Visionaries Old And New

Cathleen’s back at the mic. “Let’s have a round of applause for Maria, Jeremy, Madison and C‑J. Thank you all. We have a few minutes left for questions… Paul, you’re first.”

“Thanks, Cathleen. A comment, not a question. As you know, archeoastronomy is my specialty so I applaud Jeremy’s advocacy for the field. I agree with his notion that the Colorado Plateau’s dry, thin air generally lets us see more stars than sea‑level Greeks do. When I go to a good dark sky site, it can be difficult to see the main stars that define a constellation because of all the background dimmer stars. However, I don’t think that additional stars would change the pictures we project into the sky. Most constellations are outlined from only the brightest stars up there. Dimmer stars may confuse the issue, but I very much doubt they would have altered the makeup of the constellations a culture defines. Each culture uses their own myths and history when finding figures among the stars.”

“Thanks for the confirmation from personal experience, Paul. Yes, Sy?”

“Another comment not a question. I’m struck by how Maria’s Doppler technique and Jeremy’s Astrometry complement each other Think of a distant stellar system like a spinning plate balanced on a stick. Doppler can tell you how long the stick is. Astrometry can tell you how wide the plate is. Both can tell you how fast it’s spinning. The strongest Doppler signal comes from systems that are edge‑on to us. The strongest Astrometry signal comes from systems we see face‑on. Those are the extreme cases, of course. Most systems are be at some in‑between angle and give us intermediate signals.”

“That’s a useful classification, Sy. Madison’s and C‑J’s transit technique also fits the edge‑on category. Jim, I can see you’re about to bust. What do you have to tell us about?”

“How about a technique that lets you characterize exoplanets inside a galaxy we see as only a blurry blob? This paper I just read blew me away.”

“Go ahead, you have the floor.”

“Great. Does everyone know about Earendel?” <blank looks from half the audience, mutters about ‘Lord Of The Rings?’ from several> “OK, quick refresher. Earendel is the name astronomers gave to the farthest individual star we’ve ever discovered. It’s either 13 or 28 billion lightyears away, depending on how you define distance. We only spotted it because of an incredible coincidence — the star happens to be passing through an extremely small region of space where light in our general direction is concentrated thousands‑fold into a beam towards us. Earendel may be embedded in a galaxy, but the amplification region is so narrow we can’t see stars that might be right next to it.”

<Feder’s voice> “Ya gonna tell us what makes the region?”

“Only very generally, because it’s complicated. You know what a magnifying lens does in sunlight.”

“Sure. I’ve burnt ants that way.”

“… Right. So what you did was take all the light energy hitting the entire surface of your lens and concentrate it on a miniscule spot. The concentration factor was controlled by the Sun‑to‑lens‑to‑spot distances and the surface area of the lens. Now bring that picture up to cosmological distances. The lens is the combined gravitational field of an entire galaxy cluster, billions of lightyears away from us, focusing light from Earendel’s galaxy billions of lightyears farther away. Really small spots at both ends of the light path and that’s what isolated that star.”

“That’s what got you excited?”

“That’s the start of it. This new paper goes in the other direction. The scientists used brilliant X‑ray light from an extremely distant quasar to probe for exoplanets inside a galaxy’s gravitational lens. Like one of your ants analyzing sunlight’s glare to assess dust flecks on your lens. Or at least their averaged properties. A lens integrates all the light hitting it so your ant can’t see individual grains. What it can do, though, is estimate numbers and size ranges. This paper suggests the lensing galaxy is cluttered with 2000 free‑floating planets per main‑sequence star — stars too far for us to see.”

~~ Rich Olcott

  • Thanks to Dave Martinez and Dr Ka Chun Yu for their informative comments.

Significant Twinkles

Cathleen’s got a bit of fire in her eye. “Good exposition, Jeremy, but only just barely on‑assignment. You squeezed in your exoplanet search material at the very end. <sigh> Okay, for our next presentation we have two of our freshmen, Madison and C‑J.”

“Hello, everybody, I’m Madison. I fell in love with Science while watching Nova and Star Trek with my family. Doctor O’Meara’s Astronomy class is my first step into the real thing. C‑J?”

“Hi, I’m C‑J, like she said. What started me on Astronomy was just looking at the night sky. My family’s ranch is officially in dark sky country, but really it’s so not dark. Jeremy’s also from the High Plateau and we got to talking. We see a gazillion stars up there, probably more stars than the Greeks did because they were looking up through humid sea-level air. On a still night our dry air’s so clear you can read by the light of those stars. I want to know what’s up there.”

“Me, too, but I’m even more interested in who‘s up there living on some exoplanet somewhere. How do we find them? We’ve just heard about spectroscopy and astrometry. C‑J and I will be talking about photometry, measuring the total light from something. You can use it even with light sources that are too dim to pick out a spectrum. Photometry is especially useful for finding transits.”

“A transit is basically an eclipse, an exoplanet getting between us and its star—”

“Like the one we had in 2017. It was so awesome when that happened. All the bird and bug noises hushed and the corona showed all around where the Sun was hiding. I was only 12 then but it changed my Universe when they showed us on TV how the Moon is exactly the right size and distance to cover the Sun.”

“Incredible coincidence, right? Almost exactly 100% occultation. If the Moon were much bigger or closer to us we’d never see the corona’s complicated structure. We wouldn’t have that evidence and we’d know so much less about how the Sun works. But even with JWST technology we can’t get near that much detail from other stars.”

“Think of trying to read a blog post on your computer, but your only tool is a light meter that gives you one number for the whole screen. Our nearest star, Alpha Centauri, is 20% larger than our Sun but it’s 4.3 lightyears away. I worked out that at that distance its image would be about 8½ milliarcseconds across. C‑J found that JWST’s cameras can’t resolve details any finer than 8 times that. All we can see of that star or any star is the light the whole system gives off.”

“So here’s where we’re going. We can’t see exoplanets because they’re way too small and too far away, but if an exoplanet transits a star we’re studying, it’ll block some of the light. The question is, how much, and the answer is, not very. Exoplanets block starlight according to their silhouette area. Jupiter’s diameter is about a tenth the Sun’s so it’s area is 1% of the Sun’s. When Jupiter transits the Sun‑‑‑”

“From the viewpoint of some other solar system, of course—”

“Doesn’t matter. Jupiter could get in between the Sun and Saturn; the arithmetic works out the same. The maximum fraction of light Jupiter could block would be its area against the Sun’s area and that’s still 1%.”

“Well, it does matter, because of perspective. If size was the only variable, the Moon is so much smaller than the Sun we’d never see a total eclipse. The star‑planet distance has to be much smaller than the star‑us distance, okay?”

“Alright, but that’s always the way with exoplanets. Even with a big planet and a small star, we don’t expect to measure more than a few percent change. You need really good photometry to even detect that.”

“And really good conditions. Everyone knows how atmospheric turbulence makes star images twinkle—”

“Can’t get 1% accuracy on an image that’s flickering by 50%—”

“And that’s why we had to get stable observatories outside the atmosphere before we could find exoplanets photometrically.”

~~ Rich Olcott

Astrometers Are Wobble-Watchers

letter A Hi, Sy, what’s going on in Cathleen’s seminar?

You were right, Al.
It’s about exoplanets and how to find them.
Jeremy’s pitching astrometry.
That’s about measuring star locations in the sky.
I’ll fill you in later.

“So that’s my cultural colonialism rant, thanks for listening. On to the real presentation. Maria showed us how to look for exoplanets when they wobble along our line of sight. But what if they wobble perpendicular to that? Careful measurement should show that, right? The ancients thought that holy forces had permanently set the positions of all the stars except for the planets so they didn’t measure that close. Tycho Brahe took meticulous measurements with room‑sized instruments—”

<voice from the back> “Room‑sized? What difference does that make?”

“What if I told you that two stars are 3 millimeters apart in the sky?”

<another voice> “How far out’s your ruler? Sky stuff, you need to talk angles because that’s all you got.”

“Well there you go. That’s why Tycho went for maximum angle‑measuring accuracy. He built a sextant with a 5‑foot radius. He used an entire north‑south wall as a quadrant. His primary instrument was an armillary sphere three yards across.”

<first voice again> “Wait, a sphere, like a big bubble? Why north‑south? What’s a quadrant?”

  • I give him a nudge. “He’s just a kid, Mr Feder. Be nice. One question at a time.”
  • “But I got so many!”

“Think about Tycho’s goal. Like astrometers before him, he wanted to build an accurate map of the heavens. Native Americans a thousand years or more ago carved free‑hand star maps on cave ceilings and turtle shells. Tycho followed the Arabic and Chinese quantitative mapping traditions. There’s two ways to do that. One is to measure and map the visual angles between many pairs of stars. That strategy fails quickly because errors accumulate. Four or five steps along the way you’re plotting the same star in two different locations.”

<Feder’s voice again> “There’s a better way?”

“Yessir. Measure and map each star relative to a standard coordinate system. If your system’s a good one, errors tend to average out. The latitude‑longitude system works well for locating places on Earth. Two thousand years ago the Babylonians used something similar for places in the crystal sphere they thought supported the stars above us. Where the equinoctial Sun rose on the horizon was a special direction. Their buildings celebrated it. Starting from that direction the horizontal angle to a star was its longitude. The star’s latitude was its angle up from the horizon towards the zenith straight above. But those map coordinates don’t work for another part of the world. Astrometers needed something better.”

<Feder again> “So what did they do already?”

“They may or may not have believed the Earth itself is round, but they recognized the Pole Star’s steady position that the rest of the sky revolved around. They also noticed that as each month went by the constellations played ring‑a‑rosie in a plane perpendicular to the north‑south axis. Call that the Plane of The Ecliptic. Pick a star, measure its angle away from the Ecliptic and you’ve got an ecliptic latitude. Measure its angle around the Ecliptic away from a reference star and you’ve got a ecliptic longitude. Tycho’s instruments were designed to measure star coordinates. His quadrant was a 90° bronze arc he embedded in that north‑south wall, let him measure a star’s latitude as it crossed his meridian. His ‘Sphere’ was simply a pair of calibrated metal rings on a gimbal mounting so he could point to target and reference stars and measure the angle between them. If his calibration used degree markings they’d be about 25 millimeters apart. His work was the best of his time but the limit of his accuracy was a few dozen arcseconds.”

“Is that bad?”

“It is if you’re looking for exoplanets by watching for stellar wobble. Maria’s Jupiter example showed the Sun wobbling by 1½ million kilometers. I worked this example with a bigger wobble and a star that would be mid‑range for most of our constellations. Best case, we’d see its image jiggling by about 90 microarcseconds. Tycho’s instruments weren’t good enough for wobbles.”

~~ Rich Olcott

How Many Ways Can You Look at The Sky?

Cathleen and I were discussing her TRAPPIST-1 seminar in Al’s coffee shop when a familiar voice boomed over the room’s chatter.

“Hey, Cathleen, I got questions.”


“Yeah, Sy, he hangs out with the Astronomy crew sometimes.  You know him, too, huh?”

“From way back.  Long story.”

“What’re your questions, Vinnie?”

“I missed the start of your talk, Cathleen, but why so much hype about this TRAPPIST-1 system?  We’ve already found 3,500 stars with planets, right, and some of them have several.  What’s so special here?”

“You’re right, Vinnie, Kepler-90 has seven planets, just like TRAPPIST-1. (brandishes a paper napkin)  But that star’s more than 60 times further from us than TRAPPIST-1 is.  It’s just too far away for us to be able to learn much more about the planets than their masses and orbital characteristics.  This new system’s only 40 lightyears away, close enough that we’ve got a hope of seeing what’s in the planetary atmospheres.”

(another paper napkin)  “That ties in with the second thing that’s special.  The star’s surface temperature, 2550ºK, is so low that even though its planets orbit very close in, three of them are probably in the Goldilocks Zone.  They’re not too hot and not too cold for liquid water to exist on their surface.  IF there’s liquid water on one of them and IF there’s something living there, we should be able to detect traces of that biochemistry in the planet’s atmosphere.”

Star demographics
Observational data (dots) and four different models
of star count (vertical axis) versus temperature.
Hotter stars are to the left.

(napkin #3)  “The third special thing is that TRAPPIST-1 is the first-known planet-hosting star in its category — ultra-cool dwarf stars burning below 2700°K.  Finding those stars is hard — they’re small and dim.  No-one really knows how many there are compared to the other categories.  Some models say they should be rare, other models suggest they could be as common as G-type stars like our Sun.  IF there’s lots of ultra-cool dwarfs and IF they generally have planets like G-type stars do, then the category’s a new prime target for exoplanet hunters seeking life-signs.”

“Why’s that?”

“Because it’s easier to spot a small planet around a small star than around a big one.  Transits across TRAPPIST-1 dim its light by 1% or so.  A TRAPPIST-1 planet transiting our Sun would dim it by 1/100th of that.  The same problem hinders planet-finding methods fishing for stars that wobble because a planet’s orbiting around it.”

“Alright, I get that TRAPPIST-1 is special.  My other question is, I heard the part of your talk where you figured the odds on seeing its transits, but you lost me with the word steradian.  My dictionary says that’s an area on a sphere divided by the square of the sphere’s radius. What would that get me?  Where’d your numbers come from?”

“You need one additional piece of information.  If you take any sphere’s total surface area and divide that by r², you’ll always get 4π steradians.  You can use that to convert between absolute surface area and fraction of the sphere.  Mmm…  Sy, you own some land outside of town, yes?”

“A little.”

“And you have mineral rights?”

“Oh, yeah, that’s why I bought it.”

“And they go how far down?”

“All the way to the center of the Earth.”

“So your claim’s actually a pyramid 6370 kilometers deep.  When I moved here I learned it’s impolite to ask how much land someone has.  For round numbers I’ll assume 40 acres, which is about 1,000 square meters.  (tapping keys on her smartphone)  The Earth’s radius is 6.37×106 meters, so Sy’s claim is 1,000/(6.37×106)2 = 2.47×10-11 steradians.  Divide 4π by that and you get … 5.08×1011.  So Earth’s entire surface has room for 5.08×1011 patches matching Sy’s.  Visualize 5.08×1011 pyramids pointing in every direction from Earth’s center.  Now extend each pyramid outward to define a separate patch of sky.  Got that picture, Vinnie?”viewing cones

“Sort of.”

“TRAPPIST-1 is 3.74×1017 meters away.  TRAPPIST-1h’s orbit is a near-circle whose radius is 9.45×109 meters.  It covers π(9.45×109)2/(3.74×1017)2 = 2.00×10-15 steradians on a sphere centered on us. Divide 4π by 2.00×10-15 …  6.27×1015 sky-patches the size of TRAPPIST-1h’s orbit.  They had to pick the right patch to find TRAPPIST-1.”

“Long odds.”


~~ Rich Olcott

The Luck o’ The (insert nationality here)

“Afternoon, Al.  What’s the ruckus in the back room?”

“Afternoon, Sy.  That’s the Astronomy crew and their weekly post-seminar coffee-and-critique session.  This time, though, they brought their own beer.  You know I don’t have a beer license, just coffee, right?  Could you go over there and tell ’em to keep it covered so I don’t get busted?”

“Sure, Al.  … Afternoon, folks.  What’s all the happy?”

“Hey, Sy, welcome to the party.  Trappist beer, straight from Belgium!”

“Don’t mind if I do, Cathleen, but Al sure would like for you to put that carton under the table.  Makes him nervous.”

“Sure, no problem.”

“Thanks.  I gather your seminar was about the new seven-planet system.  How in the world do the Trappists connect to that story?”

“Patriotism.  The find was announced by a team from Belgium’s University of Liege.  They’ve built a pair of robotic telescopes tailored for seeking out rocks and comets local to our Solar System.  Exoplanets, too.  Astronomers love tying catchy acronyms to their projects.  This group’s proudly Belgian so they called their robots TRAnsiting Planets and Planetesimals Small Telescopes, ergo TRAPPIST, to honor the country’s 14 monasteries.  And their beer.  Mainly the beer, I’ll bet.”

“So the planets are a Belgian discovery?”

“Well, the lead investigator, Michaël Gillon, is at Liege, and so are half-a-dozen of his collaborators.  Their initial funding came from the Belgian government.  But by the time the second paper came out, the one that claimed a full seven planets spanning a new flavor of Goldilocks Zone, they’d pulled in support and telescope time from over a dozen other countries — USA, India, UK, France, Morocco, Saudi Arabia… the list goes on.  So it’s Belgian mostly but not only.”

“I love international science.  Next question — I see the planets are listed as TRAPPIST-1b, TRAPPIST-1c, and so on up to TRAPPIST-1h.  What happened to TRAPPIST-1a?”

“Rules of nomenclature, Sy.  TRAPPIST-1a is the star itself.  Actually, the star already had a formal name, which I just happen to have written down in my seminar notes somewhere … here it is, 2MASS J23062928 – 0502285.  You can see why TRAPPIST-1 is more popular.”

“I’m not even going to ask how that other name unwinds.  So what was the seminar topic this week?”

7 planets
TRAPPIST-1’s planets,
drawn to scale against their star. The
green ones are in the Goldilocks Zone.

“The low probability for us ever noticing those planets blocking the star’s light.”

“I’d think seeing a star winking on and off like it’s sending Morse code would attract attention.”

“That’s not close to what it was doing.  It’s all about the scale.  You know those cartoons that show planets together with their host sun?”

(showing her my smartphone) “Like this one?”

“Yeah.  It’s a lie.”

“How is it lying?”

“It pretends they’re all right next to the star.   7 planets perspectiveThis image is a little better.”  (showing me her phone)  “This artist at least tried to build in some perspective.  Even in this tiny solar system, about 1/500 the radius of ours, the star’s distance to each planet is hundreds to a thousand times the size of the planet.  You just can’t show planets AND their orbits together in a linear diagram.  Now, think about how small these planets are compared to their sun.”

“Aaaa-hah!   When there’s an eclipse, only a small fraction of the light is blocked.”

“That’s part of it.  Each eclipse (we call them transits) dims the measured brightness by only a percent or so.  But it’s worse than that.”

eclipses“How so?”

“All those orbits lie in a single plane.  We can’t see the transits unless our position lines up with that plane.  If we’re as little as 1½° out of the plane, we miss them.  But it’s worse than that.”

“How so?”

“During a transit, each planet casts a conical shadow that defines a patch in TRAPPIST-1’s sky.  You can tile TRAPPIST-1’s sky with about 150,000  patches that size.  There’s one chance in 150,000 of being in the right patch to see that 1% dimming.  In our sky there are over 6×1015 patches the size of TRAPPIST-1h’s orbit.  The team had to inspect the just right patch to find it.”

“With odds like that, no wonder TRAPPIST uses robots.”


~~ Rich Olcott

The New System’s in Tune

<We interrupt our running story line to bring you this important development…>

“Morning, Sy.  What can I get you?”

“My usual mugfull of black, Al.  What’s the Scone-of-The-Day?”

“I’m calling this The Trappist.  It’s got raspberry jam!”

“Why that name?”

“In honor of TRAPPIST-1, you know, that star they just found a bunch of planets around.”

“Your coffee shop being right next to the Astronomy building, I guess you’ve heard a lot about it.”

“Sy, you couldn’t believe.  The planetologists are going nuts of course, even though no-one’s actually seen the planets, and the astrometrics folks are lining up for telescope time ’cause they’ve got a whole new class of stars to monitor and of course the astrophysicists get to figure out how the system even works.”

“Astrometrics folks?  New class of stars?”

“Yeah, the high-precision star-measurers.  They didn’t used to pay attention to the small, dim stars because why bother.  But now … woo-hoo, whole new ballgame.”

“Nobody’s seen those planets?  How do they know they’re there?”

“Process of elimination, Sy.  The TRAPPIST telescopes picked up repetitive dark blips in the light coming from that star.  It’s a close, fast-moving star so there’s no sense supposing it’s like going behind or in front of a regular array of rocks or stars or something.  It’s not wobbling side-to-side like it would if it was a binary so it’s not traveling along with another star.  If the blips were sunspots going around as the star rotates there’d be only one rhythm, but these blips come in too complicated for that.  Besides, the star’s low-activity, too cool for lotsa sunspots.  Gotta be planets eclipsing it.”

NASA’s artistic (and cute) rendition
of the TRAPPIST-1 system
Note the close-in steam and the frost further out

“Sounds pretty good, but…”

“Hey Sy, there was something else, maybe you could explain it.  One astrophysics guy was real impressed that the planets had residences.  I didn’t understand that.”

“Residences?  That’s a new one on me.”

“Had something to do with the blip periods.  Yeah, here’s the paper napkin he wrote ’em all down on.”

Period, days
Actual /

“Oh, resonances! That I recognize, and yeah, those numbers are much more convincing.  Remember my post about gear logic?”

“Sorry, Sy, that must’ve been a long time ago and who has time to read?”

“I understand.  OK, that post explained how planets that survive the early chaos of a forming solar system tend to wind up in orbits whose relative year-lengths form ratios of small whole numbers.  In our system, for instance, the length of Pluto’s year is exactly 3/2 of Neptune’s, Neptune’s year is twice that of Uranus, and so on.  If a planet doesn’t synch up with its neighbors, it’ll collide with someone or be flung out of the system.  Put another way, a system’s not stable if its planetary orbit periods are just any old numbers.  Make sense?”

“I suppose, so…?”

“So look at this guy’s table.  The periods of each pair of adjacent objects follow that rule almost exactly.  Five times c‘s period is less than 0.25% away from eight times b‘s, and so on all the way out to h, which I take it has an uncertain period because the guy put in that question mark.  In fact, I think this system follows the rule more tightly than our Solar System does.  As far as I’m concerned that regularity in the periods makes the case for TRAPPIST-1 having planets.  You hear anything else?”

“Yeah, there was a lot of excitement about the middle three planets being in some kind of Goldilocks zone.  What’s that about?”

“Hah, I’d be excited, too.  If a planet’s too close to the star, like Mercury is to ours, it’ll be too hot for liquid water.  If the planet’s too far, any water it has would be frozen stiff.  Either way, not good for life to grow there.  In the Goldilocks zone, it’s…”

“Just right, huh, Sy?”

“On the nose, Al.  I’m going to have to read up on TRAPPIST-1.”

~~ Rich Olcott