Category Archives: Science

All these worlds…

 

Jupiter's Great Red Spot (NASA via http://wanderingspace.net/category/jupiter/)
Jupiter’s Great Red Spot (NASA via http://wanderingspace.net/category/jupiter/)

 

I started to write a Facebook post when I figured, hey, it’s been 18 months or so since I’ve posted anything here…I should probably justify the cost of this website or something.  LOL.

As you may know, NASA’s Juno probe has arrived at Jupiter and will soon start sending back epic images of the planet and it’s moons, as well as critically important data about the structure of Jupiter’s interior.  Jupiter is the most planet-est planet in the solar system because it started to form first and got first dibs on all the yummy material in the Sun’s accretion disc.  So, to understand how it formed and what it’s made of is to understand the earliest point in our solar system.  I can’t wait to see some new amazing images.  Personally, I’m hoping for a monolith…

...my God, it's full of stars...
…my God, it’s full of stars…

Fun fact.  Jupiter (the Roman god) was a notorious adulterer and most of its moons (such as Io, Europa, Callisto, and Ganymede) are named for his lovers.  Juno, however, the name of the probe that was sent to check in on Jupiter and discover it’s secrets, was the name of Jupiter’s wife.  If that’s not poetically amusing, I don’t know what is.  Well played NASA…

My purpose for writing this, however, is not to talk about Jupiter per se, but to address a set of ridiculous number of articles I’ve seen on The Tubes talking about how Jupiter is so big “it doesn’t even orbit the Sun!!”  This irritates me for a couple of reasons.  First, a title like that makes sound like we just discovered this fact, which isn’t true.  Second, it makes it sound like it’s a fantastic idea that no one ever considered and is amazing (!!), which is also not true.  For reasons unknown to me, I feel compelled to talk about it.

Obey Gravity, It’s The Law!

When Issac Newton dropped his Law of Universal Gravitation on the Royal Society back in the day (that day, by the way, was April 21st, 1686 when he read his “Discourse Concerning Gravity and its Properties”, which would become a section of his magnum opus, the Principia, to his bros), he definitively showed that the mechanism that determined how the planets moved through the sky was the same as that which determined how the apocryphal apple feel to the ground.

Bro, do you even lift?
Bro, do you even lift?

The result was a deceptively simple relationship between the force of gravitation felt between two massive bodies and the distance between them.

gravity

He noted that the force is inversely proportional to the square of the distance between the bodies.  So, if you double your distance from a mass, the gravitational force it exerts on you is decreased by 4 times.  He also pointed out that the gravitation force was proportional to each mass.  Triple the mass, triple the force.  That force is felt by each body and is ruled by the more massive of the two.  The Earth, for instance, is about 6 times more massive than the Moon, and as such contributes more to the gravitational force than the Moon.  Which is, of course, why the Moon orbits the Earth and not the other way around.  But wait, there in lies the rub; each body exerts a force on the other.  You can never think of just a single thing gravitating another thing, they are always gravitating each other!  They are essentially gravitationally locked into a single “object” that we refer to as a two-body system.  One object never orbits another object, they always orbit each other.  The “G”, by the way, is Newton’s gravitational constant, commonly referred to as “big G”, as opposed to the “little g” of 9.8 m/s² that represents the acceleration near Earth’s surface due to gravity.

Now, in a two-body system, or in any distribution of mass, there is a concept known as the center of mass.  If you’re talking about, say, the Earth by itself, or the Moon, the center of mass would be (ideally) in the center of their spheres.  Of course, neither body is perfectly uniform, so even alone the Earth’s center of mass wouldn’t be in the exact center.  Hell, the Earth isn’t even really a sphere, but that’s beside the point.  We physicists like to ignore crap like that and call everything uniform spheres and that works to an amazing degree of precision…until we have to toss a Jiffy Pop container full of hermetically sealed apes at the Moon, when we have to give it a bit more thought.

...uniform sphere my ass.
…uniform sphere my ass.

When you put two massive things together, however, the center of mass (sometimes called the center of gravity) is not in the center of either object.  If you draw a line between the two object’s individual centers of mass, the system’s center of mass will lie somewhere along that line.

IMG_8074

Where on the line that point is depends on the masses.  If the masses were exactly the same, the point would be exactly half way between them.  As one of the masses becomes more massive, the center of masses moves along the line towards it.  If one of the masses was infinite, then the center of mass would be in its center; the other mass wouldn’t matter.  The center of mass is essentially a weighted average of the centers of mass of all pieces involved.

When bodies in a two-body system are orbiting each other, they do so about the center of mass.  When referring to orbits, this point is usually known as the barycenter.  In the case of the Earth-Moon system, the barycenter is about 4,700 km from the Earth’s center; the radius of the Earth is about 6,400km.  So, both the Moon and the Earth’s individual centers of mass orbit around this point.  That means that the Earth “wobbles” as the Moon orbits.

barycenter-earth-and-moon

The barycenter of the Earth-Sun system is well within the Sun, since the Sun is around 333,000 times more massive than the Earth…but it is still not in the center.  If the Earth and the Sun were by themselves, the Sun would still “wobble”.  There is a lot of talk nowadays about the discovery of extrasolar planets.  This barycenter dance that multi-body systems do is one of the main ways we find them in the first place; look at a star, see if it wobbles, if is does, something’s orbiting it and we can immediately calculate it’s mass from the wobble.  Science is cool.

Now to the main point: Jupiter.  Jupiter is waaaay more massive than the Earth.  In fact, Jupiter is about 2.5 times more massive that all of the other planets combined!  It clearly rules the playground.  If you find the barycenter of the Sun-Jupiter system, it is, in fact, outside of the Sun.  So, the Sun does more than wobble in this case, it actually orbits around a point in space outside of itself.  If Jupiter would have accreted more mass (about 8 times more, in fact), nuclear fusion would have ignited it into a second star and it and the Sun would have been a binary star system.

Earth would have sucked about as much as Tatooine as well...
Earth would have sucked about as much as Tatooine as well…

As it stands now, it still almost is as the dynamics of the solar system are ruled by the Sun-Jupiter system; the other planets and objects are along for the ride.  It also illustrates why most of the exoplanets we find are giant Jupiter-like planets.  The more massive they are, the further between them the barycenter is and the larger the observed wobble in the star.  Earth-like planets, as I mentioned before, do it as well, but it’s way harder to detect.  We’re getting pretty good at it; as of right now, we’ve discovered about 3,500 exoplanets  in about 2,600 different planetary systems.

Pluto, by the way,  got kicked out of the planet club because it doesn’t gravitationally “rule” it’s neighborhood; it’s moons are so massive that the barycenter around which they all orbit is well outside any of the bodies and they all kind of orbit each other.  Not very planet-like.  As opposed to Jupiter that regularly tosses objects out of the solar system.

Planet 9 From Outer Space

As you can imagine, having more than two objects in the solar system makes their movements…complex.  All of the planets pull on each other really make a mess of things.  Jupiter, for instance, pulls on the Earth just as the Sun does, making your path through space a bit more spirographic than you might initially imagine.  It’s really amazing that the Jiffy Pop apes got to the Moon at all.

Both Uranus and Neptune were discovered due to their gravitational pull on the other planets, not direct observation.  In fact, you can’t see either of them with an unaided eye; you need a telescope.

...uhm, guys.
…uhm, guys.

Astronomers figured out where these planets were and where to look for them in the sky by “reverse-engineering” the orbital data of the planets they could see.  Jupiter and Saturn just didn’t quite move the way they should have.  It’s really a testament to the “Clockwork Universe” idea that Newton ushered in.

Well, now that we have ridiculous technology and can see so many things that we could see before, such as small, icy objects causing around the Kuiper belt beyond Neptune, there’s growing evidence that there might be yet another planet out there.  A massive one, none of this Pluto-sized crap.  We’re talking 10 times the mass of the Earth and about the size of Neptune.  Now, it’s still theoretical…honestly we’ve been talking about a Planet X for a long time.  It’s existence helps to explain the observed orbits of a slew of Kuiper belt objects, orbits that would be extremely improbable without a gravitational shepard.  More recently, people have conjectured that the fact that the rest of the planets are not on the equatorial plane of the Sun could be explained with a magic Planet 9.  The problem is that space is, well, big, and it’s really hard to find small, dark objects when you don’t know where to look.  Current estimates place it on an orbital plane that is about 24º or so off the ecliptic, the plane the Earth orbits the Sun on, and has an orbital period of at least 10,000 years.  If it does exist, it probably has a very eccentric orbit that ranges from 200 to 1,200 times the distance from the Earth to the Sun, almost 20 times further out than Neptune.  So, changes it will make to the rest of the system are weak and hard to detect; remember that gravitation force weakens as the square of the distance.  Plus, we have to detect them for a while to figure out where in that ridiculous orbit it might be before we can find it.  If it doesn’t find us first…

King_ghidorah_1965_01

It would be super awesome to actually see a new planet in my lifetime, though I’m not holding my breath.  If we found it today, it would take something like 20 years to get a probe there.  I’m pretty sure New Horizon’s images of Pluto are the last huzzah I’m going to get.  But who knows.  It would be amazing.  Who knows how it would change our idea of the solar system.  Was it formed with the rest of the planets and tossed out (probably by that fat kid, Jupiter) or was it a rouge planet cruising through space and get captured by the gravity of the Sun?  So many questions.

Anyway, I guess the final take home message is titles of popular science articles are stupid.  Then again, “Jupiter’s so damn BIG, it and the Sun orbit each other!!” is probably more interesting to the average person than “No surprise that the barycenter of the Sun-Jupiter system is 1.07 solar radii from the Sun’s center of mass”.  At least people are reading about science…

Thermostat’s broke, yo…

Image from http://sneerkat.com
Image from http://sneerkat.com

Man, it’s been a looooong time since I put up a new post.  That was not intentional.  It was part lack of motivation (or inspiration, as the case may be), and part being too busy doing science to sit down and write about it.  But, I’ve given myself a New Year’s resolution of sorts to give this blog the love that it deserves, so here it goes…

It’s cold outside.  Super cold, actually, thanks to the ridiculous wind that is accompanying our cold front.  Walking across campus to my office made me feel like David Attenborough traversing Greenland.  Twas good times.  (Edit: at least it was when I started writing this LOL)

In the grand scheme of things, however, it’s not even that cold.  I mean, it’s not even the coldest it’s been here, let alone truly cold.  While pumping liquid helium into the cryostat in our lab, I have experienced true cold; it was basically the exact opposite of the experience of opening your oven and inadvertently burning your face off.  You think -10 °F is cold, try -451 °F…

Temperature is an interesting thing, when you really think about it.  What exactly is it that we’re talking about when we refer to an object being “hot” or “cold”?  It all seems so arbitrary; hot or cold with respect to what?

Further, think about the fact that, unlike most other physical properties, things like mass or length or time, we don’t directly measure temperature.  Instead, we are always measuring some other physical quantities response to temperature.  In a mercury thermometer, for example, we are measuring the change in the volume of the mercury in response to a change in temperature.  In a fancier electric thermometer, like the one you put in your mouth when you’re sick, you’re measuring the change in electrical resistance of some component in response to a change in temperature.

Sometimes, the concept of temperature isn’t even defined.  Think about a piece of metal that you are heating with a torch.  What temperature is the metal?

Point is, temperature is wacky and we really take the concept for granted.  So, let’s think about it for a little bit!

The Concept of Temperature

Imagine two objects, say two cubes of metal, one “warm” and one “cool”.  You then bring them together so that they touch and then you observe what happens.  There’s all sorts of physical properties that we can observe, as stated above, things like volume and electrical resistance.  What you will observe is that after some disruption when they were brought together, eventually, everything stops changing.  The volumes, for instance, will change as soon as you touch the two cubes together, but eventually, the volume of each cube become constant.  When this happens, we say that the objects have reached equilibrium.  More specifically, they have reached what is known as thermal equilibrium.  Being in equilibrium doesn’t mean that the values of everything are the same; the cubes won’t necessarily have the same volume.  The values of volume will simply not be changing anymore.

The idea of temperature is that physical thing that tells you if you are in thermal equilibrium or not.  All systems have some sort of internal energy; consider, for instance, the kinetic energy that each molecule of the air around you has.  If you are in thermal equilibrium with your surroundings, life is great.  If, however, your surroundings have more internal energy than you do, Nature does what it needs to do to balance everything…by increasing your internal energy and decreasing the surrounds internal energy until you are in thermal equilibrium.  Of course, you perceive this as “getting hot”.  Realistically, when you heat up, your surroundings cool down, but your surroundings are so vast that you don’t really make a difference; they are like an infinite reservoir of energy.  Likewise if your surroundings have less internal energy than you do.  In this case, rather than your surroundings giving you energy, they take it away and you fell “cold”.

Back in the day, distinguished gentlemen, such as William Thompson,…

That's Lord Kelvin to you, son.
That’s Lord Kelvin to you, son.

…thought that this transfer was due to the flow of some unseen fluid they called “caloric”.  It was later established, much to Kelvin’s (pardon me…Lord Kelvin) credit that this idea was false, which ultimately led to the kinetic theory of gases and the idea that heat was transferred by atomic collisions.  He also gave us the important concept of an absolute temperature scale.  Of course, the unit of temperature, the Kelvin, one of seven fundamental units in Nature, was named after him.  Well played.

Victorian-era science was big on the weird fluids.  There was the caloric that transferred heat, the frigoric (seriously) that transferred cold, the phlogiston that was released during combustions, and let’s not forget the fantastic lumiferous æther through which light propagated.  But, I digress…

Chaos

In both cases, you are perceiving a disruption of your body’s “normal state of affairs”, a regulatory process called homeostasis.  Needless to say, we are fantastically ordered machines.  It takes a lot of energy to create and maintain that order…and Nature doesn’t like it.

There are a lot of laws that are thrown out that Nature must follow.  One that truly must be followed, however, is known as the Second Law of Thermodynamics.  This law can be stated in many ways, but the one most applicable to this discussion is that “the entropy of the Universe (a closed system) must always increase”.  Well, cool…what’s entropy.

Entropy is a deep subject.  The popular way to describe it involves the idea of chaos.  Think of water.  When frozen, the water molecules take on a rigid crystal structure and have a great deal of order to them.  As you add energy, these molecules become “agitated” until they finally break their crystalline bonds, thus becoming less ordered.  They still weakly interact, however, so they maintain a specific volume.  Heat the liquid even more and the molecules overcome this interaction as well and loose volume, becoming even less ordered, as the turn into a gas.  In physics, we would say that water vapor has more entropy than liquid water which, in turn, has more entropy than ice.  The second law says that this quantity, overall, must increase.  Nature does what it needs to do to ensure this happens.

What about a refrigerator?  Doesn’t it lower the entropy of the stuff inside?  Well, yeah…but it does this using a heat pump, that grill on the back of the device, which exudes heat into the surrounding environment, increasing its entropy.  The net effect is that overall entropy is increased.

Back to us and our homeostasis.  Based on this idea of order, we have pretty low entropy and, like the refrigerator, we radiate are ridiculous amount of heat back into the environment (some of us more than others…).  Our surroundings are constantly adding or subtracting energy from us, and we use the energy we extract from food (calories…at least we kept the word) to maintain order.  But the Universe is relentless.

I find your lack of entropy disturbing...
I find your lack of entropy disturbing…

It keeps chipping away until something finally breaks, homeostasis fails, and death occurs.  Without that inflow of energy, all of our complexity disintegrates and the second law is maintained.  Death is losing the battle against entropy.

Overall, however, we’re sticking it to the Universe.  Even though it destroys us, we serve to (minutely) raise it’s entropy over our lifetimes.  It turns out that entropy is tied to the amount of energy that can effectively do work.  When the entire Universe eventually comes to thermal equilibrium, work will not longer be able to occur.  You need “hot” and “cold” for energy to transfer.  If everything’s the same temperature, energy can’t flow and nothing interesting can happen.  All chemical reactions will cease, everything will become a near-absolute-zero soup and entropy will finally be maximized.  The inevitable heat death of the Universe…LOL the joke’s on you, Nature.

A depressing outcome in 100 trillion years…I guess being cold in the winter is the least of my concerns.  But at least my face won’t hurt when I go outside.

 

Magnets!!!

0aa

Today, for some reason, the topic of magnets has come up several times.  I decided to take it as a sign (from the magnet aliens, perhaps) and write a bit about them.

Magnets are, indeed, magical.  The lodestone has been known for millennia, though how they actually work has only been able to be explained since the invention of quantum mechanics in the early 20th century.  The lodestone is an example of a ferromagnet, the prefix “ferro” stemming from the Latin word for iron, ferrum, since iron is abundant and the first natural magnets found, like this…

IMG_1788…are made of iron.   And when they were found, I’m sure minds were blown.  But how do they work?  By that, I mean, what is the origin of magnetism?  The answer…ATOMS!!!

A really simplistic view of an atom is the good old “solar system” model we all learned back in grade school.

IMG_3376

You’ve got your nucleus chilling in the center and an electron cruising around along some path.  Electrons have charge and moving charge is what we call current.  Turns out that the flow of electrical current generates a magnetic field, a fact that my boy Hans Christian Ørstead accidentally found out in 1820.

Thanks, Wikipedia!
Thanks, Wikipedia!

He was running a lot of current through some wires, doing a completely unrelated thing.  Purely by coincidence, a magnetic compass happened to be sitting on the work bench near the wires.  He noticed that when the switch was flipped to let current run, the compass needle deflected.  That really started something because, until then, no one had ever thought that electricity and magnetism were related.  Guess what?!

Back to the atoms.  The electron cruising around can be thought of  kind of like a current running through a loop.  This creates a magnetic field that comes out of the loop, twists around, and goes back into the loop from the other side.

IMG_4752

 

So, what we get is, basically, a little bar magnet, with a north and south pole.  The arrow represents something called the magnetic moment which is intimately related to a quantum mechanical concept called spin.  The magnetic moment points in the direction of the north pole of the magnet.  Now, in most materials, these little magnets are randomly aligned, like this…

IMG_7700

But, in a ferromagnet, certain regions, called domains, have a collection of atoms that are all lined up.

IMG_9953

When they’re randomized, the material on the macroscopic scale doesn’t appear magnetic, like copper or aluminum.  However, with ferromagnetic domains, the net magnetic moment of the atoms don’t cancel out and you get permanent magnet; on the macroscopic scale, the whole piece of material has a magnetic moment.

This isn’t the only way that magnetism manifests in material, though it is the most easily observable, so it’s the one we’re most familiar with.  Another common type is called antiferromagnetism.  An example of an antiferromagnetic material is common hematite.

IMG_6346In an antiferromagnet, there is no net magnetic moment because each atom is aligned such that it is opposite to its 4 nearest neighbors, like this…

IMG_5657Before you think, “well, who gives a crap about these” (if you’ve read this far, you do LOL), realize that the reading head in every hard drive…

Hard_disk_head…is an antiferromagnet.  Their structure is key to the process of reading information off of the magnetic platter, something called giant magnetoresistance , for which the Nobel Prize in physics was given out in 2007.  Go team!

The thing that makes both of these materials “do their thing”, as it were, is the idea of spin interaction.  We’ve all had the experience of setting two bar magnets next to each other.  We know that the opposite poles repel and the like poles attract.  Well, what happens if we put a bunch of them on a fixed lattice, like what you would have in a crystal of material?  What happens if you flip one of the magnets?  What do its neighbors do?  If you just assemble some atoms of, say, iron and let them sit for a while, what structure to they take?

It turns out, in physics we can write something called the Hamiltonian.  It represents the total energy of a system.  Nature, you see, is a miser and doesn’t want to use more energy than it needs to do anything.  So, things structure themselves over time to minimize this total amount of energy.  In the case of systems like ferromagnets and antiferromagnets, we can write the Hamiltonian like this (sorry for the math LOL)…

heisenbergWhat this means isn’t really important, other than the idea that you are adding up the energy for every single spin-spin interaction in the whole material…which is nuts!  The value of J is very important; this is called the interaction coupling constant.  It’s the only difference between a ferromagnet (J > 0) and an antiferromagnet (J < 0).  What the value of that is in a real material is dictated by the electronic structure of the atoms involved and various other things.  If you take some stuff, put it together and let if evolve over time, the spins will interact according to this rule until each atom is in the most energetically favorable configuration, a configuration called equilibrium.

One of the things that made me decide to write this post in the first place was the fact that I was tasked with writing a program that would simulate this interaction.  As you can imagine, simulating every single interaction of every atom in a material just isn’t possible.  So, the program I created makes a few concessions.

First off, I only deal with a lattice of atoms that is 50×50 (so 2500 atoms).  To put that in perspective, there are on the order of 10^23 atoms of iron in one gram (that piece of lodestone above is about 2.5 kilograms).  But, this small system’s behavior is indicative of a much larger system.  I’ll test that when I get a supercomputer…

Secondly, the program only considers interaction with the four nearest atoms, since they dominate the process.  In reality, the other atoms contribute as well, but the further away they are, the less influence they have, so we are safe to ignore them.  In physics, we call this first approximation.

Finally, the system is only two-dimensional.  Matter of fact, whoever figures out how to solve the three-dimensional system is totally winning a Nobel Prize.  That’s how it goes down in physics…turns out the universe is SUPER complicated LOL.

Here’s how it works.  First, it generates a random array of spins, like this.

FM_start

Here, the red squares are spins pointing “up” and the black squares are spins pointing “down”.  The program then runs in a series of steps.  On each step, one of the 2500 atoms is randomly selected.  Then, the program makes the decision to flip it or not based on what is more energetically favorable given its neighbors configuration and it’s coupling constant.  The more energy it would take to flip a spin, the less likely it is to occur.

So, you give the program a value for that interaction constant J, let it go for a few hundred thousand step, and see how the system evolves.  If you let J be positive, then you have a ferromagnet.  After a buttload of steps (buttload = 100,000), that lattice of atoms turns into this…

FM_end They arrange themselves to the most stable state.  As you can see, those domains that I was talking about before readily form because that’s what the interaction constant dictates should happen.  This is the natural state for a ferromagnet!  Sweet!!

What about an anitferromagnet?  Well, we start with a random array again…

AFM_start…and let it arrange itself, this time letting that constant be negative.  That’s the ONLY difference between these two systems.  Do that, and you get this after a bunch of steps…

AFM_endOh SNAP!  Even this simple model (known as the 2D Ising model, btw) gives rise to the structures of both ferromagnets AND antiferromagnets as a natural progression that arises simply when you put these atoms together and let them do their thing.

For your amusement, I created two videos of these processes happening; they are linked below (as Quicktime files).  Not real great quality, but you get the idea.  They ping-pong back and forth, going from order to disorder.

Ferromagnet Ordering

Antiferromagnet Ordering

Indeed, if you started with an ordered system, like a magnetized piece of iron, and heated it up, it would break down like the video shows in reverse.  At low temperatures, the system orders itself, but at high temperatures, the energy being put into the system flips the spins and creates disorder.  If you put a bar magnet in the freezer, it will strengthen it.  Conversely, if you put it in boiling water, you will weaken it.

Different materials have different characteristic temperatures where the material changes from ordered to disordered; it turns our that iron’s is pretty high, which is why iron magnets are literally just lying around the surface of the Earth.

A completely trippy thing that you can try for yourself to in force this idea is listening to a bar magnet with a stethoscope.  The flipping of spins releases energy, which manifests as sound waves; if you listen to a bar magnet with a stethoscope, you will hear a kind of tinkling sound as the spins reorder themselves like the video show.

If you put these things IN a magnetic field, you influence the process.  Some of you may have wrapped a wire around a piece on metal, ran current through it, and magnetized the bar.  In that case, you are causing the magnetic moments of the atoms to align with the external field inside the coil of wire.  In a ferromagnet, the coupling constant says “that’s cool” and stays that after you remove the wire; that state has less energy.  If it’s a weakly magnetic material, the heat of the atmosphere will gradually cause chaos in the spin structure and cause the material to become demagnetized.

In a material like copper, the coupling constant is 0.  So, if you order them, they pretty much immediately become randomized again.  That’s why those materials can’t be permanent magnets.

That, in a nutshell, is how magnets work…well, the most common kinds, anyway.  Science rules.

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