates matters. Using the same dicey calculation I estimated the lens and Earendel velocities at 87% and 96% of lightspeed, which would put their ‘proper distances‘ around 60 and 66 trillion lightyears away. And no, I’m not going to go into ‘proper distance‘ versus ‘comoving distance‘.”

“Let’s get back to your metaphor, Cathleen. I get that Hubble and Spitzer and such generated a ton of data. What’s the panning part about?”

“Well, in the old days it would have been hired hands and graduate students spending years peering at dots on photographic plates. These days it’s computers, thank Heaven. The research team used a series of programs to filter their digital data. The software had to decide which dots are stars or noise specks and which are galaxies or arcs. Then it picked out the reddest red galaxy images, then clusters of galaxy images at the same redness level that are near each other in space, then clusters with arcs around them. I said that WFC3 covers a square 2 arcminutes on a side, remember? The sky, both hemispheres, contains almost 2½ million squares like that, although the surveys didn’t get all of them. Anyhow, after burning through cubic acres of computer time the team found 41 deep red lensing clusters.”

“Only 41.”

“Yup.”

We ponder that for a minute, then Vinnie pipes up. “Wait, the dots are in color?”

“No, but these images are generally taken through a filter that transmits only a known narrow wavelength range, infrared or whatever. Using relative dot intensity at several different wavelengths you can create ‘false color‘ images. When you find something, you know where to point spectroscopic tools to be sure you’ve found the good stuff.”

“Like a star shining less than a billion years after the Big Bang.”

“Paydirt.”

Image adapted from NASA and STScI

~~ Rich Olcott

The Red Advantage

On By rolcottIn Astronomy: Techniques, James Webb Space Telescope, Physics: Light and Relativity, Space Travel, Uncategorized1 Comment

“OK, Cathleen, I get that JWST and Hubble rate about the same for sorting out things that are close together in the sky, and I get that they look at different kinds of light so it’s hard to compare sensitivity. Let’s get down to brass tacks. Which one can see farther?”

“An excellent question, Mr Feder. I’ve spent an entire class period on different aspects of it.”

“Narrow it down a little, I ain’t got all day.”

“You asked for it — a quick course on cosmological redshift. Fasten your seat belt. You know what redshift is, right?”

“Yeah, Moire yammers on about it a lot. Waves stretch out from something moving away from you.”

I bristle. “It’s important! And some redshifts don’t have anything to do with motion.”

“Right, Sy. Redshift in general has been a crucial tool for studying everything from planetary motion to the large‑scale structure of the Universe. Your no‑motion redshift — you’re thinking of gravitational redshift, right?”

“Mm-hm. From a distance, space appears to be compressed near a massive object, less compressed further away. Suppose we send a robot to take up a position just outside a black hole’s event horizon. The robot uses a green laser to send us its observations. Space dilates along the beam’s path out of the gravity well. The expanding geometry stretches the signal’s wavelength into the red range even though the robot’s distance from us is constant.”

“So, that’s gravitational redshift and there’s the Doppler redshift that Mr Feder referred to—”

“Is that what its name is? With p‘s? I always heard it as ‘doubler’ effect and wondered where that came from.”

“It came from Christian Doppler’s name, Al. Back in the 1840s he was investigating a star. He noticed that its spectrum was the overlap of two spectra slightly shifted with respect to each other. Using wave theory he proposed that the star was a binary and that the shifted spectra arose from one star coming towards us and the other moving away. Later work confirmed his ideas and the rest is history. So it’s Doppler, not doubler, even though the initial observation was of a stellar doublet.”

“So what’s this cosmo thing?”

“Cosmological redshift. It shows up at large distances. On the average, all galaxies are moving away from us, but they’re moving away from each other, too. That was Hubble’s big discovery. Well, one of them..”

“Wait, how can that be? If I move away from Al, here, I’m moving toward Sy or somebody.”

“We call it the expansion of the universe. Have you ever made raisin bread?”

“Nah, I just eat it.”

“Ok, then, just visualize how it’s made. You start with a flat lump of dough, raisins close together, right? The loaf rises as the yeast generates gas inside the lump. The dough expands and the raisins get further apart, all of them. There’s no pushing away from a center, it’s just that there’s an increasing amount of bubbly dough between each pair of neighboring raisins. That’s a pretty good analogy to galactic motion — the space between galaxies is expanding. The general motion is called Hubble flow.”

“So we see their light as redshifted because of their speed away from us.”

“That’s part of it, Al, but there’s also wave‑stretching because space itself is expanding. Suppose some far‑away galaxy, flying away at 30% of lightspeed, sent out a green photon with a 500‑nanometer wavelength. If the Doppler effect were the only one in play, our relative speeds would shift our measurement of that photon out to about 550 nanometers, into the yellow. Space expansion at intermediate stations along its path can cumulatively dilate the wave by further factors out into the infrared or beyond. Comparing two galaxies, photons from the farther one will traverse a longer path through expanding space and therefor experience greater elongation. Hubble spotted one object near its long‑wavelength limit with a recognizable spectrum feature beyond redshift factor 11.”

“Hey, that’s the answer to Mr Feder’s question!”

“So what’s the answer, smart guy?”

“JWST will be able to see farther, because its infrared sensors can pick up distant light that’s been stretched beyond what Hubble can handle.”

~~ Rich Olcott

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

It’s Not All Black And White

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

“So what you guys are telling me is that all those pretty astro‑pictures are faked by being gray‑scale to start with and someone comes along to say ‘This is red‘ and ‘That’s blue.’ Why should we believe any of it?”

“Because those decisions aren’t arbitrary, Mr Feder. Well, most of them. Do you remember one of Al’s Crazy Theories events when you asked about the color of Mars?”

“Yeah, the guy said it’s brown except for the rusty bits floating in the atmosphere. So what?”

“So have you seen Matt Damon’s movie The Martian?”

“Sure. I can’t see a potato without gagging a little.”

“Remember how red the exterior views were? When Watney was driving his rover across Mars, the color scheme was downright crimson, wasn’t it? Does that match the pictures we’ve seen from our real Mars rovers?”

“Sure not. So which one’s right?”

“I hate to say this, but it depends on who’s using the word ‘right’ and in what context The science says ‘shades of brown,’ loud and clear with data to back that up. Camera‑equipped Mars rovers carry color‑calibration patches so we can produce accurate renditions of what the rovers saw — shades of brown. Spectroscopy from satellites in space and analytical tests by rovers on the surface agree that rocks up there chemically match rocks down here. We know what our rocks look like — shades of brown.”

“You say that like there’s a ‘but‘ coming.”

“Mm-hm. It’s called ‘artistic license.’ When The Martian was being filmed consulting scientists said the Mars scenes needed to be brown. The director insisted on red because it ‘looked right’ for the mood he was trying to get across. Besides, after a century of Mars‑based science fiction the public expects red.”

“It’s worse than that, Catherine.”

“Why’s that, Sy?”

“It’s not just the public. Initial prints of Viking‑1‘s first‑ever in‑color Mars surface views had a reddish cast. They looked fine to NASA’s leadership who expected red anyway. The PR team distributed the prints before the image‑processing team completed their signal checks against the calibration patches. Turned out that the red signal channel had been over‑weighted. The trued‑up images show brownish dirt and rocks under a purplish sky. You can find both versions on the internet if you look around enough. A properly color‑balanced Martian sunset looks blue where Earth’s are red.”

“Well, what about pictures we got from other places, like that poster of Jupiter Al had up with the poles all nasty red?”

“That’s where the colors can really get arbitrary. It’s considered bad form to tinker with the underlying gray‑scale data, but the bridge from there to a colored‑in visual image is a matter of taste, judgement and what the researcher is interested in. IF it’s a researcher — some gorgeous amateur‑created images have been done simply for the sake of beauty and that’s OK so long as the intent is made clear. For research purposes there’s basically two ways to go. OK, three. One is if you’ve got just one image, let it alone or maybe enhance the contrast. We astronomers rarely stop at one, though. We use filters or other wavelength selection gadgets to create multiple tailor‑made gray‑scale images.”

“What’s that get you?”

Jupiter’s poles in IR — images credit
NASA/JPL-Caltech/SwRI/ASI/INAF/JIRAM

“A temperature scale, for one. Thanks to the Planck curve we have a straightforward relationship between an object’s continuous spectrum and how hot it is. The Juno mission carries a mapping spectrometer, JIRAM, that can capture a near‑infrared spectrum from each pixel in its field of view. That’s the data that NASA’s people used to calculate the heat maps in Al’s poster.”

“What else?”

“Each kind of atom has a unique spectrum in the visible and UV. If a vis-UV mapping spectrometer shows pixels with sulfur spectra, you know where the sulfur is. I’ve seen lovely maps of different atomic species that have been expelled by supernovas.”

“That’s what we’re gonna get from the Webb?”

“Not quite. Atoms don’t do much in the infrared range that JWST is instrumented for. That’s where molecules absorb and emit. There’s a lot of exotic chemistry out there and we’re finally going to be able to see it.”

~~ Rich Olcott

E Pluribus

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

Mr Feder’s a determined fault‑finder. “That gold on James Webb Space Telescope‘s mirror — it’s gonna make all its pictures look funny, yellow‑like instead of whatever the real colors are.”

Cathleen bristles a little. “We astronomers have built our science on recognizing. accounting for and overcoming instrument limitations. Hubble, for instance, went up with a mirror that had been misground so its resolution was a factor of 10 worse than it was supposed to be. It took three years for NASA to install corrective optics. In the meantime we devised a whole catalog of math and computer techniques for pulling usable data out of the mess. Anyway, JWST‘s not designed to make pretty pictures.”

“I thought it was gonna replace Hubble. If it can’t take pictures, what’re we putting it up there for?”

“It’s a successor, not a replacement. JWST is designed to answer a completely different set of questions from the ones that Hubble has been used for. I’m sure we’ll keep using Hubble for as long as it continues to operate. By the way, the Hubble pictures you’ve seen aren’t what Hubble took.”

“Bunk! I’ve seen Hubble shots of the Moon and they look just like what I see through my binocs. Same colors and everything.”

“Not much color in the Moon, Mr Feder. Just different grays except for during a lunar eclipse.”

“That’s true, Al, but the resemblance is no accident. All major telescopes including Hubble, gray‑scale is all they do. Professional and amateur scientists help out by combining and coloring those gray‑scale images.”

“Wait, how do they combine images? Back in the film days I’d forget to wind forward after taking a picture and the double exposures were always a mess.”

“Film and digital are very different technologies, Mr Feder. The sensors in your camera’s film were microscopic silver halide crystals embedded in the coating. Each photon that reached a crystal transformed one silver ion to elemental silver and darkened the image there just a bit. More photons in a particular area, more darkening. There’s no reset, so when you clicked twice on a frame the new darkening supplemented what was already there. Those silver atoms and their location on the film encoded the photos you took.”

<with a sneer> “Wooo — encoded! What’d the processing labs do, count the atoms?”

“In an analog sort of way. Your lab made positive prints by shining light through your negatives onto photosensitive paper that worked the same way as the film. Shadow from the negative’s dark silver atoms prevented silver ion darkening in the corresponding part of the paper. What was bright in the original scene came out bright in the print. And vice‑versa.”

“But I was taking color photos.”

“Same analog scheme but with fancier chemistry. Your color film had three photosensitive layers. Each layer was designed to record a different set of wavelengths, red, green or blue. Blue photons would darken the blue‑sensitive layer and so on. From then on the encoding and decoding logic worked the same, color by separate color. Your eyes combine the colors. JWST‘s cameras don’t do any of that.”

“I guess not, it being a million miles away from processing labs.”

“Right, we can only work with numbers that can be transmitted back to Earth. Modern telescopes use digital sensors, dense grids of transistor‑size devices that literally count the photons that strike them. Graph how many photons hit each part of the grid during an interval and you’ve got a picture. Better yet, you can do arithmetic on the counts. That opens up a world of analytical and pictorial opportunities that were tedious or impossible with photographic data.” <opens laptop, taps keys> “Here’s a lovely example I recently received from NASA’s Astronomy Picture of the Day service. Gorgeous, hm?”

“Symbiotic R Aquarii” — Image Credit: Optical (red, blue): NASA/ESA/STScI;
X-ray (purple): NASA/CXC/SAO/R. Montez et al.;
Processing: Judy Schmidt (CC BY-NC-SA)

“Wow.”
 ”Wow.”
  ”Wow.”

“Image arithmetic in action. That’s two stars in weird orbits around each other. Ms Schmidt combined two Hubble images with one from Chandra, a separate telescope looking at a different part of the spectrum. Old‑style astrophotography couldn’t do that.”

~~ Rich Olcott

Now You See It, Now You Don’t

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

Al’s face takes on a far-away smile. “James Webb Space Telescope must look pretty up there — a golden honeycomb on a silver setting, floating in space.”

“Real artistic and all, but how come all that gold? The mirror’s what, 60 feet across. Half of that is 30 for the radius, square it is 900, times 3 plus a little for pi, makes like 3000 square feet. That’s a lot of gold and us taxpayers sent it up to space! Why not make it shiny with something cheaper?”

“Nice on-the-fly math, Mr Feder, but it’s much less gold than you think. Ever play with gold leaf?”

“Yeah, once when my cousin was decorating one of her artsy‑tartsy ceramic pieces. I went to pick up one of her leftover scraps and my breath blew it away.”

“Thin, huh? One of my astronomy magazines had an article, said the gold coating on the JWST‘s dish is only a little thicker than gold leaf, just 1000 atoms top to bottom. They don’t even apply it with a brush like people usually do. Your cousin may have artisan‑level skills but her manual techniques can’t match the precision JWST‘s design demands. The fabricators used a vapor deposition process like the semiconductor people use to make computer chips.”

“So how much gold?”

“Less than three grams per segment. That ring on your finger weighs more. The article said each segment has about $180 worth of gold, pretty small compared to the project’s ten billion dollar price tag.”

“Even so, why gold? Why not something cheaper?”

“I dunno. I see it a lot on different missions. The Insight Mars lander’s below‑deck electronics section was shrouded with gold-covered plastic panels. What’s the story, Sy?”

“Gold’s a special metal, Al. It ranks up with copper and silver for electrical conductivity but unlike them it doesn’t corrode. That’s why so many electrical switches and data cables use a thin layer of it at the contact points. The conductivity comes from the metal’s high concentration of free electrons, like an ocean of them sloshing around the atomic lattice. The free electrons also make gold an efficient reflector for electromagnetic radiation all across the spectrum from UV light way down into the radio range. The engineers for Insight and a lot of other missions put a thin gold layer on those insulation panels to protect the plastic from incoming high‑energy photons that would break up the polymer molecules. JWST needs to send every passing photon into the satellite’s detectors so gold’s high reflectivity made it the obvious candidate for the mirror coating.”

“I wonder if I’ll be able to see that honeycomb through my backyard telescope.”

“We can put numbers to that.” <drawing Old Reliable from its holster and tapping screen‑keys> “Lessee … using the small angle approximation for the sine function, to resolve a grid of 20-foot hexagons a million miles away you’d need an angular resolution of
  (20 feet) / [(106 miles)*(5280 feet/mile)]
   = 3.8×10-9 radians = 784 micro‑arcseconds
For yellow light’s 570‑nanometer wavelength, Rayleigh’s angular resolution formula gives
  aperture diameter
   =1.22*(wavelength)/(angle in radians) = 1.22*570×10-9/3.8×10-9 = 183 meters.
You’d need a telescope with a 550‑foot front end. If I remember right, Al, that’s almost ten times the width of your yard. You’d need at least a 60‑meter mirror just to see the entire dish as anything more than a yellow speckle.”

“Even with a scope like that Al would have a problem, Sy.”

“What’s that, Cathleen?”

“Viewed from the Sun, JWST‘s orbit looks straightforward — a half‑million‑mile half‑year vertical loop around the Sun‑Earth L2 point that itself circles the Sun once a year. Viewed from Earth, though, it’s a far more complicated motion. Earth’s orbit parallels JWST‘s so half the time JWST leads Earth and half it lags behind. At the extremes, JWST scoots along at twice Earth’s speed or else it appears to stop against the background stars. It’d be a challenging target for a star‑tracker program without a minute‑by‑minute computerized ephemeris.”

“He wouldn’t see the honeycomb even with that scope, Moire. JWST‘s always gonna point away from the Sun and us. The only view we’ll ever get is that pink parasol.”

~~ Rich Olcott

Which Way Is Up?

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

“OK, Moire, the Attitude Control System’s reaction wheels swing James Webb Space Telescope through whatever angle changes it wants, but how does ACS know what direction JWST‘s at to begin with? Does it go searching through that million‑star catalog to find something that matches?”

“Hardly, Mr Feder, that’d be way too much work for a shipboard computer. No, ACS consults the orientations maintained by a set of gyroscopes that are mounted on JWST‘s framework. Each one points along an unvarying bearing relative to the Universe, no matter how the satellite’s situated.”

“Gyroscopes? Like the one I had as a kid? Winding the string around the axle was a pain and then however hard I pulled the string I couldn’t keep one going for more than half a minute. It always wobbled anyway. Bad choice.”

“Not the JWST choice, NASA mostly doesn’t do toys. Actually, the gyroscope you remember has a long and honorable history. Gimbals have been known and used in one form or another for centuries. A few researchers mounted a rotor inside a gimbal set for various purposes in the mid‑1800s, but it was Léon Foucault who named his gadget a gyroscope when he used one for a public demonstration of the Earth’s rotation. People used to go to lectures like we go to a show. Science was popular in those days.”

“Wait — Foucault? The pendulum guy?”
 ”Wait — Foucault? The knife‑edge test guy?”

“Our science museum used to have a big pendulum. I loved to watch it knock down those domino thingies one by one as it turned around its circle. Then they took it out to make room for another dinosaur or something.”

“Yup. A museum’s most precious resource is floorspace. That weight swinging on a long wire takes up a lot of square feet. Foucault’s pendulum was another of his Earth‑rotation demonstrations, just a year after the gyroscope show. Yeah, Al, same guy — Foucault invented that technique you use to check your telescope mirrors. He pioneered a lot of Physics. He showed that the absorption spectrum of a gas when a light shines through it matches the spectrum it emits when you heat it up. His lightspeed measurement came within one percent of our currently accepted value. ”

Astronomer Cathleen shakes her head. “Imagine, 200 years after Kepler and Newton, yet people in Foucault’s day still needed convincing that the Earth is a globe floating in space. A century and a half later some still do. <sigh> Funny, isn’t it, how Foucault was working at the same time on two such different phenomena.”

“Not so different, Cathleen. Both demonstrate the same underlying principle — inertia relates to the Universe and doesn’t care about local conditions. Foucault was really working on inertia. He made use of two different inertial effects for his demonstrations. By the way, Mr Feder, the pendulum doesn’t turn. The Earth turns beneath the pendulum to bring those domino thingies into target position.”

“That’s hard to believe.”

“Could be why his demonstrations used two different phenomena. Given 19th Century technology, those were probably his best options.”

“If only he’d had lasers, huh?”

“One kind of modern gyroscope is laser‑based. Uses photons going around a ring. Actually, photons or pulses of them going around the same ring in opposite directions. When the ring itself rotates, the photons or pulses going against the rotation encounter the Start point sooner than their opposites do. Time the difference and you can figure the rotation rate. Unfortunately, Foucault didn’t have lasers or the exquisite timing devices we have today. But that’s not the kind of gyroscope JWST carries, anyway.”

“OK, I’ll bite. What does it use?”

“The slickest one yet, Al. If you carefully tap the rim of a good wine glass it’ll vibrate like the red line here. The dotted blue circle’s the glass at rest. Under the right conditions inertia holds the planes of vibration steady even if the glass itself rotates. People have figured out how to use that principle to build extremely accurate. reliable and low‑maintenance gyroscopes for measuring and stabilizing rotations. JWST carries a set.”

“Nothing to lubricate, eh?”

Portrait of Léon Foucault from Wikimedia under Creative Commons Attribution 3.0 Unported license.

~~ Rich Olcott

Turn This Way to Turn That Way

On By rolcottIn Astronomy: Techniques, James Webb Space Telescope, Physics: Newton and Gravity, Space Travel, UncategorizedLeave a comment

“I don’t understand, Sy. I get that James Webb Space Telescope uses its reaction wheels like a ship uses a rudder to change direction by pushing against something outside. Except the rudder pushes against water but the reaction wheels push against … what, the Universe?”

“Maybe probably, Al. We simply don’t know how inertia works. Newton just took inertia as a given. His Laws of Motion say that things remain at rest or persist in linear motion unless acted upon by some force. He didn’t say why. Einstein’s General Relativity starts from his Equivalence Principle — gravitational inertia is identical to mechanical inertia. That’s held up to painstaking experimental tests, but why it works is still an open question. Einstein liked Mach’s explanation, that we experience these inertias because matter interacts somehow with the rest of the Universe. He didn’t speculate how that interaction works because he didn’t like Action At A Distance. The quantum field theory people say that everything’s part of the universal field structure, which sounds cool but doesn’t help much. String theory … ’nuff said.”

“Hey, Moire, what’s all that got to do with the reaction wheel thing? JWST can push against one all it wants but it won’t go anywhere ’cause the wheel’s inside it. What’s magic about the wheels?”

“JWST doesn’t want to go anywhere else, Mr Feder. We’re happy with it being in its proper orbit, but it needs to be able to point to different angles. Reaction wheels and gyroscopes are all about angular momentum, not about the linear kind that’s involved with moving from place to place.”

“HAH! JWST is moving place to place, in that orbit! Ain’t it got linear momentum then?”

Newton’s Principia, Proposition II, Theorem II

“In a limited way, pun intended. Angular momentum is linear momentum plus a radial constraint. This goes back to Newton and his Principia book. I’ve got a copy of his basic arc‑splitting diagram here in Old Reliable. The ABCDEF line is a section of some curve around point S. He treated it as a succession of short line segments ABc, BCd, CDe and so on. If JWST is at point B, for instance, Newton would say that it’s traveling with a certain linear momentum along the BCd line. However, it’s constrained to move along the arc so it winds up at D instead d. To account for the constraint Newton invented centripetal force to pull along the Sd line. He then mentally made the steps smaller and smaller until the sequence of short lines matched the curve. At the limit, a sequence of little bits of linear momentum becomes angular momentum. By the way, this step‑reduction process is at the heart of calculus. Anyway, JWST uses its reaction wheels to swing itself around, not to propel itself.”

“And we’re back to my original question, Sy. What makes that swinging happen?”

“Oh, you mean the mechanical reality. Easy, Al. Like I said, three pairs of motorized wheels are mounted on JWST‘s frame near the center of mass. Their axles are at mutual right angles. Change a wheel’s angular momentum, you get an equal opposing change to the satellite’s. Suppose the Attitude Control System wants the satellite to swing to starboard. That’d be clockwise viewed from the cold side. ACS must tell a port/starboard motor to spin its wheel faster counterclockwise. If it’s already spinning clockwise, the command would be to put on the brakes, right? Either way, JWST swings clockwise. With the forward/aft motors and the hot‑side/cold‑side motors, the ACS is equipped to get to any orientation. See how that works?”

“Hang on.” <handwaving ensues> “Yeah, I guess so.”

“Hey, Moire. What if the wheel’s already spinning at top speed in the direction the ACS wants more of?”

“Ah, that calls for a momentum dump. JWST‘s equipped with eight small rocket engines called thrusters. They convert angular momentum back to linear momentum in rocket exhaust. Suppose we need a further turn to starboard but a port/starboard wheel is nearing threshold spin rate. ACS puts the brakes on that wheel, which by itself would turn the satellite to port. However, ACS simultaneously activates selected thrusters to oppose the portward slew. Cute, huh?”

~~ Rich Olcott