Ep. 303: Equilibrium

So many of the forces in space depend on equilibrium, that point where forces perfectly balance out. It defines the shape of stars, the orbits of planets, even the forces at the cores of galaxies. Let’s take a look at how parts of the Universe are in perfect balance.

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    Fraser: Astronomy Cast episode 303 for Monday, April 22, 2013 – Equilibrium
    Welcome to Astronomy Cast, our weekly facts based journey through the cosmos. Where we help you understand not only what we know, but how we know what we know.
    My name is Fraser Cain, I’m the publisher of Universe Today. With me is Dr. Pamela Gay, a professor at Southern Illinois University Edwardsville, and the director of Cosmoquest.
    Hi Pamela, how are you doing?
    Pamela: I’m doing well, how are you doing Fraser?
    Fraser: Good. So let’s give another shout out to the upcoming Astronomy Cast mad marathon.
    Pamela: Well and CosmoQuest
    Fraser: CosmoQuest, yeah. Mad marathon.
    Pamela: It’s a hangout-a-thon
    Fraser: A 24 hour hangout-a-thon, maybe more. Why maybe more? Wasn’t 24 hours enough and then someone thought “Maybe we should do 36” because… records need to be broken?
    Pamela: (Laughs) What we’re finding are a lot of awesome people that want to support us and help raise money. We want to give everyone a chance to say their piece and give us their money… umm that came out more bitter than intended. It’s one of these things that I’m watching fly by on my Twitter feed about news of the U.S. president’s upcoming budget. If the budget goes through as written, most of the field of astronomy science education that works on anything outside of the National Science Foundation that is federally funded will get de-funded, which is a euphemism for “we are all out of work”. Failure is not an option this time. We need to raise the money to keep all of our projects going and if we’re able to surpass our goals, it will allow us to hire other people who are going to be unemployed four months from now if these budgets go through.
    Fraser: Alright so 36 hours is just another demonstration of your willingness to suffer in the name of space and astronomy.
    Pamela: I’ve worked for longer than that before when we had software bugs.
    Fraser: I think you’ve been up for 36 hours right now.
    Pamela: It feels like it
    Fraser: Let’s get rolling with this episode then. What’s the date in case people want to put that in their calenders?
    Pamela: It’s June 15th and 16th 12:00pm EST through 12:00 pm EST, possibly through to 12:00 am EST.
    Fraser: Fantastic. I know I’ll jump in at points and I know various other space friends will be showing up as well and putting on a show so hopefully this will keep everyone entertained to keep the donations rolling.
    Fraser: So many of the forces in space depend on equilibrium, that point where forces perfectly balance out. It defines the shape of stars, the orbits of planets, even the forces at the cores of galaxies. Let’s take a look at how parts of the Universe are in perfect balance. I put this on the roster and I don’t remember why.
    Pamela: (Laughs) Admittedly, the list of ideas was from May of 2012.
    Fraser: I tend to brainstorm them fifty or sixty episodes in advance and sort of throw them out into the show notes and then you pick and choose from what you like. I think we both got kind of intrigued by the topic and then wondered “what does that mean to us?”.
    Pamela: I went “What type of equilibrium is it that you speak?”
    Fraser: I’m talking about the band. It’s a German folk metal band and I’m a huge fan. There is also a 2002 science fiction movie about equilibrium. So what is the classic concept of equilibrium?
    Pamela: Basically it’s anything that is balanced. You can have a chemical equilibrium which is where you have balanced numbers of reactants, you can have gravitational equilibrium otherwise known as a balanced see-saw. It’s anytime that the forces or chemical reactions or whatever it is, is balanced so that nothing is accelerating, changing, slanting or any of those things that lead to a state change.
    Fraser: I can remember being in high school and we learned the whole section on forces and being quite surprised at how when you’re standing on the ground and you’re pushing down on it, that makes sense. In fact there is an equal and opposite force pushing up from the ground and the reason that you’re not either flying out into space or sinking into the ground is because the forces on your body are an equilibrium.
    Pamela: When you’re sitting, all the muscles are in place. One of my favorite accusations is “Oh you don’t use that many muscles when you’re riding a horse, you’re just sitting there.” No, you’re moving every single muscle in the core of your body to balance because the thing you’re sitting on is moving in all sorts of different ways. It’s that concept of staying in equilibrium and staying in balance but then when you start applying it across all of the sciences you start seeing things like a balloon which is an equilibrium. The gas inside versus the elasticity of the balloon versus the air pressure outside are all forces that are in balance so that the balloon is neither shrinking nor exploding.
    Fraser: What are some classic situations in space astronomy where equilibrium is really coming into play? It’s that loss of equilibrium that causes dramatic changes.
    Pamela: I think probably the one that is most important maybe hydrostatic equilibrium in stars. This is of course a personal opinion, I’m sure there is someone else out there that will say “No, no something else is more important”. Without hydrostatic equilibrium in stars, they can’t balance out to have nuclear reactions. With a star you have the gravitational pressure that is causing the outer part of the star to try to collapse inwards getting balanced by the light pressure pushing outwards from the core of the star. It’s this balance essentially between light pressure and gravitational pressure that allows stars to have such hot dense cores that they can sustain nucleosynthesis.
    Fraser: When we first started to talk about that and I first started to understand the concept that it is the light pressure from within the star that is what is counteracting the gravitational pressure. That blew my mind.
    Pamela: Yeah we generally call it radiation pressure but the word radiation masks the fact that it’s light. It’s just light. It’s in all sorts of different energies and not all of it is visible; some of it is quite deadly. It is the light that is supporting the outer layers of the star.
    Fraser: That original balloon analogy that you used at the beginning is really perfect because in the balloon you have the air molecules bouncing around inside and that’s being balanced against the elasticity of the rubber of the balloon.
    Pamela: And the air pressure outside of the balloon.
    Fraser: And the air pressure outside of the the balloon, right. Probably more so the air pressure. With the sun it’s the photons of light bouncing around, pushing against atoms. It’s crazy.
    Pamela: Yeah, gas pressure does play a roll and convective forces play a roll, but by in large it’s that bouncing between light pressure and gravitational pressure. The star switches fuel mechanisms at various points in it’s evolution. As it goes from burning hydrogen to burning carbon, there is helium between those, as it goes through all of these different burning phases it has to adjust to a new equilibrium. As the temperature that is needed in its core and the density that is needed in the core to burn these heavier atoms is different. Every time it changes its fuel source it has to re-equilibriate.
    Fraser: Equalize? Equilibriate? Is that the word?
    Pamela: I think so.
    Fraser: We’ll just make up a word… “equilibrify”
    Pamela: (Laughs) We’re going to verb it, we’re just going to verb it.
    Fraser: (Laughs) Yeah we’re just going to verb it. So we’ve got this situation going on with the sun where it is slowly heating up because it’s using up the hydrogen and helium in its core and it’s causing it to expand a little in the core pressure. It pushes itself out of equilibrium but then they’ll move so far as it can go and then get pulled back in by the gravity.
    Pamela: My favorite cases in variable stars where they are in periodically stable equilibrium. This is simply because they have an outer layer, often of helium, that as the star starts to hit a new equilibrium point it ionizes all of the helium so the energy goes not into pushing out on the star but instead into ionizing the helium. As it continues to expand and as the momentum carries it past an equilibrium point it cools off and then the energy, as it collapses, goes into neutralizing the helium. So you keep ending up with a push and pull as the helium ionization and neutralization plays a roll in the pulsation of the star. That was extremely simplified.
    Fraser: That was rhymey too.
    Pamela: It was. Over simplified and rhymey describes that description of variables.
    Fraser: As we’ve seen with supernovae when the light pressure goes out and when the supernova has gone and converted all of its elements all the way up to iron…
    Pamela: You have a sudden lack of equilibrium.
    Fraser: Right a lack of light pressure.
    Pamela: In that case when you wreck the equilibrium, when you pull the chair leg out and the force free body diagram is no longer at balance. The outer layer of the star collapse down undergoing magnificent nuclear reactions as they go and explosions occur.
    Fraser: Kaboom!
    Pamela: Kaboom.
    Fraser: In the other way in the red giant star, it’s when the light pressure takes over right?
    Pamela: Depending on what stage you’re looking at you could have a helium flash when a shell of helium suddenly ignites around the core. Rather you end up with a helium flash and the core is a shell of hydrogen burning. All of these different things can lead to the system suddenly changing in radius to balance everything out. It’s similar in ways to what happens when you change the temperature of gas. If you have a balloon and you heat up the balloon, the air inside is going to expand. The velocities of the gas increase, the pressures of the gas against the walls of the balloon increase and so in order to compensate for this changing temperature and this new pressure inside, the entire balloon expands but if it expands too much it will overcome the elasticity of the balloon structure.
    Fraser: I think another great example of this is the hydrostatic equilibrium that planets and moons and such, face. If they don’t have enough mass they can’t pull themselves into a sphere.
    Pamela: This is gravitational hydrostatic equilibrium on a different scale and in a different way. In this case when you have small bodies, the chemical structures, the everyday bonds between the minerals allow asteroids that look like potatoes. Basically you have a chunk of matter, it gloms on, and yeah gravity plays a roll but at a certain point they are also held together with chemistry. It’s like when you’re building a sandcastle on the beach. The shape of the sandcastle is determined by the individual stickiness between the molecules and the particles of sand. As the object gets bigger and bigger, the gravity that is trying to make everything round, to make a surface with a equal gravitational potential everywhere on the surface. That gravitational pull towards and equal potential surface will start to overcome the chemical bonds between the molecules. This is where you get landslides. Earth can’t have mountains as big as Mars can because on Earth if you start building something like Olympus Mons gravity is going to flatten it as our gravity seeks to create an equal potential surface.
    Fraser: From what I understand, Mt Everest is pretty much at the limit of how big of a mountain we can actually have here on earth. It’s no surprise that it’s the biggest mountain on earth.
    Pamela: Over time it will wear down and new mountains will emerge and we’re always going to have that limit to how much forces of gravity can bend things held together through chemical properties and gravity won’t squish them back down.
    Fraser: Now where is that line? How big does an object have to be or how much mass does it need to have before it’s likely going to have that hydrostatic equilibrium?
    Pamela: The asteroid Ceres is about the limit of what we’re looking at. It’s a reasonable fraction of the size of the moon but Vesta comes close, it’s fairly round. The largest of the asteroids are approaching that stage and Ceres, the largest of the asteroids, is a dwarf planet. It meets the criteria by being in hydrostatic equilibrium.
    Fraser: So I wanted to go another direction and talk about something that is quite exotic. I love these opposing forces so for example a neutron star. You have this situation where gravity is pulling it in doing the inward force but now you’ve got neutrons that are pushing back.
    Pamela: Yeah and it’s degeneracy system. With a white dwarf you have an electron degeneracy pressure. This is where it’s the force of the electrons against each other. As the Pauli exclusion principle prevents atoms from sharing the exact same spin and energy level so all of the electrons have to configure themselves just right in a white dwarf so that they don’t defy the exclusion principle. In this process they form one solid set of orbitals throughout the entire white dwarf and it’s the electrons, getting as close as they can without breaking the rules of physics, that essentially supports the white dwarf.
    Fraser: One big diamond right?
    Pamela: That’s when you start looking at the carbon atoms in a carbon rich white dwarf. When you put too much pressure on that degenerate electron gas, those electrons and the protons in the atoms that they were surrounded by end up joining forces. An electron plus a proton put tightly enough together is going to produce a neutron, a positron and a neutrino. Positron flies away, the neutrino flies away and what you’re left with is a neutron star that is, in this case, held together by the neutrons getting as close as they can before, in this case, other forces of physics are defied.
    Fraser: Right well it’s the gravity pulling it together and the neutrons defining the limit of how small and how big this object is going to be.
    Pamela: In this case you have the neutrons getting together, pretty much, at densities not too different from what you have at the core of an atom. The strong and the weak force are defining what happens when you create a neutron star. It’s when you break down those specific rules and the neutrons get smooshed together that we end up with an exotic matter that we don’t even know what it is and an object that we call a black hole.
    Fraser: Right and if the gravity is just too much then even the neutrons can’t keep it in balance and it just turns into a black hole. I guess the thing with a black hole is do we know of any force that can be pushing against the gravity of the black hole, pulling inward?
    Pamela: No.
    Fraser: Alright, so that could be a run away limit at that point right?
    Pamela: Trying to speculate anything we can’t get away with at this point. It’s a black hole physics breaks down as we move inside, I know you like to make stuff up. We can’t define a form of matter that would exist at sufficient densities to explain black holes. Some people call it a quark soup, other people say “we don’t know”, other people make up stuff like going through to other universes… no, no, that’s not what’s happening. We just don’t know. It’s part of what makes science exciting that there is still stuff to learn.
    Fraser: To flip this whole conversation around, at what point does the gravitational force, when it’s too strong and there is nothing to push back against it, begin to collapse beyond what we can really understand. On the flip side the universe has surprised us with dark energy as the opposite situation which is a repulsive force that is seemingly continuing to expand the universe beyond gravity’s ability to pull it back together.
    Pamela: You have to be careful because we don’t know if it’s a force. We know the effect that dark energy has and the effect that dark energy has is it acts like a pressure. It could be that dark energy is energy getting injected into the system, it could be that it’s an actual field that is… there is all sorts of stuff, weee dooon’t knoooow.
    Fraser: Sure, but I think the outcome of the fact is that the universe itself isn’t in equilibrium.
    Pamela: That’s true, we are not in equilibrium as a universe and that’s disturbing. Within the universe it’s really kind of awesome how the entire tale from the way stars are formed to the way they die as one of our own astronomical punctuated equilibrium. In biology they talk about punctuated equilibrium in terms of evolution and how plants and animals change to fit a variety of niches. When we look out across the universe what we see is that because things weren’t perfectly smooth after the big bang and after the formation of the cosmic microwave background, because we had a patchy distribution of matter, it was able to find places that eventually came out of gravitational equilibrium and in this case it was gas pressure versus gravitational pressure. The gas collapsed down to form stars and the stars over time went through their own phases of different levels of equilibrium as they went from burning one fuel to burning another fuel to sometimes exploding or collapsing. All throughout our structural evolution we’ve seen galaxies collapse down into formation and we’ve seen systems that were made into spheres due to two disc like things collapsing. Everything we have is the result of two things getting out of equilibrium and creating a new thing in their wake.
    Fraser: I think one of the last places that we see equilibrium is in orbits right? Again with gravity pulling things inward and then we have this centripetal force as things are going around in circles or ellipses around these objects right?
    Pamela: The way to think about centripetal force is one of these artifacts that exists in appearance but gets messy when you try and define its reality.
    Fraser: Yeah, momentum.
    Pamela: What is actually happening is that you have an object that is trying very hard to move in a straight line and there is nothing slowing the speed that it has but it’s path, it’s velocity is changing because it’s direction is changing. Gravity is working to constantly change the direction of an object that is moving at a speed that, because orbits end up being ellipses, may change as the object gets closer or further from the object doing the pulling. The bulk of what you see with orbits is that direction is ever constantly changing as the object is getting yanked on in a straight line.
    Fraser: There is a great example of how to mentally get yourself to orbit where you shoot a cannonball out of a cannon and it shoots a few hundred yards down range. You shoot it harder and it goes further and you eventually shoot it hard enough that it’s going around so far that it never hits the ground it just keeps going around in orbit. You still have that gravity pulling that cannon ball inward but you have its momentum trying to escape and it gets held in this perfect balance.
    Pamela: It’s velocities trying to stay constant, the forces changing the velocities that accelerates it along a curve and gravity always wins.
    Fraser: I always think about the orbit of the objects in the solar system. Think about how the planets are going around the sun in the same way for billions of years. If there were any instabilities in the orbit, if they weren’t in equilibrium, then they would spiral inward and crash into the sun or they would spiral outward and escape from the solar system or they might crash into other objects in the solar system.
    Pamela: What I love is what you’re thinking as on such a limited time scale. The planets have orbits that are in equilibrium for the time scale of the human race but in the past we knew that they weren’t in equilibrium. We know that Saturn and Jupiter were in a resonance that flung Uranus and Neptune out much further than where they formed. We know that there is a period of heavy bombardment that was triggered by all of this as things careened all over the inner solar system including an object roughly the size of Mars that hit Earth which generated our moon. What we perceive as orbits in equilibrium simply means that nothing bad is apparently going to happen. The orbits are constantly experiencing small degrees of change. Mars in particular we can see how it’s poles migrate over time so there is constant change going on and the planets are not in true complete equilibrium.
    Fraser: Take a look at say Phobos, the Mars moon, that is not in equilibrium.
    Pamela: And eventually will crash into the surface.
    Fraser: Yeah and is going to get torn up in the next 10 million years or so then impact the surface of Mars.
    Pamela: Our own moon is migrating away but the sun will blast us to smithereens before it has a chance to escape.
    Fraser: I would love to see some sort of simulation of a really sped up time lapse of the past and future of the solar system. Just see the positions of all of the planets as they moved inward and outward and things disappeared and moons drifted away and then the sun went into its red giant phase to the impact that has and it turns into a white dwarf and then run that clock for trillions of years as whatever planets are left continue to orbit around the sun. That’s what you’re getting at right? We have this sense of scale of human history but in fact if you play it out across the billions or trillions of years then there are many more movements that are happening.
    Pamela: Yeah and creating that animation is actually something that is not too difficult but it’s the type of thing that is extraordinarily hard to get funding to do. You’re really looking at one beleaguered, PhD level astrophysicist working very hard for a year and then a programmer to doing the graphics so you’re looking at a one year salary for three people so you’re pretty animation would run about $300,000 once you factor in medical insurance and university overheads. So if you find me the money, I’ll make you the animation.
    Fraser: Awesome, okay, alright… I will not.
    Pamela: (Laughs)
    Fraser: Thanks for the offer. We’ll just fake it instead. Cool, thanks a lot Pamela and we’ll talk to you next week.
    Pamela: Okay, sounds great.
    This transcript is not an exact match to the audio file. It has been edited for clarity.

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