Transcript from Epic of Evolution: Life, the Earth and the Cosmos (BEP 210A)

February 2, 2000 - Lecture by Michael Wysession

“My religion consists of a humble admiration of the illimitable superior spirit who reveals himself in the slight details we are able to perceive with our frail and feeble mind.” (Albert Einstein)

Okay, let me pick up where I left off on Monday. To give a recap of where we are so far, we started with a cloud of dust and gas, and we pulled it together with gravity, and it began to spin due to the conservation of angular momentum. Along the equator of the spinning cloud (the plane of the ecliptic), matter was thrown outward a little bit. And as the cloud condensed further, the sun eventually ignited when it reached a hot enough temperature due to the compression from gravity. The matter of this giant fried egg in space began to lump together due to gravity, and these lumps eventually became planetesimals (the seeds of planets), which kept colliding until we were left with a few major planets. And that’s essentially where we are now. This whole process happened very quickly, probably within the first tenth of a billion years, if not less. The story since then, which I will talk about today, has essentially been a process of cooling down from this initially hot solar system.

For a show and tell today, I will give a little slide show on what it is that we ended up with in our solar system. [slide 1] The basic idea here is we started with a cloud of gas and dust. It began to contract, flattened out into a disk shape, congealed into clumps, and then into planets. This is what we ended up with. The lines show the orbits of the planets. [slide 2] To prove that we’re not making this up, though I did ask you to take all this stuff on faith, I will show you this. A lot of amazing pictures have come from the Hubble telescope, and many are of galaxies and large-scale features of the universe. This is a smaller feature, but one of the most amazing. This little sac-like object here is a proto-solar system. This is an accretionary disk. This may eventually become a sun with planets revolving around it. This is what our solar system looked like 4.6 billion years ago. We can actually see these things forming. Remember, however, that the light has taken a long time to reach us, so at this instant there may already be a fully-formed solar system, complete with planets.

I should add that we’ve also been able to see evidence of other planets. I don’t know what the number is now (it’s up to over 20), but we now see that there really are other planets in other solar systems. The planets that we’ve been able to see are only very big planets, even much bigger than Jupiter. We see them by either the gravitational wobble that they cause in their suns as they move around them, or the eclipse of the suns as they move in front of them. But we know that there are other solar systems, and we know that there are other planets that have formed through this process. [slide 3] This is an artist’s conception of what it might look like in this early planetary nebula, with thousands of little planetesimals and clumps of rock and dust floating around. It certainly looks very different than our current solar system, which is mostly empty space in comparison. [slide 4] We end up with orbits that mostly don’t overlap. I mentioned that Pluto is the exception. It actually does swing inside the orbit of Neptune, and will eventually hit Neptune on one of these swings, or it will at least swing close enough to Neptune that the gravitational pull will throw Pluto into the center of the solar system, and it will hit something else. But Pluto is a tiny little rock. It’s like a little pebble. It’s very small compared to the other planets. Most planets follow these elliptical orbits that do not overlap. This belt here, the asteroid belt, exists between the orbits of Mars and Jupiter, and was probably another planet that didn’t survive one of these giant impacts.

[slide 5] Well, what do we end up with? If you look around the inner part of the solar system, you see mostly a bunch of dead rocks, and I’m speaking not biologically but geologically. They don’t do anything anymore. You’ve all seen “Nova” programs, with Earth’s volcanoes and earthquakes. I’ll talk more about how Earth is very geologically active and alive in that sense. Mars, Mercury, and the Moon aren’t undergoing any changes. They’re just cold cinders floating around in space now, though they have some very interesting features. [slide 6] Let’s start with Mercury. The thing you see on surfaces of all planets [slide 7] is the process of meteor impacts and the craters that this forms. This is an artist’s diagram of what one of these impacts might look like on the Earth. [slide 8] And indeed, we do see some of them on the Earth. This is Meteor Crater in Arizona. Here is a highway for scale. This is a pretty small crater as far as craters go. It is recently formed, which is why we can still see it. It turns out that if Earth kept track of all of the meteors that have hit it, the surface would look just like that of the Moon or Mercury: totally covered with craters. There are active geological processes of erosion that remove these things off the Earth’s surface. But meteor impacts still happen everywhere in the solar system, and can still happen to the Earth, though most of the objects that are now floating around in the solar system are fairly small. But let’s look at Mercury. Mercury has been geologically dead for almost its whole history, and as a result, if you look at its surface you see crater on top of crater. Clearly, over the history of the solar system, or at least at some point, (and we know it was primarily at the beginning), these impacts were the primary activity on the surface of planets. It would have been very hard to have life occurring early in the history of the solar system because every time one of these impacts occurred it was like a giant nuclear explosion. These asteroids come in at about 10 kilometers a second. That’s the distance from here to the Mississippi River, in a second. And they actually vaporize large volumes of rock, which gets hurled into the atmosphere, blocking the light from the Sun. We think this process has caused some major extinctions of life on the Earth, such as the death of the dinosaurs 65 million years ago.

[slide 9] Here is one example of a large crater. This is the Caloris Basin on Mercury. It is 1,300 kilometers in diameter. What’s even more interesting is that on the other side of Mercury there are all these rifts and fractures. This impact essentially blew the back end of the planet off, with the shock waves of the impact refocusing at the opposite side of the sphere. And we can understand how this process could shatter a planet, which it probably did in the case of the asteroid belt. [slide 10] If we look at the moon, we see areas that have this same old look to it: craters on top of craters. We also see some more recent features and they’re called “maria,” the Latin word for “seas.” We used to think they were oceans when we looked at them through telescopes, many years ago. There has never been any water on the moon to speak of. But these maria do represent 3.5 billion-year-old lava flows that covered much of the moon. The moon has since been geologically inactive, but there was an episode of active volcanism here, so the numbers of craters in these areas are many fewer than in the older areas of the moon.

[slide 11] Venus is a fascinating example. The atmosphere of Venus is almost totally carbon dioxide. Now, you would think if you were a plant you might really enjoy this, right? Plants breathe in carbon dioxide. The surface of Venus, however, is at a temperature of about 900 degrees Fahrenheit, so plants wouldn’t really be very happy there. The surface of Venus is also under about 90 atmospheres of pressure, which is about equivalent to being under 1 kilometer of water. So the pressure is tremendously high, the temperature is high and this yellow-orange haze is due to sulfuric acid in the atmosphere. It is not a terribly hospitable place. We’ve tried to put robotic landers on Venus, and they last for a matter of minutes or hours before they dissolve or burn up or crush. We don’t know what happens to them. Maybe there are a bunch of Venusians there with bazookas blowing them up. I don’t know, but most likely it’s simply that the conditions that exist on this planet are tremendously inhospitable. [slide 12] But Venus has been geologically active, and it probably still is a little bit. Here’s a computer reconstruction of the topography of one region, showing a volcano with lava flows. [slide 13] We would expect that Venus is still geologically active, because it is almost the same size as the Earth. Here’s Venus and Earth compared next to each other, and there are certainly great similarities in their sizes. But Venus is a little bit closer to the sun, and this contributes to it being 900 degrees Fahrenheit at the surface. And that’s an interesting point I’m going to come back to. Life exists here on Earth where we have a comfortable temperature range for organisms that are based on water because water exists as a liquid here. Water would be vaporized on Venus.

[slide 14] Let’s go to the next planet on the other side of us, Mars, where the temperature ranges on the surface from about -130 degrees to -40 degrees. That’s the warmest it gets on Mars; about -40 degrees. So here we go a little bit further out from Earth, and now we’re too cold. The atmosphere of Mars is also primarily carbon dioxide, and I’ll talk later about why this happens. This is due to a runaway greenhouse effect (the same is true for Venus). Mars has a thin atmosphere, but it’s about one-hundredth that of the Earth’s atmosphere, so it’s really not very significant. For anyone who’s interested in this, there’s a great series of science fiction books by Kim Stanley Robinson (Green Mars, Blue Mars and Red Mars) that tell what it would take to colonize Mars. It might be possible to do, though it would be an incredible challenge. We haven’t given up on the possibility that life once existed on Mars, though it would have been a very primitive sort of life.

[slide 15] Mars looks pretty inhospitable now. This is what it looks like when you land on Mars. It’s just dust and rock and very strong, cold winds. [slide 16] But there is evidence of running water on Mars. These are stream channels. Water has flowed on the surface on Mars. [slide 17] Here is another picture of this. Water flowed through these valleys. [slide 18] And in fact, the white stuff here in this picture is frost. Mars has thin polar caps that form annually. Where is all this water now? Is it frozen underground like permafrost? Are those stream channels just the result of impacts that heat up the ground, causing water frozen underground to melt and flow briefly before freezing up again? If running water has existed here, then life could have formed. But it is unlikely that life would be currently thriving. [slide 19] Mars has been very geologically active in the past. The largest volcano in our solar system is on Mars. It’s called Olympus Mons (Mount Olympus). It would span from New York to Boston. But there’s no sign of volcanism currently. [slide 20] Mars is right next to the asteroid belt, and it has captured a couple asteroids as satellites. It has two satellites, Phobos and Deimos, and are just big rocks. This is a picture of Phobos, and it is a little pebble compared to a planet. You can see how it is oddly shaped from other various impacts. Phobos got captured by Mars due to frictional braking when it passed through Mars’ atmosphere.

Let us now move further from the Sun. If you go out to the bigger planets Jupiter, Saturn, Uranus and Neptune, you see something different. They are all very big. They are mostly hydrogen. They have compositions that are very similar to the sun. If they had gotten a bit larger, they could have become stars on their own, and it is quite common to have stars orbiting each other in pairs. These planets have little solar systems of their own. They all have several satellites. Jupiter and Saturn probably both have at least 20 satellites. I’m sure we haven’t found them all. And these moons probably formed out of the accretionary disk as part of mini-disks around these large planets. Material began to orbit around these planets because they got so big. [slide 21] We’re interested in a couple of these moons, geologically. These are four moons of Jupiter: Io, Europa, Callisto and Ganymede. Io is interesting because it is the most geologically active planetary body object other than the Earth. This slide shows the volcanoes that are constantly erupting, only it is liquid sulfur that they erupt. Io is very active, and the heat for this activity is due to the tidal forces of Jupiter that continually squeeze and stretch it, the way the Earth exerts tidal forces on the moon.

Europa is a hot topic within NASA right now. If you want to submit a proposal to NASA to get a space mission launched, it stands the best chance of getting funded if it involves Europa. The search for life is at the top of NASA’s list of current priorities. The reason is that we think that Europa has a liquid saltwater ocean. Not at the surface. The top 100 kilometers or so of Europa is totally frozen layer of ice, but beneath that it likely has a liquid ocean, and if it has a saltwater ocean, it could easily have life in there, at least at the single-celled level. There are several missions on their way or planned to go to Europa to try to find out if this is true. Callisto and Ganymede are similar in the sense that they have these icy surfaces, and maybe underneath there might be some liquid. [slide 22] I’ll zoom in on these moons. In this shot of Io you can see one of these sulfur eruptions occurring, spewing sulfur out into space. [slide 23] And this is Europa. The surface is all ice, and these are all cracks in the ice that form as the ice shifts and moves around due to the tidal forces from Jupiter. It is beneath this ice that we expect there to be an ocean.

[slide 24] Saturn is very much like Jupiter, only it has larger rings than any other planet. There’s nothing special about rings. Several planets have rings. Rings are moons that have gotten too close to the main planet and have been pulverized due to the tidal forces. If Io were a little closer to Jupiter those tidal forces would actually break the planet apart and pulverize it. A moon can be a certain distance to a large planet before it gets shattered and broken apart, a distance called the Roche limit. Clearly, at least one former moon entered into this danger zone and was destroyed. [slide 25] This image uses different colors to show the different compositions of the rings, suggesting that they came from different moons, or different parts of moons (crust, mantle, core). [slide 26] This is an artist’s rendition of what it would be like to float around in the rings of Saturn amongst all this shattered rock and ice.

[slide 27] Uranus, shown here in a schematic picture behind one of its moons (Miranda), has a small set of rings that also represents the remains of a moon that got too close. Uranus is an interesting exception to the rule of planets rotating the same direction that they revolve around the Sun. Uranus seems to rotate on its side. This might be the result of a large collision, like the one that formed Earth’s Moon. The impacting proto-planet might have hit Uranus near a pole, knocking i on its side. [slide 28] Neptune is also a big ball of gas like Jupiter, Saturn and Uranus. [slide 29] And we have occasional visitors that come from far out in the solar system. This is a picture of a comet, with it’s classic tail. Comets seem quite spectacular to us because their tails can extend for tens of millions of kilometers, but their size is on the order of only kilometers. For instance, Halley’s Comet is probably only 5 kilometers across. It is the size of University City, but it leaves a dramatic tail as the energy from the sun strips ice and gas off of the surface of the comet. But in terms of the volume of the solar system, they are totally inconsequential.

[slide 30] I will leave you with this picture of the Earth. This is what I am going to focus on for the rest of the class. This is our planet, and it is clearly different than any of the other planets. The most important feature in terms of surface geology is all this water. We see a lot of ocean, as well as clouds, which are primarily water vapor. There is all of this liquid ocean water right at the surface of the Earth because the temperature is just right for the Earth to allow this. There are several factors involved. The Earth has just the right atmospheric temperature and pressure to keep the water liquid. Is this chance? Is it always this way? Is there a feedback process that keeps the climate just right? It actually turns out that the Earth has gone through some wild changes in climate. There are times when almost the whole surface of the Earth has frozen, and then times when all the ice has melted and it has been very warm. There have been some huge climate changes, but they have fluctuated about a level that is very comfortable for like. The water is also important because it is a tremendous agent of erosion that constantly changes the shape of the surface of the Earth. So this is what we’ve got here on Earth, and we don’t have anything even remotely similar to it anywhere else in the solar system.

Let me pick up where I left off with the formation of the solar system, and talk about how the Earth began to get to look the way it is. When I last left you, the Earth was just a homogeneous ball of rock. Something must have happened to change this, because I told you on Monday that the Earth is very layered. In fact, I went through these layers -- the inner core is solid iron, the outer core is liquid iron, the mantle and crust are layers of rock. So what happened? Well, the Earth began to heat up in a very big way, and there are a half dozen sources of that heat that helped to raise the temperature of the Earth. Remember, things were initially very cold, so we’re starting at almost absolute zero here. Frozen rocks out in space. First of all, we have the impacts of the planetesimals. When the first bits of dust started sticking together, they were moving no faster than the gas in the nebular disk: meters per second. They stuck to each other only through weak surface forces called Van der Waals forces. But once these rock balls got to greater than about 1 kilometer in size, they began to whiz about at speeds approaching 10 kilometers a second. When they hit the surface of the growing Earth, they bring in a lot of energy. An explosion like a nuclear blast results. A lot of heat is generated from this. Imagine that this eraser is a planetesimal, and the table is the surface of the Earth. As I strike the table with the eraser, I am transferring energy from the eraser (planetesimal) to the table (Earth). On Monday I talked about the last part of this, where the kinetic energy of motion is transferred into heat. But where did that kinetic energy come from? Well, I gave the eraser that energy by lifting it up. I gave it some amount of gravitational potential energy, and that potential energy went into the kinetic energy when it came down to strike the table, and that kinetic energy went into heat. Now, nobody was standing there lifting planetesimals up off the Earth and dropping them. Where did that gravitational energy come from? Well, Claude will probably talk more about the energy involved with the universe, but you have a tremendous amount of gravitational potential energy in this expanding universe, with all of these objects pulled far apart from each other. When they come together, they release a tremendous amount of this gravitational potential energy that first goes into energy of motion as they move towards each other, and then goes into heat when they collide.

Second, you have the gravitational collapse of the rock of the Earth, and this is sort of the same thing as the heat of impacts, but on a more subtle scale. Take this ball of new Earth and just squeeze it a little. Pull the rock together, squeezing out most of the spaces that may be in between grains of rock. That means that all of the rock falls a little bit further in towards the center. This is really the same thing as the impacts. You are converting potential energy into kinetic energy and then into heat as you squeeze these things closer and closer together. More heat means you are raising the temperature of the Earth. Next, there is the increase in temperature due to the physical compression of the Earth. This is a law of physical chemistry: when you squeeze things, they heat up. If any of you have ever pumped up a basketball or a bicycle tire, you may have noticed that after you are done, your bicycle pump is hot. This is because you are repeatedly squeezing the air inside the pump. When you squeeze the air, the atoms, which are bouncing around at some level, have a smaller area to bounce around in, so they bounce around a lot more and hit the side of the bicycle pump much more frequently. It is those collisions that you feel as heat. The same thing happens with the Earth. As more and more material sticks to the Earth and the gravitational force becomes greater, the rock is compressed and temperature raises. If you could suddenly expand the Earth, it would also cool off instantly. The process is reversible. In fact, Claude mentioned that this is how things are cooled off with refrigerators. You pump the heat out by allowing gas to expand, which makes it cools down.

One of the most important sources of heat for the Earth was radioactivity. Certain isotopes of elements are not stable, and they decay. The atoms lose some particles until they have a more stable configuration. That process of breaking apart releases energy, and we know that because elements like uranium and plutonium are radioactive and release energy that can be dangerous to people. It turns out that this is going to be very important in the next lecture, because people would never have evolved without it. Earth would look like the moon or Mercury. It would just be a dead cinder if it weren’t for the fact that the radioactivity in the Earth keeps the Earth at a slow boil. It’s like a plate warmer. It keeps the Earth warm enough to be interesting, make continents, and allow for life to evolve onto land. Early on, however, there were a lot of very short-lived isotopes that released a tremendous amount of energy, and this played a very important role in heating the Earth up.

The second to last thing I’m going to talk about is a collapse of the iron core. The Earth was in the process of heating up slowly due to the factors I have just mentioned. We have the earth compressing and gravitationally collapsing, and more small planetesimals keep impacting, and we’ve got radioactivity cooking away, and at some point something is going to begin to melt. Now, it is an interesting property of chemistry that different materials melt at different temperatures. Obviously, ice in a glass melts before the glass itself does. It turns out that metals tend to melt at a much lower temperature than rock. This is very important, because what happened was that the interior of the Earth began to reach temperatures high enough (greater than 1000-1500 degrees K) that little bits of iron began to melt. Droplets of liquid iron began to form inside the Earth. Once you have iron in he form of liquid droplets, however, the iron becomes much more mobile. The droplets are able to flow through pore spaces within the Earth. The liquid iron is much heavier than rock, so it began to sink. The droplets of iron began to rain down through the Earth and flow toward the center. Once you have all this heavy iron sinking down to form Earth’s core, go back to step 2 and really accelerate the release of heat through gravitational collapse. A lot more gravitational potential energy is released as this iron falls down through the Earth towards the center. That melts more iron, which sinks faster, and there was probably a catastrophic runaway effect that happened very suddenly. It would have happened long before the Earth had actually reached its full size. The Earth was still growing during this time, still adding more planetesimals, but at some critical point the iron melted and flooded down to form the Earth’s core.

This may have released enough heat to melt the rock of the mantle, but if it didn’t, then the next thing did. This was the impact of the proto-moon with the early Earth. The moon that modern day wolves howl at is the offspring of the Earth and something else that hit the Earth, something that was probably roughly the size of the current moon. We call this the proto-moon: the first moon. The moon was not captured by the Earth. It was not a separate asteroid that got caught in orbit around the Earth. The moon was not pulled out of the Pacific Ocean by a passing star (this was actually proposed by George Darwin, son of Charles Darwin). The moon was formed from the remains of a truly amazing collision. I have a slide of it that doesn’t really do it justice, but I’ll show it anyway. [slide 31] This is a computer simulation that shows the proto-moon crashing into the Earth, with material being strewn outwards on all sides. The proto-Earth and proto-Moon are both being totally deformed, broken apart. If the Earth hadn’t already been molten, this heat from this collision would have done it. At this point, the Earth was probably totally liquid, totally molten rock and metal. One of the biggest clues that the moon came from such an impact is the fact that when we brought rocks back from the moon (and the moon is the only place we’ve actually gone to and picked up stuff and brought it back and analyzed it), it is remarkably similar in composition to Earth rocks. When you look at asteroids, even asteroids that we know that have come from Mars, they have very different, unique compositions. But the composition of the moon is too similar in many ways to the Earth to be coincidental. However, it is missing most of its iron. It seems to be missing most of what would have been in the core of this proto-moon. It is thought that the core of the proto-moon got swallowed by the Earth, and the lighter stuff got thrown out into orbit around the Earth, to later recondense into a new mini-planet, so to speak.

Once the Earth was totally molten, it was very easy for it to become layered, and there was really no impediment at this point for the development of the iron core and the rocky mantle. The rocky mantle, however, is not entirely homogeneous. There are some differences in the rock. Most importantly, when you look at a slice of the most of the outer half of the planet is the mantle, but there is a little bit of stuff at the top that has a different composition. The rock that makes up the continents is a little bit lighter, and this is called continental crust. At the same time, another layer of rock is a little bit heavier than the mantle, and this is the rock at the core-mantle boundary. You can think of the crust as being the scum of the Earth, and core-mantle boundary rock as being the dregs of the Earth. We actually use those terms in geophysical discussions: scum and dregs. These terms provide a good physical sense of how these layers came about. Imagine that you have a pot of soup cooking. You often get a layer of froth or scum that floats up on top. Why is up there? Because it’s lighter than stuff underneath it and so it floats up to the surface. And even while the soup is boiling, this layer is too light to sink back down, so it just moves around at the top. Continental crust is just like this. It is rock that is too light to ever sink back down, so the continents just bounce around at the surface while the mantle “boils”. This is fortunate for us for a variety of reasons. The continents, continental rock, cannot sink back down into the mantle. This is different from ocean seafloors, which don’t last long at the surface. Oceanic crust eventually sinks back into the mantle, usually under the edges of continents. The ocean sea floor moves toward a continent, turns the corners, and heads back down into the mantle. Our mantle is constantly turning over like a big conveyor belt. But the continents just get bounced around like rafts on top of a pond, as they are too light to ever sink down. The continents have been doing this for a long time, as they were formed very early on.

At the same time there is this very unusual layer at the core-mantle boundary, and these dregs probably also began to form right at the beginning. As the Earth has continued to cook, the dregs have more efficiently filtered out, and this layer has grown. Let me stress that all of the dramatic events leading up to the melting of Earth happened very quickly, probably within the first 100 million years or so. In other words, this happened in the first 0.1 billion years out of Earth’s 4.56-billion-year-old history. For the next 4.46 billion years, and for many billion years to come, the story has been one of a slow process of cooling down. Our sun will die, and the Earth will be burned to a cinder, which will happen in another 4 billion years or so, and the Earth will still be slowly chugging along. The continents will still be moving about, making volcanoes and earthquakes, right until the end. So we had this fast and exciting beginning, and the rest of the history has been pretty slow. Now, early on, in the first few hundred million years, Earth did not look like it looked now. There wasn’t stable land at the surface. Earth’s surface probably looked like the lava ponds that form within crater of active volcanoes. The lava glows red as it bubbles to the surface of the crater, but it instantly forms a black crust where it meets the cold air. This crust doesn’t last long at the surface because the lava in the caldera is convecting so actively that the crust soon gets subsumed and sucked back down, where it melts again. New crust forms to take its place, and the process is repeated. Probably for a few hundred million years this is what the surface of the Earth looked like. No life could have formed at this time because you were constantly destroying the surface of the Earth and bringing it back down into the hot mantle and melting it. However, within some period of time (and we don’t really know how long it took), the rock of the mantle began to solidify. We started with a molten Earth, but over time we began to develop a solid mantle. The mantle is mostly solid now. There are just a few places where there is liquid magma. Some of it comes back up as lava at volcanoes. As the mantle began to solidify, the motion of convection began to calm down a little bit. Now, the oldest Earth rock that we have evidence from is about 4.1 billion years ago. I should add that the first life we find remnants of existed almost 4 billion years ago, so as soon as we seem to have stable rock, stable crust at the surface, life began to take hold. Some of these earliest rocks are interesting, however, because they are actually altered sedimentary rocks, and sedimentary rock is rock that forms from particles of a previous rock that have been eroded from some older crust. For instance, we’re currently forming sedimentary rock in the Gulf of Mexico. The Rocky Mountains get eroded, the sandy sediment washes down the Mississippi, and gets dumped in the bottom of the Gulf of Mexico. Here it gets compacted down from the weight of more and more sand, and it begins to get squeezed into a new rock. It’s that type of sedimentary rock that’s around 4 billion years old, so there must have been even older crust that was eroded to form this sedimentary rock. So we know that by maybe 4.2 billion years ago (we don’t know the exact date) there was modern-looking crust forming, and there was liquid water that could erode it and create sediments. There were oceans forming. Clearly it wasn’t all molten or you wouldn’t have liquid water -- it would all boil off. Once we had water, we had oceans and puddles, and this is what Ursula needs to start her discussion about the origin of life on Earth.

The last thing I want to leave you with today is to compare the Earth and the moon. The Earth is still active. The continents are moving about, we have oceans, we have volcanoes. And the moon has been geologically inert for 3.5 billion years. Why is this so? It is the same reason that elephants have flat ears, or that weasels can’t ever get skinnier than a certain size. It is due to the fact that larger objects have a greater surface area-to-volume ratio. The surface area-to-volume ratio is a principle like several we will touch upon in this course that transcends different sciences. You may not believe this, but if I take two cubes that have identical shapes but different sizes, they will have different surface area-to-volume ratios. Imagine one cube that is 1 meter on each side, and one cube that is 2 meters on each side. For the smaller cube, the surface area is 6 square meters, and the volume is 1 cubic meter. This gives a surface area-to-volume ratio of 6. For the larger cube, the surface area is 24 square meters (6 faces, 2x2 on each face), and the volume is 8 cubic meters (2x2x2). This gives a surface area-to-volume ratio of 3 (24 divided by 8). The same holds true for spheres as well as cubes. The moon is smaller than the Earth, so it has a greater surface area-to-volume ratio, so it cools off more quickly. There’s nothing magical about this. A way to think about it is that if you have a smaller sphere, the heat has a shorter distance it has to go to reach the outside. If you have a smaller planet like Mercury or the moon, any point inside the moon is never that far from the surface. As the moon cools off, the heat doesn’t have far to go, so it reaches the surface quickly, it radiates off out into space, and the Moon cools off quickly. The larger the planet, the further the heat has to go to reach the surface, so the longer it takes. Here, a lower surface area-to-volume ratio means you have a lot of hot rock, but not a lot of surface from which the heat can radiate into space, so you have trouble cooling off. And so the Earth has trouble cooling off, and it’s still warm. I mentioned elephants. Elephants are big, so they have a low surface area-to-volume ratio. This means that they have trouble keeping cool. How do they do it? They have large ears with very active vein systems through them, so their blood circulates rapidly through their ears, and it helps them cool off, just like the radiator of a car. I also mentioned weasels, which are predators that crawl through tunnels to eat rodents and other mammals. The thinner they are, the more efficient they are in crawling through tunnels. But the thinner they are, the greater their surface area-to-volume ratio becomes, and the more food they have to eat because they lose their heat more quickly. So there is an optimum size thinness for weasels: they want to be thin to get more rodents, but they don’t want to be so thin that they have to eat a lot more. We have gone from the formation of the Earth to the size of weasels. But we should not be surprised, as many things in the universe are related by the same laws of physics. The upshot of all this is that the Earth is big enough that it is still hot, and therefore still geologically active. In the next lecture I will talk about the forms that this geological activity takes.