Plutonic Goofyness

On By rolcottIn Astronomy: Planetary Science, UncategorizedLeave a comment
goofy-and-dp-pluto
Is Pluto wearing a space helmet?
No, that helmet is Pluto.
(Based on a cartoon by Andy Diehl)

Andy Diehl brings up a question worth considering over a tasty beverage.  How come Pluto’s a dog and Goofy’s a dog but Pluto gets the collar end of the leash?  Hardly seems fair.

Which brings us to that other controversial Pluto, the one that NASA’s New Horizon spacecraft visited last July.  (News flash — on 28 October, NASA announced that they’d received the very last of the data NH accumulated during that 2½-hour visit.)  Official Astronomy has reclassified Pluto from “planet” to “dwarf planet,” but NH honcho Alan Stern and much of the rest of the world say, “No way!”

The traditionalist position is, “But we’ve always called Pluto the ninth planet.”  Well, “always” only goes back to when the preternaturally persistent Clyde Tombaugh discovered the object in 1930.  At the time he found it Pluto was indeed the ninth “planet” out from the Sun.  However, it spends about 10% of each orbit* closer to the Sun than the eighth planet, Neptune.  So should we call it the “seven-and-a-fraction-th” planet?

No, because (1) that contravenes Official Astronomy’s rules, and (2) it’d be silly.

So what are the rules for what’s a planet?

  1. The object must be in orbit around its star.
  2. The object must be massive enough to be rounded by its own gravity.
  3. It must have cleared the neighborhood around its orbit.

“Rounded” is a bit tricky.  It doesn’t mean “spherical” because if you spin a  sphere, centrifugal forces move mass towards its equator.  Earth’s equator is 13.3 miles further away from its center than its poles are.  Miller’s Planet in the Interstellar movie is also a spheroid, even further deformed by elongation towards the black hole it orbits, yet it still rates as “rounded by its gravity” and qualifies as a planet.

“Clearing the neighborhood” means “my gravity dominates the motion of everything in my orbit.”  Earth and Jupiter, both acknowledged planets, each have retinues of asteroids in the Trojan positions, at the same distance from the Sun as the host planet but in regions 60º ahead of or behind it.  Even so, both planets often suffer messy encounters (remember Chicxulub and Chelyabinsk?) with asteroids and such that hadn’t gotten the memo.

Neptune meets all three criteria.  Its gravity dominates Pluto’s motion even though Pluto’s in a separate orbit.  For every three of Neptune’s trips around the Sun, Pluto makes exactly two.  The gravitational converse doesn’t hold, though.  Pluto’s mass is 0.1% of Neptune’s so the big guy doesn’t care.

pluto-orbits-1This video, from an Orbits Table display at the Denver Museum of Nature and Science, shows a different Plutonian weirdness.  We’re circling the Solar System at about 50 times Earth’s distance from the Sun (50 AU).  Reading inward, the white lines represent the orbits of Neptune, Uranus, Saturn and Jupiter.  The Asteroid Belt is the small greenish ring close to the Sun.  The four terrestrial planets are even further in.  The Kuiper Belt is the greenish ring that encloses the lot.

The  yellow-orange line is Pluto’s orbit.  Most of the Solar System lies within a thin pancake, the Plane of The Ecliptic. Pluto’s orbit is inclined 17º out of the Plane.  That’s odd.

Theory says that the System evolved from an eddy in a primordial cloud of dust and gas.  Gravity shrank that blob of stuff to form a disk at the eddy’s equator as it drew 99.9% of the system’s mass to form the Sun at the disk’s center.

Newton’s First Law is all about Conservation of Momentum.  When applied to circular motion, it says that if you’re whirling in a certain plane, you’ll continue whirling in that plane unless something knocks you out of that plane.  Hence, the Plane of The Ecliptic.

Pluto’s path is a puzzling challenge to the theory.  It was only a minor puzzle until the 1990’s when astronomers discovered a plethora of Pluto-type objects outside of Neptune’s orbit.  Most run way out of the Plane.  Worst is Eris, at inclination 44º .  Clearly, Pluto’s not special.  It belongs to a large tribe that Astrophysicists must explain if they’re to claim to  understand the Solar System.

~~ Rich Olcott

* – During its current 248-year orbit, Pluto was inside Neptune’s orbit between 1979 and 1999.

Hoppin’ water molecules

On By rolcottIn Astronomy: Planetary Science, Astronomy: Techniques, UncategorizedLeave a comment

chladny-2Before you get any further in this post, follow this link to Steve Mould’s demonstration of  Chladni figures.  (I’ll wait here.)  It’s a neat demo and the effect plays into some recent discoveries in planetary science.

Steve’s couscous grains dance to the vibrations of the iron plate they’re sitting on.  The patterns happen because he controls where those vibrations happen.  Or more importantly, don’t happen (see his fingers pinching the plate?).

The study of vibration goes back to Pythagoras, the ancient Greek geek who determined that a plucked stretched string invariably exhibits a whole number of peaks and nodes.  (A node is a point on the string that doesn’t move, like those dots on the chart).  I’m so tempted to yammer about the relationship between nodes and quantum mechanics, but I’ve already posted on that topic.sines

The important point for this post is that Steve’s demonstration shows individual particles, each moving under the influence of random impacts, nonetheless winding up at a common destination.  They’re repeatedly kicked away from points where the iron plate is fluctuating strongly.  If a particle suddenly finds itself on a non-fluctuating nodal point (or nodal line, which is just a collection of nodal points), it stays there because why not?

The basic principle applies to numerous phenomena in Physics, Chemistry and other Sciences.  The particles in Chladni’s experiment were grains of sand.  Steve used coucous grains, which work better in video.  But they could also be molecules.  On the Moon.

Back in the 2000s there was intense debate in the lunar astronomy community.  One argument went, “The Solar Wind teems with hydrogen ions (H+).  The Moon’s surface rocks are mostly silicon oxides.  Those H+ ions will yank oxygen O2- ions off exposed rocks to make H2O molecules.  There has to be water on the Moon!”

The other side of the argument (in real Science there’s always at least one other side) went, “Maybe so, but Solar radiation also contains high-energy electrons and photons that’ll rip those molecules apart.  Water can’t survive up there!”

If/when we plant a Moon colony, the colonists will need water.  Either it gets shipped up from Earth — EXPENSIVE — or we find and mine water up there.  NASA did the only thing that could be done — they sent up a spacecraft for a close look.   When the Lunar Reconnaissance Orbiter (the LRO) launched in 2009 it carried half-a-dozen instruments.  One of them was the Lyman Alpha Mapping Project (LAMP) camera.

LAMP was the embodiment of a sly trick.  Buried in starlight’s ultraviolet spectrum are photons (a.k.a. Lyman-α  light) with a wavelength of 121.6 nanometers.  They’re generated by excited hydrogen atoms and they’re (mostly) absorbed by hydrogen atoms but reflected by rock that doesn’t contain hydrogen.

LAMP’s camera was designed to be sensitive to just those Lyman-α photons.  As LRO circled the Moon, the LAMP camera recorded what fraction of those special photons was bouncing off the Moon.  By subtraction, it told us  what fraction was being absorbed by surface hydrogen.

LAMP did find water.  The fun facts are its form and location — it was frost, buried in “fluffy soils” in the walls of craters.
water-moonThis photo, part of the LAMP exhibit at the Denver Museum of Nature and Science, shows why.  It’s a model of a cratered Moon lit by sunlight.

An H2O molecule may develop anywhere on the Moon’s surface.  Then it experiences life’s usual slings and arrows (well, electrons and photons) that might blast it apart or might merely give it a kinetic kick to somewhere else.  That process continues until the molecule or a descendant drops into a nice shady crater.

The best craters would be the ones in the polar regions, where sunlight arrives at a low angle and the crater walls are permanently shadowed like the one at the top in the model.  That’s exactly were LAMP found the most dark spots.  HAH —  Chladni in space!

But there’s more.  In 2012, NASA’s MESSENGER spacecraft produced evidence for water on Mercury, the hottest planet in the Solar System.  Once again, those molecules were hiding in polar craters along with a few other surprising molecular species.  That knocked my socks off when I read the scientific report.

~~ Rich Olcott

A better idea for Life on Titan

On By rolcottIn Astronomy: Planetary Science, Chemistry, UncategorizedLeave a comment

Oh, I do love it when a theoretician comes in from the dugout and turns the game around.  Billy Beane did that for the Oakland baseball team (see Moneyball, the book or the movie).  Now a team led by James Stevenson in Dr Paulette Clancy’s lab at Cornell has done it for the scientific game of “What’s Life?”

Yeah, we’ve all seen the functional criteria: metabolism, self-regulation, growth, responsiveness, reproduction.  But structurally, everyone since Robert Hooke has known that living organisms are made of cells.  For the past 60 years we’ve known that those cells wear a cell membrane, a flexibly fluid two-layer construction of partly-oily molecules designed to separate watery cell contents from watery outside.

The standard membrane model is on the left in these sketches.  The zigzags represent long (15-20 carbons) hydrocarbon chains (the oily part); the red circles they’re bonded to stand for phosphate-containing groups that prefer a watery environment.  The polka dots are salts and other molecules floating in water.  The whole thing depends on  “oil and water don’t mix.”

ambipolar
Alternative membrane structures
(diagram on the right adapted from the Stevenson paper)

But Titan’s liquid environment is hydrocarbons, non-polar and therefor inhospitable to dissolved salts.  In a year-ago post I followed other people in proposing that cells living in Titan’s lakes might use an inverted membrane structure (the middle sketch).  It’d separate oily inside from oily outside by interposing a thin layer of watery.

That might work on worlds whose temperature range matches ours.  Stevenson and his team pointed out that it’s seriously unworkable on cold worlds like Titan (surface temp -290ºF).  The watery parts would be frozen granite-hard and the oily parts would be stiff as high-grade candle wax.  If there are living cells on Titan, they can’t use either two-layer membrane design as they move, grow and do those other life-ish things.

conga-line
Acrylonitrile molecules
in ambipolar array
(adapted from Stevenson)

Stevenson’s team asked the next question, “What else might work?”  They decided to investigate single-layer structures with no salty component at all.  Such membranes could be held together by electric forces between charges that are slightly separated within the same ambipolar molecule (right-most sketch of the three above). For instance, a nitrogen atom holds onto its electrons more tightly than a carbon atom does, so a bonded C≡N pair will be slightly negative on the N side, slightly positive on the C side.

And to avoid the candle-wax problem the tails on those molecules would have to be short.

Titan’s atmosphere is 98% nitrogen and most of the rest is methane and hydrogen, so the group looked at nine ambipolar nitrogen-carbon-hydrogen molecules with short tails.  For each compound they asked, “Would a membrane made of this stuff be stable on Titan?  If so, would that membrane be flexible?”

Those questions are hard to answer experimentally (-290ºF is cold) so the team resorted to advanced molecular dynamics simulation programs that they just happened to have lying around because that’s what the authors do in their day-jobs.

Basically, what the programs do is arrange some virtual molecules (including solvent) in a starting configuration, then let them move around step-by-step under the influence of their mutual attractions and repulsions.  Meanwhile, the programs keep track of the total energy (and a few other things) for the entire assemblage.  Run the simulation until things settle down (if they do); see what virtually happens.

acrylonitrile-azotosome
Virtual acrylonitrile vesicle
(also from Stevenson)

In many (not all) of the computer runs, the molecules under test did indeed form a more-or-less regular membrane floating in the “solvent.”  Only some were “stable,” with calculated energies indicating they’d hold together for days or longer.  Some would even be able to form hollow spheres (vesicles) at least as large as a small virus.  Significantly, “flexibility” values for the stable membranes are in the same range as Earthly cell membranes.

It’s an exciting paper if you’re interested in alien life forms.  Among other things, it suggests that astronomers can’t limit their surveys to planets that exhibit signs of atmospheric O2.

But Life also depends on information storage and transfer.  Earth uses DNA, a huge polar molecule unsuited to Life on Titan.  How might Titan’s Life handle that problem?

~~ Rich Olcott

Life and energy on Titan, maybe

On By rolcottIn Astronomy: Planetary Science, Chemistry, Uncategorized2 Comments

Say you’re an astrobiologist tasked with designing a world that would be able to support life we’d be able to recognize as such.  What absolute essentials would you need to include?

Abundant liquid water?  Biologists have found algae thriving inside desert rocks, moistened only by dew seeping in through microscopic pores.  A comfortable temperature?  We’ve found bacteria living in environments as cold as 5ºF and as warm as 250ºF.  A solid surface to grow on?  Arthur C Clarke (A Meeting with Medusa) wrote about complex life-forms floating in the 3,000-mile-deep atmosphere of Jupiter.  OK, that’s science fiction, but Clarke’s the guy who invented geostationary satellites for telecommunications and GPS.gibbs-energies

Many scientists would say that the obvious essential is a source of chemical energy.  I’d add, “and an efficient mechanism to convert the source energy to a form that can be transported within an organism.”  To my knowledge, all life-forms now on Earth have met the second prerequisite by using the ATP molecule for intra-cellular energy transport.  But life has been amazingly creative in finding ways to build those ATPs.  The tall diagram lists some biologic energy sources in decreasing order of how much energy is released.

All the Biology textbooks tell us that Earth’s energy cycle starts with the Sun.  Solar photons energize plant photosynthesis which creates loads of ATP molecules.  Some of them power a multistep process which combines CO2 and H2O to release O2 and create carbohydrates (CH2O)x.  (Glucose, for instance, is (CH2O)6.  Guess where the term “carbohydrate” came from.)  Earth’s biologic carbon cycle completes when other life “burns” carbohydrates to exploit the energy stored therein.  On this chart, “burn” means “combine with O2” and usually doesn’t involve fire.

Notice that “Make (CH2O)x” is at the bottom of the chart — that process absorbs a lot of energy per carbon atom.  Conversely, “Burn (CH2O)x” releases energy which is why we like sugar too much.

In the past couple of decades we’ve learned that’s not the only way, or maybe even the dominant way, that Earth-life makes its ATPs.  Microbes have evolved a surprising number of “front ends” to the energy machinery.  Here in Colorado we’ve got problems in old mines where microbes build ATPs by oxidizing iron pyrite (FeS) to sludgy rust (Fe2O3) and sulfuric acid (H2SO4).  Works great for them, not so good for downstream organisms.

Iron compounds are such a good energy source that many scientists believe (it’s still controversial) that Earth’s hematite and magnetite deposits were laid down half-a-billion years ago by archaea, microorganisms that preceded bacteria.

Way down on the energy-source scale are the methanogens, archaea that use molecular hydrogen to convert CO2 to methane (CH4).  They only live in zero-oxygen environments — peat bogs, ocean-bottom hydrothermal vents and subsurface veins that are perilous to mine.

Earthly biology participates in many cyclic processes.  The bi-level diagram below highlights two — oxygen cycling between O2 and oxygen compounds, and carbon cycling between CO2 and living tissues (which contain carbohydrates).

If it weren’t for light-driven photosynthesis ( ~~ is a photon), pretty soon all our O2 would be locked up in the ground where it came from.  In a sense, Earth uses life and carbon to get oxygen back up into the atmosphere.  Astronomers look for O2 in a planetary atmosphere as a sign of life.titan-cycles-2

Maybe Titan does something similar.  Titan’s atmosphere contains methane (CH4) and H2 but the quantities aren’t right.  The purple “Lyman α” and blue “Balmer α” lines on the energy chart denote particularly strong solar photons that can break up C-H bonds and generate H2 in Titan’s upper atmosphere.  We understand the relevant processes pretty well and can calculate how much methane, acetylene (C2H2) and H2 should be up there.

The calculated quantities pretty much match what astronomers found in Titan’s upper atmosphere.  But they’re not what Cassini-Huygens found on the ground.  Acetylene just isn’t there, and a (somewhat precarious) computer simulation indicates that there’s much less ground-side H2 than you’d expect from simple diffusion.  Dr Chris McKay has put those clues and the energy stack together to suggest that something on Titan inhales acetylene and hydrogen and exhales methane.

Something alive, maybe?

~~ Rich Olcott

A Brief History of Atmospheres

On By rolcottIn Astronomy: Planetary Science, Chemistry, UncategorizedLeave a comment

miller-ureyLong ago in a far-away career, I taught a short-course about then-current theories on the origin of life.  The lab portion of the course centered on the 1952 Miller-Urey experiment the first demonstration that amino acids could be produced abiotically.

Imagine my surprise when I learned that Miller’s original lab apparatus is on exhibit at the Denver Museum of Nature and Science, where I volunteer now.

The diagram’s notes describe the basic experiment.  Load up the system with whatever gases you think might have been in the primeval atmosphere.  Start cooling water running through the condenser (double-wall tubing below the upper sphere) and gently heat the water sample you’ve put in the bottom sphere.  Vapors travel up the tube into the top sphere where there’s a spark arcing between two electrodes (the black lines at 45º).  Water vapor passing by sweeps any gas-spark reaction products back down to the bottom sphere.

Let the whole thing stew for a while (Miller ran his for a week, we let ours go for two), then draw off and analyze a sample of the solution in the bottom sphere.  In Stanley’s day his analytical techniques found 5 amino acids.  In 1971 (I think) we found (I think) 8 or 9.  More recent work-ups of Miller’s sealed original samples found 25, including all 20 considered essential to life.  So yeah, if you supply enough energy to a methane-ammonia-water system (Miller added hydrogen to that; we didn’t, for safety reasons) you can make the building blocks for proteins.

The experiment has been repeated probably thousands of times by different researchers in the last half-century.  Some replications were duplicates of Miller’s, some started with recipes derived from other theories about what Earth’s early atmosphere looked like.

And there’s the problem.  In Miller’s day we thought that Earth’s atmosphere was basically comet-tail concentrate.  That’d be mostly water vapor along with a couple of volatiles like methane and ammonia.  Later on we realized that much of our atmosphere is volcano belch — a hodgepodge of carbon dioxide, carbon monoxide, methane, hydrogen, sulfur gases, nitrogen, argon, helium, various acids, multiple kinds of rock dust….  Some of that is left-overs from Earth’s initial stages; some has been generated by subsequent geological processes like serpentinization, which can generate both methane and hydrogen.

If you’re running a Miller experiment you’re free to load the apparatus with whatever mixture you think other scientists might think is reasonable for an Earth on the verge of Biology.  No oxygen, though — the chemistry of ancient rocks rules out significant atmospheric O2 before about 3½ billion years ago.

Now the researchers are playing variations on the theme, asking whether conditions on (or within) Titan could also generate complex compounds that given a billion years could self-organize into anything we’d recognize as life.  So what did Titan’s atmosphere look like a few billion years ago?

That’s a toughie, because we don’t have on-the-ground (or out-of-the-ground) data like we have for Earth.  We’ll have to make do with theory, which starts with this chart.

solar_system_escape_velocity_vs_surface_temperature-svg
Molecular escape velocities

At any given temperature you can calculate the average energy per gas molecule (any kind of gas).  Combine that with the known mass of a specific kind of molecule and you can compute its speed.

On any given world you can calculate the minimum speed (the escape velocity) that an object (rocket, rock or gas molecule) needs to have in order to overcome the world’s gravitational pull.

The chart combines both calculations for some important molecules for worlds in the Solar System that have atmospheres.  For instance, Earth’s average temperature (give or take a few dozen degrees) is  300ºK=27ºC≈80ºF.  From the chart, hydrogen and helium should be able to (and do) leave our atmosphere quickly.  However, Earth’s gravity is sufficient to hold onto its original dowry of the heavier species.  By contrast, the four massive planets would have to warm up by hundreds of degrees before they lose even the light gases.

Sure enough, Titan’s atmosphere is mostly nitrogen.  The astronomers measure its methane and hydrogen content in parts per thousand but those concentrations aren’t the same going from top to bottom of Titan’s atmosphere.  Therein lies an intriguing tale, but it’ll have to wait for the next post.

~~ Rich Olcott

Fifty Shades of Ice

On By rolcottIn Astronomy: Planetary Science, Chemistry, UncategorizedLeave a comment

earth-vs-titan-sea

This week we dip a little deeper into Titan’s weirdness trove.  Check the diagram.  Two kinds of ice??!?  What’s that about?

diamond-and-ice
Carbon allotropes
and water polymorphs

As everyone knows, diamonds and pencil lead (graphite, and I loved learning that graphite is an actual dug-from-the-ground mineral whose name came from the Greek verb “to write”) are both pure carbon, mostly.  Same atoms, just arranged differently.

Graphite‘s carbon atoms are laid out in sheets of hexagons.  Adjacent sheets are bonded together but not as strongly as are the atoms within each sheet.  Sheets can slide past each other, which is why we use graphite as a lubricant and why pencils can write and erasers can unwrite.

Diamond‘s atoms are also laid out in sheets of (rumpled) hexagons, but now the bonds between sheets are identical to the bonds within a sheet.  Turn your head sideways and you’ll see that sheets run vertical, too.  In fact, each carbon atom participates in four sheets, three vertical and one horizontal.  All that symmetrical bonding makes diamond one of the hardest substances we know of.

Neighboring carbon atoms form bonds by sharing electrons between their positive nuclei.  Neighboring water molecules (H2O) don’t share electrons but they do tend to line up with their somewhat positive hydrogen atoms pointing towards nearby somewhat negative oxygens.  That’s a loose rule in liquid water but it dominates when the molecules freeze into ice.

Most of the ice on Earth has an Ice-Ih structure, where the oxygen atoms are arranged in the same pattern as the carbons are in graphite.  Water’s hexagonal sheets aren’t quite flat, but the 6-fold symmetry gives us snowflakes.  There’s a hydrogen atom between each pair of oxygens, but it’s not half-way between.  Instead, each oxygen tightly holds its own two hydrogens while it pulls at further-away hydrogens owned by two neighboring oxygens.

But water molecules have other ways to arrange themselves.  A small fraction of Earth’s ice has a diamond-like Ice-Ic structure with each oxygen participating in four hexagon sheets.  Again, hydrogens are on the lines between them.

Water’s such a versatile molecule that it doesn’t stop with two polymorphs.  Ice scientists recognize seventeen distinct crystalline varieties, plus three where the molecules don’t line up neatly.  (None of them is Vonnegut’s “Ice-nine.”)  Each polymorph exists in a  unique temperature and pressure range; each has its own set of properties.  As you might expect, ices formed at high pressure are denser than liquid water.  Fortunately, Ice-Ih is lighter than water and so ice cubes and icebergs float.

As cold as Titan is and as high as the pressure must be under 180 miles of Ice-Ih and watery ammonia sea (even at 10% of Earth’s gravity), it’s quite likely* that there’s a thick layer of Ice-something around Titan’s rocky core.

clathratesThe primary reason we think Titan is so wet is that Titan’s density is about halfway between rock and water.  We know there are other light molecules on Titan — ammonia, methane, etc.  We don’t know how much of each.  Those compounds don’t have water’s complex phase behavior but many can dissolve in it.  That’s why that hypothetical “Ammonia sea” is in the top diagram.

But wait, there’s more.  Both graphite and water ice are known to form complex polymorphs, clathrates, that host other molecules.  This diagram gives a hint of how that can happen.  Frozen water under pressure forms a large number of more-or-less ordered cage clathrate structures that can host  Titan’s molecular multitude.

At Titan’s temperatures ice rocks would be about as hard as granite.  Undoubtedly they’ll have surprising chemistry and interesting histories.  We can expect clathrate geology on Titan to be as complex as silicate geology is on Earth.

Geochemist heaven, except for the space suits.

~~ Rich Olcott

* – A caveat: we know a great deal about Earth’s structure because we live here and have been studying it scientifically for centuries. On the other hand, most of what we think we know about Titan’s interior comes from mathematical models based on gravitational observations from the Cassini mission, plus 350 photos relayed back from the Huygens lander, plus experiments in Earth-bound chemistry labs. Expect revisions on some of this stuff as we learn more.

The Titanic Winds of Titan (And Venus)

On By rolcottIn Astronomy: Planetary Science, Uncategorized2 Comments

Last week we saw that the atmosphere of Saturn’s moon Titan wasn’t quite as weird as we thought.  But there another way it’s really weird, completely unlike Earth but yet very much like Venus.  Titan’s a superrotater, a world whose atmosphere circles the planet much faster than its surface does.

Let’s start with a relatively simple Earthside phenomenon, a hurricane.  Warm air rises, right?  When the warmth comes from bathtub-temperature sea-water, it’s wet warm air.  As the air rises it cools and releases the moisture as rain.  But the air can’t just keep rising forever or we’d squirt out all our atmosphere. So where does it go?

From a physicist’s perspective, that’s the key question.   If we can track/predict the path of a small parcel of air molecules through a weather system, then we’ve got at least a rough understanding of how that system works.

For the past half-century, atmosphere physicists have been engaged on a project grandly entitled the General Circulation Model (GCM), a software mash-up of the Ideal Gas Law, Newton’s Laws of motion, thermodynamic data for solid/liquid/gas transformations, the notoriously difficult Navier-Stokes equations for viscous fluids, and careful data management for input streams from thousands of disparate sources.  Oh, and it’s important that the Earth is a rotating spheroid rather than a flat plane.

hurricane-en-svg
How a tropical cyclone works
Illustration by Kevin Song, from Wikimedia Commons

Kevin Song’s diagram summarizes much of what we know about hurricanes.  An air packet rises until it hits the tropopause (the top edge of the troposphere), then expands horizontally.  While the packet’s spreading out, the planet’s rotation generates Coriolis “forces” that bend straight-line radial paths into the spirals we’ve seen so often in satellite photos.

A hurricane may look big on your weathercaster’s screen, but it’s less than 0.1% of Earth’s surface area.  Nonetheless, many of the same principles that drive a hurricane underlie global weather patterns.

wind-cells-and-jets-2Air warmed by the equatorial Sun rises, only to sink as it heads poleward.  Our packet loops between the Equator and about 30ºN (see the diagram).

Actually that loop is a slice through a big doughnut that stretches all the way around the Earth.  Another doughnut lies southward just below the Equator.  Two more pairs of doughnuts reside polewards of those as indicated by the other arrows in the diagram.  The doughnuts act like a set of interlocking gears, each reinforcing and moderating the motion of its neighbors.

Thanks to the same geometric phenomenon that spins a hurricane, air packets in these doughnuts don’t loop back to the points they started from.  The Earth turns under the packets as they journey, so each packet takes a spiraling tour around the planet.

Because of all those doughnuts, on average Earth wears a set of cloud-top necklaces.  Regions within 15º of the Equator are rain-forested, as are the Canadian and Siberian forested belts near 60ºN.  The world’s most prominent deserts cluster beneath the dry downdrafts near the 30º latitudes.  Jupiter, “the Easter egg planet,” gets its pink and blue bands from similar doughnuts except that Jupiter has room for many more of them.

Those green circles in the diagram are important, too.  They also represent Earth-circling doughnuts, but ones whose winds flow parallel to Earth’s surface rather than perpendicular to it.  The ones close to the surface give rise to the trade winds.  The high-altitude ones are the jet streams that steer storm systems and give the weathercasters something to talk about, especially in the wintertime.

Jet streams flow briskly — 60 to 200 mph, on a par with a middling hurricane.  Here’s a benchmark: Earth’s equatorial circumference is 25,000 miles, so Ecuadorian palm trees circle the planet at (25000 miles/24 hours)=1041 mph.  Our jet streams go about 15% of that.  Theory and GCM agree that the jets are powered by the Coriolis effect — spiraling air packets in the primary donuts cooperate to push jet stream air packets like oars on a galley ship.  That adds up.

Titan and Venus can’t possibly work that way.  Both of them rotate much more slowly than Earth (Titan about 30 mph, Venus only 4), so Coriolis forces are negligible.  But Titan’s jet streams do 75 mph and Venus’ race at 185.  What powers them?  The physicists are still arguing.

~~ Rich Olcott

Titan’s Atmosphere Is A Gas

On By rolcottIn Astronomy: Planetary Science, Chemistry, UncategorizedLeave a comment

One year ago I kicked off these weekly posts with some speculations about how Life might exist on Saturn’s moon Titan. My surmises were based on reports from NASA’s Cassini-Huygens mission, plus some Physical Chemistry expectations for Titan’s frigid non-polar mix of liquid ethane and methane. Titan offers way more fun than that.

The environment on Titan is different from everything we’re used to on Earth. For instance, the atmosphere’s weird.earth-vx-titanTitan’s atmosphere is heavy-duty compared with Earth’s — 6 times deeper and about 1½ times the surface pressure. When I read those numbers I thought, “Huh? But Titan’s diameter is only 40% as big as Earth’s and its surface gravity is only 10% of ours. How come it’s got such a heavy atmosphere?”

Wait, what’s gravity got to do with air pressure? (I’m gonna use “air pressure” instead of “surface atmospheric pressure” because typing.) Earth-standard sea level air pressure is 14.7 pounds of force per square inch. That 14.7 pounds is the total weight of the air molecules above each square inch of surface, all the way out to space.

(Fortunately, air’s a hydraulic fluid so its pressure acts on sides as well as tops. Otherwise, a football’s shape would be even stranger than it is.)

Newton showed us that weight (force) is mass times the the acceleration of gravity. Gravity on Titan is 1/10 as strong as Earth’s, so an Earth-height column of air on Titan should weigh about 1½ pounds.

But Titan’s atmosphere (measured to the top of each stratosphere) goes out 6 times further than Earth’s. If we built out that square-inch column 6 times taller, it’d weigh only 9 pounds on Titan, well shy of the 22 pounds the Huygens lander measured. Where does the extra weight come from?

My first guess was, heavy molecules. If gas A has molecules that are twice as heavy as gas B’s, then a given volume of A would weigh twice as much as the same volume of B. An atmosphere composed of A will press down on a planet’s surface twice as hard as an atmosphere composed of B.

Good guess, but doesn’t apply. Earth’s atmosphere is 78% N2 (molecular weight 28) and 21% O2 (molecular weight 32) plus a teeny bit of a few other things. Their average molecular weight is about 29. Titan’s atmosphere is 98% N2 so its average molecular weight (28) is virtually equal to Earth’s. So no, those tarry brown molecules that block our view of Titan’s surface aren’t numerous enough to account for the high pressure.

My second guess is closer to the mark, I think. I remembered the Ideal Gas Law, the one that says, “pressure times volume equals the number of molecules times a constant times the absolute temperature.” In symbols, P·V=n·R·T.

Visualize one gas molecule, Fred, bouncing around in a cube sized to match the average volume per molecule, V/n=R·T/P. If Fred goes outside his cube in any direction he’s likely to bang into an adjacent molecule. If Fred has too much contact with his neighbors they’ll all stick together and become a liquid or solid.

The equation tells us that if the pressure doesn’t change, the size of Fred’s cube rises with the temperature. Just for grins I calculated the cube’s size for standard Earth conditions: (22.4 liters/mole)×(1 cubic meter/1000 liters)×(1 mole/6.02×1023 molecules)=37.2×10-27 cubic meter/molecule. The cube root of that is the length of the cube’s edge — 3.3 nanometers, about 8.3 times Fred’s 0.40-nanometer diameter.∗

titan-boxes
Fred and neighbors

Earth-standard surface temperature is about 300°K (absolute temperatures are measured in Kelvins). Titan’s surface temperature is only 94°K. On Titan that cube-edge would be 8.3*(94/300)=2.6 times Fred’s diameter — if air pressure were Earth-standard.

But really Titan’s air pressure is 1.5 times higher because its column is so tall and contains so much gas. The additional pressure squeezes Fred’s cube-edge down to 2.6*(1/1.5)=1.8 times his diameter. Still room enough for Fred to feel well-separated from his neighbors and continue acting like a proper gas.

The primary reason Titan’s atmosphere is so dense is that it’s chilly up there. Also, there’s a lot of Freds.

~~ Rich Olcott

∗ – For the technorati… The cube-root of the Van der Waals volume for N2. And yeah, I know I’m almost writing about Mean Free Path but I think the development’s simpler this way.

Superluminal Superman

On By rolcottIn Mathematics: Dimensions, Physics: Light and Relativity, UncategorizedLeave a comment

Comic book and movie plotlines often make Superman accelerate up to lightspeed and travel backward in time.  Unfortunately, well-known fundamental Physics principles forbid that.  But suppose Green Lantern or Dr Strange could somehow magic him past the Lightspeed Barrier.  Would that let him do his downtimey thing?

Light_s hourglass
Light’s Hourglass

A quick review of Light’s Hourglass.  According to Einstein we live in 4D spacetime.  At any moment you’re at a specific time t relative to some origin time t=0 and a specific 3D location (x,y,z) relative to a spatial origin (0,0,0).  Your spacetime address is (ct,x,y,z) where c is the speed of light.  This diagram shows time running vertically into the future, plus two spatial coordinates x and y.  Sorry, I can’t get z into the diagram so pretend it’s zero.

The two cones depict all the addresses which can communicate with the origin using a flash of light.  Any point on either cone is at just the right distance d=√(x²+y²+z²) to match the distance that light can travel in time t.  The bottom cone is in the past, which is why we can see the light from old stars.  The top cone is in the future, which is why we can’t see light from stars that aren’t born yet.

If he obeys the Laws of Physics as we know them, Superman can travel anywhere he wants to inside the top cone.  He goes upward into the future at the rate of one second per second, just like anybody.  On the way, he can travel in space as far from (ct,0,0,0) as he likes so long as it’s not farther than the distance that light can travel the same route at his current t.

From our perspective, the Hourglass is a stack of circles (spheres in 3D space) centered on (ct,0,0,0).  From Supey’s perspective at time t he’s surrounded by a figure with radius ct that Physics won’t let him break through.  That’s his Lightspeed Barrier, like the Sonic Barrier but 900,000 times faster.

Suppose Green Lantern has magicked Supey up to twice lightspeed along the x-axis.  At moment t, he’s at (ct,2ct,0,0), twice as far as light can get.  In the diagram he’s outside the top cone but above the central disk.

Now GL pours on the power to accelerate Superman.  Each increment gets the Man of Steel closer to that disk.  He’s always “above” it, though, because he’s still moving into the future.  Only if he were to get to infinite speed could he reach the disk.

However, at infinite speed he’d go anywhere/everywhere instantaneously which would be confusing to even his Kryptonian intellect.  On the way he might run into things (stars, black holes,…) with literally zero time to react.

But the plotlines have Tall-Dark-and-Muscular flying into the past, breaching that disk and traveling downwards into the bottom cone.  Can GL make that happen?

Enter the Lorentz correction.  If you have rest mass m0 and you’re traveling at speed v, your effective mass is m=m0/√[1-(v/c)²]. That raises a couple of issues when you exceed lightspeed.

Suppose GL decelerates Superluminal Supey down towards lightspeed.  The closer he approaches c from higher speeds, the smaller that square root gets and the greater the effective mass.  It’s the same problem Superman faced when accelerating up to lightspeed.  That last mile per second down to c requires an infinite amount of braking energy — the Lightspeed Barrier is impermeable in both directions.

The other problem is that if v>c there’s a negative number inside that square root.    Above lightspeed, your effective mass becomes Bombelli-imaginary.  Remember Newton’s famous F=m·a?  Re-arrange it to a=F/m.  A real force applied to an object with imaginary mass produces an imaginary acceleration.  “Imaginary” in Physics generally means “perpendicular in some sense” and remember we’re in 4D here with time perpendicular to space.

GL might be able to shove Superman downtime, but he’d have to

  1. squeeze inward at hiper-lightspeed with exactly the same force along all three spatial dimensions, to make sure that “perpendicular” is only along the time axis
  2. start Operation Squish at some time in his own future to push towards the past.

Nice trick.  Would Superman buy in?

~~ Rich Olcott

Superman flying at lightspeed? Umm… no

On By rolcottIn Mathematics: Dimensions, Physics: Light and Relativity, UncategorizedLeave a comment

Back when I was in high school I did a term paper for some class (can’t remember which) ripping the heck out of Superman physics.  Yeah, I was that kind of kid.  If I recall correctly, I spent much of it slamming his supposed vision capabilities — they were fairly ludicrous even to a HS student and that was many refreshes of the DC universe ago.FTL SupermanBut for this post let’s consider a trope that’s been taken off the shelf again and again since those days, even in the movies.  This rendition should get the idea across — Our Hero, in a desperate effort to fix a narrative hole the writers had dug themselves into, is forced to fly around the Earth at faster-than-light speeds, thereby reversing time so he can patch things up.

So many problems…  Just for starters, the Earth is 8000 miles wide, Supey’s what, 6’6″?, so on this scale he shouldn’t fill even a thousandth of a pixel.  OK, artistic license.  Fine.

Second problem, only one image of the guy.  If he’s really passing us headed into the past we should see two images, one coming in feet-first from the future and the other headed forward in both space and time.  Oh, and because of the Doppler effect the feet-first image should be blue-shifted and the other one red-shifted.

Of course both of those images would be the wrong shape.  The FitzGerald-Lorentz Contraction makes moving objects appear shorter in the direction of motion.  In other words, if the Man of Steel were flying just shy of the speed of light then 6’6″ tall would look to us more like a disk with a short cape.

Tall-Dark-And-Muscular has other problems to solve on his way to the past.  How does he get up there in the first place?  Back in the day, DC explained that he “leaped tall buildings in a single bound.”   That pretty much says ballistic high-jump, where all the energy comes from the initial impulse.  OK, but consider the rebound effects on the neighborhood if he were to jump with as much energy as it would take to orbit a 250-lb man.  People would complain.

Remember Einstein’s famous E=mc²?  That mass m isn’t quite what most people think it is.  Rather, it’s an object’s rest mass m0 modified by a Lorentz correction to account for the object’s kinetic energy.   In our hum-drum daily life that correction factor is basically 1.00000…   When you get into the lightspeed ballpark it gets bigger.

Here’s the formula with the Lorentz correction in red: m=m0/√[1-(v/c)2].  The square root nears zero as Superman’s velocity v approaches lightspeed c.  When the divisor gets very small the corrected mass gets very large.  If he got to the Lightspeed Barrier (where v=c) he’d be infinitely massive.

So you’ve got an infinite mass circling the Earth about 7 times a second — ocean tides probably couldn’t keep up, but the planet would be shaking enough to fracture the rock layers that keep volcanoes quiet.  People would complain.

Of course, if he had that much mass, Earth and the entire Solar System would be orbiting him.

On the E side of Einstein’s equation, Superman must attain that massive mass by getting energy from somewhere.  Gaining that last mile/second on the way to infinity is gonna take a lot of energy.

But it’s worse.  Even at less than lightspeed, the Kryptonian isn’t flying in a straight line.  He’s circling the Earth in an orbit.  The usual visuals show him about as far out as an Earth-orbiting spacecraft.  A GPS satellite’s stable 24-hour orbit has a 26,000 mile radius so it’s going about 1.9 miles/sec.  Superman ‘s traveling about 98,000 times faster than that.  Physics demands that he use a powered orbit, continuously expending serious energy on centripetal acceleration just to avoid flying off to Vega again.

The comic books have never been real clear on the energy source for Superman’s feats.  Does he suck it from the Sun?  I sure hope not — that’d destabilize the Sun and generate massive solar flares and all sorts of trouble.

Not even the DC writers would want Superman to wipe out his adopted planet just to fix up a plot point.

~~ Rich Olcott