Rotation, Revolution and The Answer

“Sy, I’m startin’ to think you got nothin’. Al and me, we ask what’s pushing the Moon away from us and you give us angular momentum and energy transfers. C’mon, stop dancin’ around and tell us the answer.”

“Yeah, Sy, gravity pulls things together, right, so how come the Moon doesn’t fall right onto us?”

“Not dancing, Vinnie, just laying some groundwork for you. Newton answered Al’s question — the Moon is falling towards us, but it’s going so fast it overshoots. That’s where momentum comes in, Vinnie. Newton showed that a ball shot from a cannon files further depending on how much momentum it gets from the initial kick. If you give it enough momentum, and set your cannon high enough that the ball doesn’t hit trees or mountains, the ball falls beyond the planet and keeps on falling forever in an elliptical orbit.”

“Forever until it hits the cannon.”

“hahaha, Al. Anyway, the ball achieves orbit by converting its linear momentum to angular momentum with the help of gravity. The angular momentum pretty much defines the orbit. In Newton’s gravity‑determined universe, momentum and position together let you predict everything.”

“Linear and angular momentum work the same way?”

“Mostly. There’s only one kind of linear momentum — straight ahead — but there are two kinds of angular momentum — rotation and revolution.”

“Aw geez, there’s another pair of words I can never keep straight.”

“You and lots of people, Vinnie. They’re synonyms unless you’re talking technicalese. In Physics and Astronomy, rotation with the O gyrates around an object’s own center, like a top or a planet rotating on its axis. Revolution with the E gyrates around some external location, like the planet revolving around its sun. Does that help?”

“Cool, that may come in handy. So Newton’s cannon ball got its umm, revolution angular momentum from linear momentum so where does rotation angular momentum come from?”

“Subtle question, Vinnie, but they’re actually all just momentum. Fair warning, I’m going to avoid a few issues that’d get us too far into the relativity weeds. Let’s just say that momentum is one of those conserved quantities. You can transfer momentum from one object to another and convert between forms of momentum, but you can’t create momentum in an isolated system.”

“That sounds a lot like energy, Sy.”

“You’re right, Al, the two are closely related. Newton thought that momentum was THE conserved quantity and all motion depended on it. His arch‑enemy Leibniz said THE conserved quantity was kinetic energy, which he called vis viva. That disagreement was just one battle in the Newton‑Leibniz war. It took science 200 years to understand the momentum/kinetic energy/potential energy triad.”

“Wait, Sy, I’ve seen NASA steer a rocketship and give it a whole different momentum. I don’t see no conservation.”

“You missed an important word, Vinnie — isolated. Momentum calculations apply to mechanical systems — no inputs of mass or non‑mechanical energy. Chemical or nuclear fuels break that rule and get you into a different game.”

“Ah-hahh, so if the Earth and Moon are isolated…”

“Exactly, and you’re way ahead of me. Like we said, no significant net forces coming from the Sun or Jupiter, so no change to our angular momentum.”

“Hey, wait, guys. Solar power. I know we’ve got a ton of sunlight coming in every day.”

“Not relevant, Al. Even though sunlight heats the Earth, mass and momentum aren’t affected by temperature. Anyhow, we’re finally at the point where I can answer your question.”

“About time.”

“Hush. OK, here’s the chain. Earth rotates beneath the Moon and gets its insides stirred up by the Moon’s gravity. The stirring is kinetic energy extracted from the energy of the Earth‑Moon system. The Moon’s revolution or the Earth’s rotation or both must slow down. Remember the M=m·r·c/t equation for angular momentum? The Earth‑Moon system is isolated so the angular momentum M can’t change but the angular velocity c/t goes down. Something’s got to compensate. The system’s mass m doesn’t change. The only thing that can increase is distance r. There’s your answer, guys — conservation of angular momentum forces the Moon to drift outward.”

“Long way to the answer.”

“To the Moon and back.”

~~ Rich Olcott

Several Big Sloshes

“I call distraction, Sy. You were going to explain how come the Moon’s drifting away from us but you got us into radians and stuff. What’s that got to do with the Moon flying away by dragging a big wave around the Earth?”

“It’s not dragging a localized bulge of water like you’re thinking, Vinnie, nothing like that wave on Miller’s Planet. For that matter, the Miller’s Planet wave had a sharply‑rising front which also doesn’t look like the textbook tidal bulge.”

“There’s a textbook on this stuff?”

“Many, Al. Heavy-duty people have spent a lot of time on tides. Think about all the military and commercial navies that depend on boats being able to leave port and dock on schedule.”

“And not run aground <heh heh>”

“Well, yes, Vinnie. Anyhow, like a lot of pre‑computer Physics, that work was based on a simplified ideal system — a moon orbiting a smooth planet with a world‑covering ocean. Water’s drawn horizontally towards the sub‑lunar points making an egg‑shaped surface and everything’s neat.”

“Probably nothing like real life.”

“Of course. Here’s a video I built from satellite altimetry data. The grey dot is roughly the point underneath the Moon as that day progressed. The red‑to‑blue height scale’s in meters.. Not as neat as theory, is it?”

“Wow, that’s a mess. Looks like the Moon’s pulling water along the Canada‑Alaska coast okay, and the western Pacific starts to get a dome going. But the water never catches up before the Moon’s gone.”

“Hey, Vinnie, look how the tides just go round and round New Zealand. And what’s that, Hudson Bay, it’s a pinwheel.”

“Yeah, and in between Africa and Madagascar it’s completely out of phase from what it oughta be.”

“What you’re looking at is slosh. Once again, reality overwhelms a pretty theory. Each basin has its own preferred set of oscillations. None of them match up with the Moon. But the other thing — “

“Tiny numbers. Everything’s like less than a couple meters, not not a big bulge at all.”

“Bingo, Vinnie. Against Earth’s 6.4‑million‑meter radius, those small chaotic sloshes don’t make for effective energy transfer driving the Moon away from us. That theory’s toast.”

“So what’s doing it?”

“There’s two theories that I know of, and they’re probably both right. The first one is Earth tides — that bump you think of as traveling around the planet, but the bump is rock instead of water.”

“That can’t be a big effect. Rocks don’t bend.”

“On a planetary scale they’re not as solid as you think, Vinnie. The rock crust is brittle and really thin, less than half a percent of Earth’s radius. It floats on molten outer mantle which has the fluidity of tapioca pudding. When that structure gives under stress the crust layer cracks. The seismologists and GPS techs have measured surface motion all over the world. When they analyze the maps, the lunar component accounts for up to a meter of coordinated vertical daily movement. Figure the whole Earth is continually being squeezed and pulled to that extent and you’ve got a lot of energy being expended every 24 hours.”

“How about the other theory?”

“There’s no direct evidence, so far as I know, but it seems reasonable on physical grounds. We’ve got two gyrations going on here, right? The Moon is on a 29½‑day orbit while the Earth rotates about thirty times faster. But the two motions use different frames. The Earth’s spin axis runs through the geometric center of the planet and tilts 23° from its orbit axis. Meanwhile the whole Earth‑Moon system rotates about its barycenter, their common center of gravity, which stays inside the Earth about ¾ of the way moonward from the Earth’s middle. That rotation is about 5° away from Earth’s orbit’s axis. Imagine a molten blob near the barycenter, happily following the Moon in the Earth-Moon frame, but the rest of the planet is saying, ‘No, no, you’re supposed to be moving hundreds of miles an hour in a different direction!‘ If the blob’s the least bit lighter or heavier than its neighbor blobs, inertial forces expend energy to kick it out of there.”

“So we got two ways to transfer energy steady-like.”

“I think so.”

~~ Rich Olcott

Here’s a Different Angle

“OK, Sy, so there’s a bulge on the Moon’s side of the Earth and the Earth rotates but the bulge doesn’t and that makes the Moon’s orbit just a little bigger and you’ve figured out that the energy it took to lift the Moon raised Earth’s temperature by a gazillionth of a degree, I got all that, but you still haven’t told Al and me how the lifting works.”

“You wouldn’t accept it if I just said, ‘The Moon lifts itself by its bootstraps,’ would you?”

“Not for a minute.”

“And you don’t like equations. <sigh> OK, Al, pass over some of those paper napkins.”

“Aw geez, Sy.”

“You guys asked the question and this’ll take diagrams, Al. Ante up. … Thanks. OK, remember the time Cathleen and I caught Vinnie here at Al’s shop playing with a top?”

“Yeah, and he was spraying paper wads all over the place.”

“I wasn’t either, Al, it was the top sending them out with centri–…, some force I can never remember whether it’s centrifugal or centripetal.”

“Centrifugal, Vinnie, –fugal– like fugitive, outward‑escaping force. It’s one of those ‘depends on how you look at itfictitious forces. From where you were sitting, the wads looked like they were flying outward perpendicular to the top’s circle. From a wad’s point of view, it flew in a straight line tangent to the circle. It’s like we have two languages, Room and Rotor. They describe the same phenomena but from different perspectives.”

“Hey, it’s frames again, ain’t it?”

“Newton’s inertial frames? Sort‑of but not quite. Newton’s First Law only holds in the Room frame — no acceleration, motion is measured by distance, objects at rest stay put. Any other object moves in a straight line unless its momentum is changed by a force. You can tackle a problem by considering momentum and force components along separate X and Y axes. Both X and Y components work the same way — push twice as hard in either direction, get twice the acceleration in that direction. Nice rules that the Rotor frame doesn’t play by.”

“I guess not. The middle’s the only place an object can stay put, right?”

“Exactly, Al. Everything else looks like it’s affected by weird, constantly‑varying forces that’re hard to describe in X‑Y terms.”

“So that breaks Newton’s physics?”

“Of course not. We just have to adapt his F=m·a equation (sorry, Vinnie!) to Rotor conditions. For small movements we wind up with two equations. In the strict radial direction it’s still F=m·a where m is mass like we know it, a is acceleration outward or inward, and F is centrifugal or centripetal, depending. Easy. Perpendicular to ‘radial‘ we’ve got ‘angular.’ Things look different there because in that direction motion’s measured by angle but Newton’s Laws are all about distances — speed is distance per time, acceleration is speed change per time and so forth.”

“So what do you do?”

“Use arc length. Distance along an arc is proportional to the angle, and it’s also proportional to the radius of the arc, so just multiply them together.”

“What, like a 45° bend around a 2-foot radius takes 90 feet? That’s just wrong!”

“No question, Al. You have to measure the angle in the right units. Remember the formula for a circle’s circumference?”

“Sure, it’s 2πr.”

“Which tells you that a full turn’s length is times the radius. We can bridge from angle to arc length using rotational units so that a full turn, 360°, is units. We’ll call that unit a radian. Half a circle is π radians. Your 45° angle in radians is π/4 or about ¾ of a radian. You’d need about (¾)×(2) or 1½ feet of whatever to get 45° along that 2-foot arc. Make sense?”

“Gimme a sec … OK, I’m with you.”

“Great. So if angular distance is radius times angle, then angular momentum which is mass times distance per time becomes mass times radius times angle per time.”

“”Hold on, Sy … so if I double the mass I double the momentum just like always, but if something’s spinning I could also double the angular momentum by doubling the radius or spinning it twice as fast?”

“Couldn’t have put it better myself, Vinnie.”

~~ Rich Olcott

Two Against One, And It’s Not Even Close


On a brisk walk across campus when I hear Vinnie yell from Al’s coffee shop. “Hey! Sy! Me and Al got this argument going you gotta settle.”

“Happy to be a peacemaker, but it’ll cost you a mug of Al’s coffee and a strawberry scone.”

“Coffee’s no charge, Sy, but the scone goes on Vinnie’s tab. What’s your pleasure?”

“It’s morning, Al, time for black mud. What’s the argument, Vinnie?”

“Al read in one of his astronomy magazines that the Moon’s drifting away from us. Is that true, and if it is, how’s it happen? Al thinks Jupiter’s gravity’s lifting it but I think it’s because of Solar winds pushing it. So which is it?”

“Here you go, Sy, straight from the bottom of the pot.”

“Perfect, Al, thanks. Yes, it’s true. The drift rate is about 1¼ nanometers per second, 1½ inches per year. As to your argument, you’re both wrong.”

“Huh?”
 ”Aw, c’mon!”

“Al, let’s put some numbers to your hypothesis. <pulling out Old Reliable and screen‑tapping> I’m going to compare Jupiter’s pull on the Moon to Earth’s when the two planets are closest together. OK?”

“I suppose.”

“Alright. Newton’s Law tells us the pull is proportional to the mass. Jupiter’s mass is about 320 times Earth, which is pretty impressive, right? But the attraction drops with the square of the distance. The Moon is 1¼ lightseconds from Earth. At closest approach, Jupiter is almost 2100 lightseconds away, 1680 times further than the Moon. We need to divide the 320 mass factor by a 1680‑squared distance factor and that makes <key taps> Jupiter’s pull on the Moon is only 0.011 percent of Earth’s. It’ll be <taps> half that when Jupiter’s on the other side of the Sun. Not much competition, eh?”

“Yeah, but a little bit at a time, it adds up.”

“We’re not done yet. The Moon feels the big guy’s pull on both sides of its orbit around Earth. On the side where the Moon’s moving away from Jupiter, you’re right, Jupiter’s gravity slows the Moon down, a little. But on the moving-toward-Jupiter side, the motion’s sped up. Put it all together, Jupiter’s teeny pull cancels itself out over every month’s orbiting.”

“Gotcha, Al. So what about my theory, Sy?”

“Basically the same logic, Vinnie. The Solar wind varies, thanks to the Sun’s variable activity, but satellite measurements put its pressure somewhere around a nanopascal, a nanonewton per square meter. Multiply that by the Moon’s cross‑sectional area and we get <tap, tap> a bit less than ten thousand newtons of force on the Moon. Meanwhile, Newton’s Law says the Earth’s pull on the Moon comes to <tapping>
  G×(Earth’s mass)×(Moon’s mass)/(Earth-Moon distance)²
and that comes to 2×1011 newtons. Earth wins by a 107‑fold landslide. Anyway, the pressure slows the Moon for only half of each month and speeds it up the other half so we’ve got another cancellation going on.”

“So what is it then?”
 ”So what is it then?”

“Tides. Not just ocean tides, rock tides in Earth’s fluid outer mantle. Earth bulges, just a bit, toward the Moon. But Earth also rotates, so the bulge circles the planet every day.”

“Reminds me of the wave in the Interstellar movie, but why don’t we see it?”

“The movie’s wave was hundreds of times higher than ours, Al. It was water, not rock, and the wave‑raiser was a huge black hole close by the planet. The Moon’s tidal pull on Earth produces only a one‑meter variation on a 6,400,000‑meter radius. Not a big deal to us. Of course, it makes a lot of difference to the material that’s being kneaded up and down. There’s a lot of friction in those layers.”

“Friction makes heat, Sy. Rock tides oughta heat up the planet, right?”

“Sure, Vinnie, the process does generate heat. Force times distance equals energy. Raising the Moon by 1¼ nanometers per second against a force of 2×1021 newtons gives us <taping furiously> an energy transfer rate of 4×10‑23 joules per second per kilogram of Earth’s 6×1024‑kilogram mass. It takes about a thousand joules to heat a kilogram of rock by one kelvin so we’re looking at a temperature rise near 10‑27 kelvins per second. Not significant.”

“No blaming climate change on the Moon, huh?”

~~ Rich Olcott

Moon Shot

<chirp, chirp> “Moire here.”

“Hi, Mr Moire, it’s Jeremy. Hey, I’ve been reading through some old science fiction stories and I ran across some numbers that just don’t look right.”

“Science fiction can be pretty clunky. Some Editors let their authors play fast and loose on purpose, just to generate Letters to The Editor. Which author and what story?”

“This is Heinlein, Mr Moire. I know his ideas about conditions on Mars and Venus were way off but that was before we had robot missions that could go there and look. When he writes about space navigation, though, he’s always so specific it looks like he’d actually done the calculations.”

“OK, which story and what numbers?”

“This one’s called, let me check, Gentlemen, Be Seated. It’s about these guys who get trapped in a tunnel on the Moon and there’s a leak letting air out of the tunnel so they seal the leak when one of the guys —”

“I know the story, Jeremy. I’ve always wondered if it was Heinlein or his Editor who got cute with the title. Anyway, which numbers bothered you?”

“I kinda thought the title came first. Anyway, everybody knows that the Earth’s gravity is six times the Moon’s, but he says that the Earth’s mass is eighty times the Moon’s and that’s why the Earth raises tides on the Moon except they’re rock tides, not water tides, and the movement makes moonquakes and one of them might have caused the leak. So why isn’t the Earth’s gravity eighty times the Moon’s, not six?”

“Read me the sentence about eighty.”

“Umm … here it is, ‘Remember, the Earth is eighty times the mass of the Moon, so the tidal stresses here are eighty times as great as the Moon’s effect on Earth tides.‘ I checked the masses in Wikipedia and eighty is about right.”

“I hadn’t realized the ratio was that large, I mean that the Moon is that small. One point for Heinlein. Anyway, you’re comparing north and east. The eighty and the six both have to do with gravity but they’re pointing in different directions.”

“Huh? I thought gravity’s pull was always toward the center.”

“It is, but it makes a difference where you are and which center you’re thinking about. You’re standing on the Earth so the closest center to you is Earth’s and most of the gravity you feel is the one-gravity pull from there. Suppose you’re standing on the Moon —”

“One-sixth, I know, Mr Moire, but why isn’t it one‑eightieth?”

“Because on the Moon you’re a lot closer to the center of the Moon than you were to the center of the Earth back on Earth. Let’s put some numbers to it. Got a calculator handy?”

“Got my cellphone.”

“Duh. OK, Newton showed us that an object’s gravitational force is proportional to the object’s mass divided by the square of the distance to the center. Earth’s radius is about 4000 miles and the Moon’s is about a quarter of that, so take the mass as 1/80 and divide by 1/4 squared. What do you get?”

“Uhh … 0.2 gravities.”

“One-fifth g. Close enough to one-sixth. If we used accurate numbers we’d be even closer. See how distance makes a difference?”

“Mm-hm. What about Heinlein’s tidal stuff?”

“Ah, now that’s looking in the other direction, where the distance is a lot bigger. Earth-to-Moon is about 250,000 miles. Standing on the Moon, you’d feel Earth’s one‑g gravity diminished by a factor of 4000/250000 squared. What’s that come to?”

“Umm… the distance factor is (4000/250000)² … I get 250 microgravities. Not much. Heinlein made a good bet with his characters deciding that the leak was caused by a nearby rocket crash instead of a moonquake.”

“How about Heinlein’s remark about the Moon’s effect on Earth?”

“Same distance but one eightieth the mass so I divide by 80 — three microgravities. Wow! That can’t possibly be strong enough to raise tides here.”

“It isn’t, though that’s the popular idea. What really happens is that the Moon’s field pulls water sideways from all directions towards the sub‑Lunar point. Sideways motion doesn’t fight Earth’s gravity, it just makes the water pile up in the center.”

“Hah, piled-up water. Weird. Well, I feel better about Heinlein now.”

~~ Rich Olcott

Only a H2 in A Gilded Cage

“OK, Susan, you’ve led us through doing high-pressure experiments with the Diamond Anvil Cell and you’ve talked about superconductivity and supermagnetism. How do they play together?”

“It’s early days yet, Sy, but Dias and a couple of other research groups may have brought us a new kind of superconductivity.”

“Another? You talked like there’s only one.”

“It’s one of those ‘depends on how you look at it‘ things, Al. We’ve got ‘conventional‘ superconductors and then there are the others. The conventional ones — elements like mercury or lead, alloys like vanadium‑silicon — are the model we’ve had for a century. Their critical temperatures are generally below 30 kelvins, really cold. We have a 60‑year‑old Nobel‑winning theory called ‘BCS‘ that’s so good it essentially defines conventional superconductivity. BCS theory is based on quantum‑entangled valence electrons.”

“So I guess the unconventional ones aren’t like that, huh?”

“Actually, there seem to be several groups of unconventionals, none of which quite fit the BCS theory. Most of the groups have critical temperatures way above what BCS says should be the upper limit. There are iron‑based and heavy‑metals‑based groups that use non‑valence electrons. There are a couple of different carbon‑based preparations that are just mystical. There’s a crazy collection of copper oxide ceramics that can contain five or more elements. Researchers have come up with theories for each of them, but the theories aren’t predictive — they don’t give dependable optimization guidelines.”

“Then how do they know how to make one of these?”

“Old motto — ‘Intuition guided by experience.’ There are so many variables in these complex systems — add how much of each ingredient, cook for how long at what temperature and pressure, chill the mix quickly or anneal it slowly, bathe it in an electrical or magnetic field and if so, how strong and at what point in the process… Other chemists refer to the whole enterprise as witch’s‑brew chemistry. But the researchers do find the occasional acorn in the grass.”

“I guess the high‑pressure ploy is just another variable then?”

“It’s a little less random than that, Sy. If you make two samples of a conventional superconductor, using different isotopes of the same element, the sample with the lighter isotope has the higher critical temperature. That’s part of the evidence for BCS theory, which says that electrons get entangled when they interact with vibrations in a superconductor. At a given temperature light atoms vibrate at higher frequency than heavy ones so there’s more opportunity for entanglement to get started . That set some researchers thinking, ‘We’d get the highest‑frequency vibrations from the lightest atom, hydrogen. Let’s pack hydrogens to high density and see what happens.'”

“Sounds like a great idea, Susan.”

“Indeed, Al, but not an easy one to achieve. Solid metallic hydrogen should be the perfect case. Dias and his group reported on a sample of metallic hydrogen a couple of years ago but they couldn’t tell if it was solid or liquid. This was at 5 megabars pressure and their diamonds broke before they could finish working up the sample. Recent work has aimed at using other elements to produce a ‘hydrogen‑rich’ environment. When Dias tested H2S at 1.5 megabar pressure, they found superconductivity at 203 kelvins. Knocked everyone’s socks off.”

“Gold rush! Just squeeze and chill every hydrogen‑rich compound you can get hold of.”

“It’s a little more complicated than that, Sy. Extreme pressures can force weird chemistry. Dias reported that shining a green laser on a pressurized mix of hydrogen gas with powdered sulfur and carbon gave them a clear crystalline material whose critical temperature was 287 kelvins. Wow! A winner, for sure, but who knows what the stuff is? Another example — the H2S that Dias loaded into the DAC became H3S under pressure.”

“Wait, three hydrogens per sulfur? But the valency rules—”

“I know, Sy, the rules say two per sulfur. Under pressure, though, you get one unattached molecule of H2 crammed into the space inside a cage of H2S molecules. It’s called a clathrate or guest‑host structure. The final formula is H2(H2S)2 or H3S. Weird, huh? Really loads in the hydrogen, though.”

“Jupiter has a humungous magnetic field and deep‑down it’s got high‑density hydrogen, probably metallic. Hmmm….”

~~ Rich Olcott

Zeroing In on Water

<chirp, chirp> “Moire here.”

“Hi, Sy, it’s me, Vinnie. I just heard this news story about finding water on the Moon. I thought we did that ten years ago. You even wrote about it.”

“The internet never forgets, does it? That post wasn’t quite right but it wasn’t wrong, either.”

“How can it be both?”

“There’s an old line in Science — ‘Your data’s fine but your conclusions are … nuts.’ They use a different word in private. Suppose you land on a desert island and find a pirate’s treasure chest. Should the headlines say you’d found a treasure?”

“Naw, the chest might be empty or full of rocks or something.”

“Mm-hm. So, going back to that post… I was working from some reports on NASA’s Lunar Reconnaissance Orbiter. Its LAMP instrument mapped how strongly different Moon features reflected a particular frequency of ultraviolet light. That frequency’s called ‘Lyman‑alpha.’ Astronomers care about it because it’s part of starlight, it’s reflected by rock, and it’s specifically absorbed by hydrogen atoms. Sure enough, LAMP found some places, typically in deepshadow craters, that absorbed a lot more Lymanalpha than other places.”

“And you wrote about how hydrogen atoms are in water molecules and the Moon’s deep crater floors near the poles are sheltered from sunlight that’d break up water molecules so LAMP’s dark spots are where there’s water. And you liked how using starlight to find water on the Moon was poetical.”

“Uhh… right. All that made a lot of sense at the time and it still might be true. Scientists leapt to the same hopeful conclusion when interpreting data from the MESSENGER mission to Mercury. That one used a neutron spectrometer to map emissions from hydrogen atoms interacting with incoming cosmic rays. There again, the instrument identified hydrogen collected in shaded craters at the planet’s poles. Two different detection methods giving the same positive indication at the same type of sheltered location. The agreement seemed to settle the matter. The problem is that water isn’t geology’s only way or even its primary way to accumulate hydrogen atoms.”

“What else could it be? Hydrogen ions in the solar wind grab oxide ions from Moon rock and you’ve got water, right?”

“But the hydrogens arrive one at a time, not in pairs. Any conversion would have to be at least a two‑step process. The Moon’s surface rocks are mostly silicate minerals. They’re a lattice of negative oxide ions that’s decorated inside with an assortment of positive metal ions. The first step in the conversion would be for one hydrogen ion to link up with a surface oxide to make a hydroxide ion. That species has a minus‑one charge instead of oxide’s minus‑two so it’s a bit less tightly bound to its neighboring metal ions. Got that?”

“Gimme a sec … OK, keep going.”

“Some time later, maybe a century maybe an eon, another hydrogen ion comes close enough to attack our surface hydroxide if it hasn’t been blasted apart by solar UV light. Then you get a water molecule. On balance and looking back, we’d expect most of the surface hydrogen to be hydroxide ions, not water, but both kinds would persist better in shadowed areas.”

“OK, two kinds of hydrogen. But how do we tell the difference?”

“We evaluate processes at lower‑energies. Lyman‑alpha photons pack over 10 electronvolts of energy, enough to seriously disturb an atom and blow a molecule apart. O‑H and H‑O‑H interact differently with light in the infra‑red range that just jiggles molecules instead of bopping them. For instance, atom pairs can stretch in‑out. Different kinds of atom bind together more‑or‑less tightly. That means each kind of atom pair resonates at its own stretch energy, generally around 6 microns or 0.41 electronvolts. NASA’s Cassini mission had a mapping spectrometer that could see down into that range. It found O‑H stretching activity all over the Moon’s surface.”

“But that could be either hydroxyls or water.”

“Exactly. The new news is that sensors aboard NASA’s airborne SOFIA mission map light even deeper into the infra‑red. It found the 3‑micron, 0.21‑electronvolt signal for water’s V‑shape scissors motion. That’s the water that everybody’s excited about.”

“Lots of it?”

“Thinly spread, probably, but stay tuned.”

~~ Rich Olcott

To Swerve And Project

A crisp Fall dawn, crisp fallen leaves under my feet as I jog the path by the park’s lake.

“Hey! Moire! How about these red sunrises and sunsets? Remind you of Mars?”

“Morning, Mr Feder. Not much, and definitely not dawn or dusk. Those tend more to blue, as a matter of fact.”

“Waitaminnit, Moire. I seen that Brad Pitt Martian movie, him driving hisself all alone across that big plain — the place is blood‑red.”

“Think a minute, Mr Feder. If he was all alone, who was running the cameras?”

“Uhhh, right. Movie. Yeah, they were really on Earth so they could director the lighting and all. But they said they’d scienced the … heck out of it.”

“Oh they did, better than most movies, but artistic license took over in a couple of places. People expect Mars to be red, not mostly clay colored like it really is, so the producers served up red.”

“Wait, I remember the conversation about Earth is blue because of the oceans and Mars is red because of its rusty atmosphere. So what’s with the sky colors?”

“Looking up at sunlight through an atmosphere is very different from looking down at the surface. It all has to do with how what’s in the atmosphere interacts with sunlight. Take Earth’s blue sky, for instance.”

“My favorite color.”

“Sure it is. OK, the Sun’s disk takes up much less than 1% of the sky but that’s enough to give us all our sunlight photons. A fraction of them run into something on the way down to Earth’s surface. What happens depends on how big the something is compared to the photon wavelength. Much larger things, maybe an airplane, completely block the photons and we get a shadow.”

“Obviously.”

“Yeah, but life’s more interesting for smaller somethings. For things like air molecules and dust particles that are much smaller than the the wavelength of visible light, the waves generally swerve around the particle. How much they swerve depends on the wavelength — extreme blue light bends about ten times more than extreme red light for the same scattering particle. So suppose there’s a kid a few miles away from us looking at the sky while we’re looking at it here. There’s a sunbeam with a rainbow‑load of photons headed for the kid, but there are dust particles in the way. Get the picture?”

“Sure, sure, get on with it.”

“So some of the light swerves. The red swerves a little but the blue light swerves ten times as much, enough that it heads straight for us. What color do we see when we look in that direction?”

“Blue, of course.”

“Blue everywhere in the lit‑up sky except when we look straight at the Sun.”

“What about these pretty red sunsets and the red skies over the wildfires?”

“Two different but related phenomena. Sunsets first. An incoming photon with just the right wavelength may simply be absorbed by a molecule. Doesn’t happen often, but there’s lots of molecules. Turns out that oxygen and ozone absorb blue light more strongly than red light. When we’re looking horizontally towards a sunset we’re looking through many more oxygen molecules than when we look vertically. We see the red part of a blue‑filtered version of that swerve rainbow.”

“And the fire skies?”

“The fires released huge amounts of fine smoke particles, just the right size for color‑scattering. Blue light swerves again and again until it’s either absorbed or shot out to space. Red light survives.”

Upper image – Golden Gate Bay under fiery skies, Sept 2020
Lower image – Sunset from Gusev Crater, Mars
Credit: NASA/JPL/Texas A&M/Cornell

“So what’s different about Mars?”

“Three things — Mars dust is different from Earth’s, its atmosphere is a lot thinner, and there’s practically no atmospheric water or oxygen. Rusty Mars dust is the size of smoke particles. With no rain or snow to settle out the dust, it stays aloft all the time. Rust is red because it absorbs blue light and reflects only the red part. With less diffused sunlight, Mars’ sky is basically the black of space overlaid with a red tint. Sunsets are blue‑ish because what blue light there is can travel further.”

“Earth skies are better.”

~~ Rich Olcott

Question Time

Cathleen unmutes her mic. “Before we wrap up this online Crazy Theories contest with voting for the virtual Ceremonial Broom, I’ve got a few questions here in the chat box. The first question is for Kareem. ‘How about negative evidence for a pre-mammal civilization? Played-out mines, things like that.‘ Kareem, over to you.”

“Thanks. Good question but you’re thinking way too short a time period. Sixty‑six million years is plenty of time to erode the mountain a mine was burrowing into and take the mining apparatus with it.

“Here’s a different kind of negative evidence I did consider. We’re extracting coal now that had been laid down in the Carboniferous Era 300 million years ago. At first, I thought I’d proved no dinosaurs were smart enough to dig up coal because it’s still around where we can mine it. But on second thought I realized that sixty-six million years is enough time for geological upthrust and folding to expose coal seams that would have been too deeply buried for mining dinosaurs to get at. So like the Silurian Hypothesis authors said, no conclusions can be drawn.”

“Nice response, Kareem. Jim, this one’s for you. ‘You said our observable universe is 93 billion lightyears across, but I’ve heard over and over that the Universe is 14 billion years old. Did our observable universe expand faster than the speed of light?‘”

“That’s a deep space question, pun intended. The answer goes to what we mean when we say that the Hubble Flow expands the Universe. Like good Newtonian physicists, we’re used to thinking of space as an enormous sheet of graph paper. We visualize statements like, ‘distant galaxies are fleeing away from us‘ as us sitting at one spot on the graph paper and those other galaxies moving like fireworks across an unchanging grid.

“But that’s not the proper post-Einstein way to look at the situation. What’s going on is that we’re at our spot on the graph paper and each distant galaxy is at its spot, but the Hubble Flow stretches the graph paper. Suppose some star at the edge of our observable universe sent out a photon 13.7 billion years ago. That photon has been headed towards us at a steady 300000 kilometers per second ever since and it finally reached an Earth telescope last night. But in the meantime, the graph paper stretched underneath the photon until space between us and its home galaxy widened by a factor of 3.4.

“By the way, it’s a factor of 3.4 instead of 6.8 because the 93 billion lightyear distance is the diameter of our observable universe sphere, and the photon’s 13.7 billion lightyear trip is that sphere’s radius.

“Mmm, one more point — The Hubble Flow rate depends on distance and it’s really slow on the human‑life timescale. The current value of the Hubble Constant says that a point that’s 3×1019 kilometers away from us is receding at about 70 kilometers per second. To put that in perspective, Hubble Flow is stretching the Moon away from us by 3000 atom‑widths per year, or about 1/1300 the rate at which the Moon is receding because of tidal friction.”

“Nice calculation, Jim. Our final question is for Amanda. ‘Could I get to one of the other quantum tracks if I dove into a black hole and went through the singularity?‘”

“I wouldn’t want to try that but let’s think about it. Near the structure’s center gravitational intensity compresses mass-energy beyond the point that the words ‘particle’ and ‘quantum’ have meaning. All you’ve got is fields fluctuating wildly in every direction of spacetime. No sign posts, no way to navigate, you wouldn’t be able to choose an exit quantum track. But you wouldn’t be able to exit anyway because in that region the arrow of time points inward. Not a sci‑fi story with a happy ending.”

“<whew> Alright, folks, time to vote. Who presented the craziest theory? All those in favor of Kareem, click on your ‘hand’ icon. … OK. Now those voting for Jim? … OK. Now those voting for Amanda? … How ’bout that, it’s a tie. I guess for each of you there’s a parallel universe where you won the virtual Ceremonial Broom. Congratulations to all and thanks for such an interesting evening. Good night, everyone.”

~~ Rich Olcott

Smart Dinosaurs?

<chirp, chirp> “Moire here, what can I do for you while staying six feet away?”

“Hi, Sy, this is Cathleen. you’re invited to to an experiment.”

“What sort of experiment?”

“You’ve been to a few of our ‘Crazy Theory’ events. We can’t do those now, of course, but we’re trying it online. Interested?”

“Sounds like fun. Email me the details and I’ll dial in.”


“Hi, everyone, welcome to our first-ever online ‘Crazy Theories’ seminar. I’m afraid it’ll be a bit different from our traditional affairs. Everyone but the presenter’s on mute so don’t bother shouting encouragement or booing. Any spitballs or wadded-up paper napkins you throw you get to clean up. As always at the end we’ll take a vote to award the Ceremonial Broom for the craziest theory. Type your questions and comments in the chat box; we’ll get to them after the presenter finishes. Everybody got all that? OK, our first presenter is from my Planetology class. Go ahead, Kareem.”

“Hey, everybody. I’m Kareem and my Crazy Theory isn’t mine, personally, but it’s the one that got me into Planetology class. Its was in this science fiction novel I read a couple of years ago. The story’s complicated and has a lot of science that I didn’t understand, but the part that caught my imagination was his idea that what killed off the dinosaurs was smart dinosaurs.”

<consults notes>

“A little history first. In the late 1970s two scientists named Alvarez discovered that all around the Earth there’s a thin layer of soil with more than ten times the normal amount of an element called iridium. They found that the layer was 66 million years old, which just matched the end of the Cretaceous Era when the last of the dinosaurs died off. They knew that some meteorites have a lot of iridium so in 1980 they suggested that a meteor strike must have done the deed.

“That idea was so controversial that John McLoughlin came up with his own explanation and based his book on it. He supposed that about 66 million years ago evolution produced intelligent dinosaurs that took over the planet the way that we humans have in our time. They weren’t huge like T‑rex but they were big enough to use Triceratops as draft and meat animals and smart enough to develop lots of iridium‑based technology like we use copper. Anyway, they got into a world war and that was what wiped everything out and left behind the traces of iridium.”

<gulps down soda>

“McLaughlin’s book came out in 1988. Since than we’ve learned that the Alvarez guys were basically right although there was some other stuff going on, too. But the book got me thinking that maybe there could have been a world‑wide civilization and the only things left after 66 million years were bones and this trace of a metal they used. Humans have only been around for like a hundred thousand years and we’ve only been doing metals big‑time for a few hundred which is teeny compared to a million years. A paleontologist wouldn’t even be able to detect a time period that small. So my Crazy Theory is, maybe there were smart dinosaurs or something and we just haven’t found evidence for them.”

<burp>

“Ever since then I’ve kept an eye out for publications about what a vanished civilization might leave behind for us to discover. In this book Weisman lays out survival times for our civilization’s stuff — plastic, houses, roads and so on. Pretty much everything but Mount Rushmore and the Chunnel will have dissolved or eroded away much sooner than a million years. Really readable if you want more details.”

<more soda>

“I also found a paper, ‘The Silurian Hypothesis,’ that took a more technical approach. Their big library research project pulled results from scores of geologic isotope analysis and fossil survey reports looking for ancient times that resemble Earth’s sudden change since the start of the Industrial Age — climate, species declines, whatever. They found about a dozen, but as they said, ‘the known unique markers might not be indicative, while the (perhaps) more expected markers are not sufficient.’ In other words, my Crazy Theory might be crazy. Or maybe not.”

~~ Rich Olcott