Tag: Walt

Sussing Out The Unseeable

On By rolcottIn Astronomy: Techniques, Cosmology, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hello, Mr Moire.”

“Afternoon, Walt. Pizza time again?”

“No, too public. Poor craft to be seen too often in the same place. There’s a park bench by the lake.”

“I know the spot.”

“Fifteen minutes.”

“Twenty.”

“Afternoon, Walt. What are your people curious about this time?”

“Word is that astronomers uncovered a huge amount of matter they’d been searching for. We’re interested in concealment techniques, so we want to know how it was hidden and how was it found.”

“Forty percent of all baryonic matter—”

“Baryonic?”

“Made out of atoms. Baryons are multi-quark particles like protons and—”

“Leave the weeds and get back to the topic. Where was that 40% hiding?”

“In plain sight, all over the sky, in strands forming a network that connects galaxies and galaxy clusters. They’re calling it the Cosmic Web.”

“Something that big … how was hidden?”

“Some techniques I’m sure you’ll recognize. First, the material in the strands is diffuse — just an atom or two per cubic meter. An Earth laboratory would be proud to pump down a vacuum ten million times more dense.”

<taking notes> “Spread your forces so there’s no prime target for counter‑attack, mm‑hm. But if the material’s that thin, surely it doesn’t mass much.”

“Remember how big space is. These filaments span the widths of multiple galaxies. Do the math. A thread could be on the order of 100 million lightyears long by 1000 lightyears in diameter. A lightyear is 1016 meters. The thread has a volume of about 1062 cubic meters. At 10-26 kilogram per cubic meter that’s 1036 kilograms which is comparable to the mass of a small galaxy. That’s just one thread. Add them up and you get roughly half the baryons in the Universe, all hiding in the Web.”

“Concealment by dispersal, got it. What’s another technique?”

“Camouflage. No, not tiny uniforms in a woodland pattern. These atoms fade into the background because oncoming light waves pass right by them unless the wave has exactly the right wavelength for an absorption.”

“So how did astronomers detect these scattered and camouflaged atoms?”

“A couple of different ways. X‑rays, for one.”

“But these atoms are camouflaged against passing light. X‑rays are light waves.”

“X‑rays the atoms emit. Everybody thinks that space is cold, but those lonely atoms bounce around with a kinetic energy equivalent to million‑degree temperatures. When two of them collide some of that kinetic energy escapes as high‑frequency light, X‑ray range. Not a whole lot, because the atoms are sparse, but enough that European and Japanese space telescopes were able to tweeze it out of the background.”

“Use sensitive mics to pick up whispered convo in the opposing line.”

<pause> “Right, more or less. What do you know about refraction?”

“Mmm… Newton and his prism, splitting white light into different colors. I’ve no idea how that works.”

“The short answer is that the speed of light depends on its wavelength and the medium it’s traversing. In a perfect vacuum, light always goes at top speed just like Einstein said, but charged particles in its path slow it down.”

“Even those atoms in space that you said can’t absorb light?”

“Yup. It’s called virtual coupling; quantum’s involved. One inaccurate way to describe the interaction is that atoms occasionally absorb wrong‑wavelength photons but spit them right back out again after a brief delay. Short wavelengths see more of that effect than long wavelengths do. With me?”

<pause> “Go on.”

“Does the phrase ‘Fast Radio Burst’ sound familiar?”

“Of course, but probably not the way you mean.”

“Ah. Right. For this context, Fast Radio Bursts are isolated pulses of radio‑frequency light from incredibly bright extra-galactic sources we don’t understand. They’re all over the sky. A pulse lasts only a millisecond or so. What’s important here is that refraction skews each pulse’s wavelength profile as it travels through the intergalactic medium. Researchers analyze the distortions to detect and characterize Web filaments in the direction each pulse came from.”

“Intercept the oppo’s communications to the front.”

“That’s about the size of it.”

“Bye.”

“Don’t mention it.”

The Cosmic Web
Visualization: Frank Summers (STScI); Simulation: Martin White and Lars Hernquist, Harvard University

~ Rich Olcott

A Carefully Plotted Tale

On By rolcottIn Cosmology, Physics: Quantum Mechanics, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hello, Mr Moire. Remember me?”

“Yes, I do, Walt. I hope your people were satisfied with what you brought them from our last meeting.”

“They were, which is why I’m calling. Buy you pizza at Eddie’s, fifteen minutes?”

“Make it twenty.”

We’re at the rear‑corner table, Walt facing both doors, naturally. “So, what’s the mysterious question this time?”

“Word on the street is that the CPT Law’s being violated. We want to know who’s involved, and what’s their connection with ChatGPT.”

Good thing I’ve just bit into my pizza so I can muffle my chuckle in my chewing. “What do you know about anti‑matter?”

“Inside‑out atoms — protons outside whizzing around electrons in the nucleus.”

“Common misconception. One proton has the mass of 1800 electrons. An atom built as you described would be unstable — the thing would fly apart. You’ve got anti‑matter’s charges arranged right but not the particles. Anti‑matter has negative anti‑protons in the nucleus and positrons, positive electrons, on the outside.”

<writing rapidly in his notebook> “You can do that? Just flip the sign on a particle?”

“No, positrons and such are respectable particles in their own right, distinct from their anti‑partners. Electric charge comes built into the identity. What’s important is, an anti‑atom behaves exactly like a normal atom does. Maxwell’s Equations and everything derived from them, including quantum mechanics, work equally well for either charge structure.”

“There’s a bit of Zen there — change but no‑change.”

“Nice. Physicists call that sort of thing a symmetry. In this case it’s charge symmetry, often written as C.”

“The C in CPT?”

“Exactly.”

“What about the P and T?”

“When someone says something is symmetrical, what do you think of first?”

“Right side’s a reflection of left side. Symmetrical faces look better but they’re usually less memorable.”

“Interesting choice of example. Anyway, reflection symmetry is important in common physical systems.”

“Classical Greek and Cambodian architecture; the Baroque aesthetic without the decorative frills.”

“I suppose so. Anyway, we call reflection symmetry Parity, or P for short.”

“And T?”

“Time.”

“Time’s not symmetrical. It’s always past‑to‑future.”

“Maybe, maybe not. In all our physical laws that deal with a small number of particles, you can replace t for time with –t and get the same results except for maybe a flipped sign. Newton’s Laws would run the Solar System in reverse just as well as they do forward.”

“But … Ah, ‘small number of particles,’ that’s your out. If your system has a large number of particles, you’re in chaos territory where randomness and entropy have to increase. Entropy increase is the arrow for one‑way time.”

“Good quote.”

“I’ve been in some interesting conversations. You’re not my only Physics source. So CPT is about Charge AND Parity AND Time symmetries. But you can’t simply add them together.”

“You multiply them. Technically, each of them is represented by a mathematical operator—”

“Step away from the technically.”

“Understood. This’ll be simpler. If a system’s atoms have positive nuclei, set C=1, otherwise set C=–1. If the system’s naturally‑driven motion is counterclockwise set P=1, otherwise P=–1. If time is increasing, set T=1, otherwise set T=–1. Okay?”

“Go on.”

“You can summarize any system’s CPT state by multiplying the prevailing symmetry values. The product will be either +1 or –1. The CPT Law says that in any universe where quantum mechanics and relativity work, one CPT state must hold universe‑wide.”

“Make it real for me.”

“You know the Right-hand Rule for electromagnetism?”

“Grab the wire with your right hand, thumb pointing along the current. Your fingers wrap in the direction of the spiraling magnetic field.”

“Perfect. Suppose C*P*T=+1 for this case. Now reverse the charge, making C=–1. What happens?”

“Ssss… The magnetic spin flips orientation. That’s a reflection operation so P=–1. The C*P*T calculation is (+1)*(–1)*(–1)=+1, no change.”

“The CPT Law in action. The CPT violation you’ve heard about is only observed in rare weak‑force‑mediated radioactive decays of a carefully prepared nucleus. That was a 1956 Nobel‑winning discovery, though the right person didn’t win it.”

“1956. Decades before A.I.”

“Yup, ChatGPT is off the hook. For that.”

“Bye.”

“Don’t mention it.”

~ Rich Olcott

  • Thanks to Caitlin, the hand model.

A Loose-end Lagniappe

On By rolcottIn Astronomy: Planetary Science, Mathematics: Spherical Harmonics, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“We have some loose ends to tie up. Too early for pizza. Coffee at Cal’s?”

“Hello, ‘Walt‘. Fifteen minutes?”

“Confirmed.”

He’s at a back table, facing the door, of course. He points to the steaming mug and strawberry scone beside it on the table. I nod to acknowledge. ”So, Walt, what are these loose ends?”

“My people say that Juno‘s not on a 53‑day orbit any more. NASA’s jiggled it down to 33 days. What’s that do to the numbers you gave me?”

<sliding a folded paper scrap across the table> “I had a hunch you’d want more so I worked up estimates. Juno started with a 53‑day orbit but a Ganymede flyby dropped it to 43 days. A Europa flyby took Juno to a 38‑day orbit. Now it’s swerved by Io and we’re at 33 days. I threw in the 23‑day line for grins, no extra charge.”

“Half the orbit size but no significant change in the close‑in specs. That’s surprising.”

“Not really. It’s like a dog’s butt wagging its tail. At close approach, we call it perijove, Juno is only 76 500 kilometers out from Jupiter’s center. Its orbit thereabouts is pretty much nailed down by the big guy’s central field. But there’s no second attractor to constrain the orbit’s other extreme millions of kilometers out. Do an Oberth burn near perijove or arrange for a gravity tweak from a convenient moon, you get a big difference at the far end.”

“That wraps that.” <reaches for his cane, then settles back to do a Columbo> “Just one more thing, Moire. I came in with a question about the Sun’s effect on Juno. You took care of that pretty quick but spent a load of my time and consultancy budget on these spherical harmonics. How come?”

“As I recall, you and your people kept coming back for more detail. Also, the 225 000‑kilometer radius I got from R2‘s structure was essential in calculating these close‑in numbers. You’re getting your money’s worth. I’ll even throw in a lagniappe.”

“A free gift? I never trust them.”

“Such a mean world you live in, Walt.” <displaying an image on Old Reliable> “Here it is, take it or leave it.”

Top: F000 plus a time-varying contribution from F660
Bottom: C0 plus a time-varying contribution from C4

“What is it?”

“It’s a bridge between the physics of light and sound, and the physics of atoms and stars. When I say ‘coordinates,’ what words spring to your mind?”

“Traverse and elevation.”

“Interesting choice. Any other systems?”

“Mm, latitude, longitude and altitude. And x‑y‑z if you’re in a classroom.”

“Way beyond the classroom. You use spreadsheets, right?”

“Doesn’t everyone?”

“Rows‑columns‑sheets is x‑y‑z. On digital screens, pixels‑lines‑luminosity is x‑y‑z. Descarte’s rectilinear invention is so deeply embedded in our thinking we don’t even notice it. Perpendicular straight‑line coordinates fit things that are flat or nearly so, not so good for spheres and central‑force problems. Movement there is mostly about rotation, which is why your first two picks were angular instead of linear.”

“Okay, but our choice of coordinates is our choice. What have x‑y‑z or your Fnnm to do with natural things?”

“Overtones and resonance. Look at that black line in the movie. It could be a guitar string or a violin string, doesn’t matter. One end’s fixed to the instrument’s bridge, the other end’s under somebody’s finger. All other points on the string are free to move, subject to tension along the string. Then someone adds energy to the string by plucking or bowing it.”

“At one of those peaks or valleys, right?”

“Nope, anywhere, which goes to my point. The energy potentially could contort the string to any shape. Doesn’t happen. The only stable shapes are combinations of sine waves with an integer number of nodes, like C4‘s quartet. Adding even more energy gives you overtones, waves that add in‑between nodes to lower‑energy waves. C0‘s no‑nodes black line could run along x, y or z in any flat system.”

“So you’re going to tell me that your C‘s, J‘s and R‘s support wave structures for spheres.”

“Indeed. All four giant planets have stripes along their J arcs. Solar seismologists have uncovered C, R and maybe J wave structures inside the Sun.”

“Bye.”

“Don’t mention it.”

~ Rich Olcott

Completing The Triad

On By rolcottIn Astronomy: Planetary Science, Mathematics: Spherical Harmonics, UncategorizedLeave a comment

Walt’s mustache bristles as he gives me the eye. ”You claim three harmonics control how the Sun’s gravity could affect spacecraft orbits around a target planet like Jupiter. You said we don’t have to care about Jupiter’s gravitational zones and isolating the sectors probably isn’t doable. What’s the third?”

Time to twist the screws. ”Three harmonic systems, Walt, all working together and you’ve got their names wrong. They control nothing, they’re a framework for analysis. And Jupiter’s special. Solar gravity doesn’t affect its zonal harmonic arcs but that’s only because Jupiter’s polar axis is nearly perpendicular to its orbital plane. Zonal‑effect N‑S twisting at Jupiter is pennies on a C‑note. Any mission we send to Mars, Saturn or Uranus we’ll care a lot about their zonal harmonics because their axes have more tilt. An 82° tilt for Uranus, can’t get much more tilted than that. Sectorial harmonics may still help us navigate there because Uranus probably has a lot less magnetism than Jupiter.”

That rocks him but he comes back strong. ”The third kind of harmonic?!! C’mon, give!”

“Radial, the center‑out dimension. The gravitational force between bodies depends on center‑to‑center distances so yeah, your people would be interested.”

“I presume radial harmonics have numbers like Jn and Cm do?”

“They do. Sorry, this’ll get technical again but I’ll go as light as I can. Each radial harmonic is the product of two factors. You know about factors, right?”

“Sure, force multipliers.”

“You would know that kind. More generally, factors are things that get multiplied together. I’ll call the general radial harmonic Rn. It’s the product of two factors. The first is a sum of terms that begin with rn, where r is the distance. For instance, R3‘s first factor would look like a*r³+b*r²+c*r+d, where the a,b,c,d are just some numbers. Different radial harmonics have different exponents in their lead terms. You still with me?”

“Polynomials from high school algebra. Tell me something new.”

“The second factor decreases exponentially with n*r. No matter how large rn gets, when you multiply an rn polynomial by something that decreases exponentially, the (polynomial)×(exponential) product eventually gets really small.”

“Give me a second. … So what you’re saying is, at a big enough distance these radial harmonics just die away.”

“That’s where I was going.”

“How far is ‘enough’?”

“Depends on n. Higher values of n shut down faster.”

“So these Cms and Jns and Rns just add together?” <pauses, squints at me suspiciously> “Is there some reason you used n for both Jn and Rn?”

“No but yes, and yes. You combine a C, a J and an R using multiplication to get a full harmonic F, except there are rules. The J and R must belong to the same n. The m can’t be larger than n. From far away we’d model Jupiter’s gravity as F000=R0×J0×C0, which is an infinite sphere — R0 never dies away and J0×C0 says ‘no angular dependence.’ The Sun’s gravity acts along R0 and that’s what keeps Jupiter in orbit. If the problem demands combining full harmonics, you use addition.” <rousing a display on Old Reliable> “Here’s how a particular pair of harmonics combine to increase or decrease spherical gravity in specific directions.”

“But Juno doesn’t see those gravity lumps until it gets close‑in. How close?”

“R2‘s down to less than a part per thousand at three planetary radii, call it 225 000 kilometers away from the planet’s center.”

“How much time is it closer than that distance?”

“Complicated question. A precise answer requires some calculus — is your smart phone set up for elliptic integrals?”

“Of course not. A good estimate will do.”

“Okay, here’s the plan. What we’d like is total time spent while Juno travels along the ellipsoidal arc between points A and D where the orbit crosses the 225 000‑km circle. Unfortunately, Juno speeds up approaching point P, slows down going away — calculating the A‑D time is tricky. I’ll assume Juno travels straight lines AB and CD at the A-speed. I’ll also approximate the orbit’s close pass as a semicircle at P‑speed.” <tapping> “I get a 3.6-hour duration, less than 0.3% of the full 53-day orbit. Will that satisfy your people?”

“You’ll know if it doesn’t.”

~~ Rich Olcott

Sectorial Setbacks

On By rolcottIn Astronomy: Planetary Science, Mathematics: Spherical Harmonics, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Moire, you were holding out on me. Eddie’s, fifteen minutes.”

“Not so fast, Walt. That wasn’t me holding out, that was you leaving too soon. From now on you’re paying quite a bit more. And it’ll be thirty minutes.”

“So we’re negotiating, hmm?”

“That’s about the size of it. You still interested?”

“My people are, they sent me back here. Oh well. Thirty minutes.”

Thirty-three minutes later I walk into Eddie’s. Walt’s already gotten a table. He beckons, points to the freshly‑served pizza, raises an eyebrow.

“Apology accepted. What made your people unhappy?”

“You told me flat‑out that the Sun’s gravity couldn’t affect those zonal harmonics. Do you have anything to back that up?”

“Symmetry. Zonal harmonics and latitude are about north‑south. Each Jn is a pole‑to‑pole variation pattern. The only way solar gravity can tilt Jupiter’s north‑south axis is to exert torque along the zonal harmonics. Jupiter’s equator is within 3° of edge‑on to the Sun.” <showing an image on Old Reliable’s screen> “Here’s what the Sun sees looking at J10, for instance. Solar pull on any northern zone segment, say, would be counteracted by an equal pull on the corresponding southern segment of the same zone. No net torque, no tilt. J0‘s the only exception. It’s simply a sphere that doesn’t vary across the whole planet. The Sun’s pull along J0‘s arc can’t tilt Jupiter.”

“Okay, so the zonal picture’s too simple. Just one set of waves, running up and down the planet—”

“No, not running. One way to characterize a wave is by how its components change with time. You’re thinking like ocean waves that move from place to place as time goes by. There’s also standing waves like on a guitar string, where individual points move but the peaks and valleys don’t. There’s time‑only waves like how the day length here changes through the year. And there’s static waves where time’s not even in the equation. Jupiter’s stripes don’t move, they’re peaks and valleys in a static wave pattern. By definition, the zonal harmonic system is static like that. But you’re right, it’s only part of the picture.”

“Give me the part the Sun’s gravitational field does play with.”

“That’d be two parts — sectorial and radial harmonics. Sectorial is zonal’s perpendicular twin. Zonal wave patterns show variation along the polar axis; sectorial wave patterns Cm vary around it. I’m keeping it non‑technical for you but Cm‘s actually cos(m*x) where x is the longitude.”

“Just don’t let it go any farther.”

“I’ll try not to. My point is that each sector pattern can be labeled with a positive integer just like we did with the zones.”

“If the Jn arcs aren’t affected by solar gravity, why would I care about these Cms?”

“You wouldn’t, except for the fact that mass distribution across Jupiter’s sectors is probably lumpy. We know the Great Red Spot holds its position in the southern hemisphere and the planet’s magnetic field points way off to the side. Maybe those features mark off‑center mass deficits and concentrations. Suppose a particular sectorial wave’s peak sits directly over a mass lump or hole. Everything under that harmonic’s influence is tugged back and forth by solar gravity each time the wave traverses the day side. Juno in its N‑S path just isn’t an efficient sensor for those tugs. Good sectorial sensing would require an orbiter on an E‑W path, preferably right over the equator.  Any orbital wobbles we’d see could be fed into a sectorial gravity map. Cross that with the zonal map and we’d be able to locate underlying mass variations by latitude and longitude.”

“Not a good idea. Gravity’s not the only field in play. You’ve just mentioned Jupiter’s magnetic field. I’ve read it’s stronger than any other planet’s. If your E‑W orbiter’s built with even a small amount of iron, you’d have a hard time deciding which field was responsible for any observed irregularities.”

“Good point. The idea’s even worse than you think, though. Jupiter’s sulfur‑coated moon—”

“Io. Yes, your induction‑heating idea might even be real. What about it?”

“I haven’t written yet about the high‑voltage Io‑to‑Jupiter bridge made of sulfur, oxygen and hydrogen ions. Jupiter’s magnetism plays a complicated game with them but the result is a chaotic sheet of radiating plasma around the planet’s equator. An E‑W orbiter in there would be tossed about like a paper boat on the ocean.”

~~ Rich Olcott

A Pencil In Space

On By rolcottIn Astronomy: Planetary Science, Mathematics: Spherical Harmonics, Physics: Newton and Gravity, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“I have a question I think you’ll find interesting, but it’s best we talk in person. Care for pizza?”

“If you’re buying.”

“Of course. Meet me at Eddie’s, twenty minutes. Bring Old Reliable.”

“Of course.”

Tall fellow, trimmed chevron mustache, erect bearing except when he’s leaning on that cane. “Moire?”

“That’s me. Good to meet you, Mr … ?”

“No names. Call me … Walt.”

We order, find a table away from the kitchen. “So, Walt, what’s this interesting question?”

“Been following this year’s Jupiter series in your blog. Read over the Kaspi paper, too, though most of that was over my head. What I did get was that his conclusions and your conclusions all come from measuring very small orbit shifts which arise from millionths of a g of force. Thing is, I don’t see where any of you take account of the Sun’s gravity. If the Sun’s pull holds Jupiter in orbit, it ought to swamp those micro-g effects. Apparently it doesn’t. Why not?”

“Well. That’s one of those simple questions that entail a complicated answer.”

“I’ve got time.”

“I’ll start with a pedantic quibble but it’ll clarify matters later on. You refer to g as force but it’s really acceleration. The one‑g acceleration at Earth’s surface means velocity changes by 980 meters/second per second of free fall. Drop a one kilogram mass, it’ll accelerate that fast. Drop a 100 kilogram mass, it’ll experience exactly the same acceleration, follow?”

“But the second mass feels 100 times the force.”

“True, but we can’t measure forces, only movement changes. Goes all the way back to Newton defining mass in terms of force and vice‑versa. Anyway, when you’re talking micro‑g orbit glitches you’re talking tiny changes in acceleration. Next step — we need the strength of the Sun’s gravitational field in Jupiter’s neighborhood.”

“Depends on the Sun’s mass and Jupiter’s mass. No, wait, just the Sun’s mass because that’s how it curves spacetime. The force depends on both masses.”

I’m impressed. “And the square of the very large distance between them.” <tapping on Old Reliable’s screen> “Says here the Sun’s field strength out there is 224 nano‑g, which is pretty small.”

“How’s that compare to what else is acting on Juno?”

<more tapping> “Jupiter’s local field strength crushes the Sun’s. At Juno’s farthest point it’s 197 micro‑g but at Juno’s closest point the field’s 22.7 million micro‑g and the craft’s doing 41 km/s during a 30-minute pass. Yeah, the Sun’s field would make small adjustments to Juno’s orbital speed, depending on where everybody is, but it’d be a very slow fluctuation and not the rapid shakes NASA measured.”

“How about side‑to‑side?”

“Good point, but now we’re getting to the structure of Juno’s orbit. Its eccentricity is 98%, a long way from circular. Picture a skinny oval pencil 8 million kilometers long, always pointed at Jupiter while going around it. It’s a polar orbit, rises above Jupiter on the approach, then falls below going away. The Sun’s effect is greatest when the orbit’s at right angles to the Sun‑Jupiter line. The solar field twists the oval away from N‑S on approach, trues it back up on retreat. That changes the angle at which Juno crosses Jupiter’s gravitational wobbles but won’t affect how it experiences the zonal harmonics.”

“Tell me about those zonal things.”

“A zone is a region, like the stripes on Jupiter, that circles a sphere at constant latitude. Technically, zonal harmonic Jn is the nth Legendre polynomial in cos(θ)—”

“Too technical.”

“Gotcha. Okay, each Jn names a shape, a set of gravitational ripples perpendicular to the polar axis. J0‘s a sphere with no ripples. Jupiter’s average field looks like that. A bigger n number means more ripples. Kaspi’s values estimate how much each Jn‘s intensity adds to or subtracts from J0‘s strength at each latitude. The Sun’s field can modify the intensity of J0 but none of the others.”

Walt grabs his cane, stands, drops a C‑note on the table. “This’ll cover the pizza and your time. Forget we had this conversation.” And he’s gone.

“Don’t mention it.”

~~ Rich Olcott

  • Thanks to Will, who asked the question.