Hydrostatic equilibrium Gravity is constantly trying to shrink all bodies- e.g. the Earth, Jupiter, the Sun. Why don't they contract? "Big" bodies (whether gas, solid, or liquid) are held up against gravity by a PRESSURE GRADIENT. The pressure increases as one goes into the body, to balance the increasing weight that has to be supported. (This slide was swiped from the "Stars" class, but THE SAME EXACT IDEA HOLDS FOR THE EARTH.) "Small" bodies can be held up by inter-atomic or inter-molecular forces. A metal bolt is NOT in hydrostatic equlibrium. The forces between the atoms are enough to conteract the weak self-gravity pull of one end of the bolt on the other. Where is the dividing line between "small" and "large"? Depending on the material, about a few hundred kilometers. The largest asteroid (Ceres- diameter= 1000 km) is big enough to be in hydrostatic equilibrium (which by the way is why it is the only asteroid to be classified as a "dwarf planet"). Most asteroids are "small" and not in hydrostatic equilibrium. This is why Ceres is approximately spherical and most asteroids are far from spherical.
Equation of hydrostatic equilibrium This equation gives dP/dr - the change of pressure with radius- for a body in hydrostatic equilibrium.
Barometric Equation For a (low mass) atmosphere around a planet, the EHE can be solved to give the barometric equation giving pressure as a function of height.
Pressure vs. height in Earth's atmosphere A graphical representation of the previous equation for the case of the Earth's atmosphere. Solution of the equation of hydrostatic equilibrium for an atmosphere around a massive planet results in the barometric equation, which shows that the pressure falls off exponentially with height. A characteristic size scale is the "scale height" which is the change in height to have the pressure change by a factor of 1/e (about 37%). The scale height for the Earth's atmosphere is about 7700 meters. As you can see, Mt. Everest is somewhat more than one scale height above sea level, and the pressure there is only about a third that at sea level.
Pressure vs height in air and oceans The top diagram is similar to the previous one (but note that X and Y axes are interchanged!). The bottom graph shows the change of pressure with depth in the ocean. The different form of pressure change in air and in oceans (exponential vs. linear) is due to the fact that air is compressible, while water is pretty much incompressible.
Pressure and temperature vs height This shows how the density and temperature changes with altitude for our atmosphere. This is a linear-log plot, so that the almost exponential falloff in density is almost a straight line. (Deviations from a straight line are due to temperature variations- if the blue line plotted *pressure*, rather than density, it would be straighter.) The temperature goes down, then up, then down, then up! See next graph for another view of temperature vs height.
Temperature vs. height in our atmosphere This shows the behavior of temperature with height. The temperature reversals are used as boundaries between the layers of the atmosphere- troposphere, stratosphere, mesosphere and thermosphere.
There is no "simple" explanation for this temperature structure. One must look in detail at the mechanisms which heat and cool the air at different heights.
Near the surface of the Earth (troposphere) temperature decreases with height, as you probably have experienced if you have ever hiked or driven up a mountain. To understand this, we must realize that the atmosphere is heated by radiation both from above (sunlight) AND FROM BELOW (thermal radiation from Earth). The surface of the Earth, at a temperature of 250 to 300 K, radiates in the 10 to 12 micron region *UP* from the surface. As the radiation heats the air near the ground, it is "used up", so there is less as one goes up, and so the air temperature decreases with increasing height where this heating mechanism dominates (troposphere).
Above the the tropopause, the air warms with increasing height, defining the stratosphere. This behavior is due to the presence of ozone in the stratosphere. As ozone absorbs solar UV photons (which of course come from ABOVE the layer) the air is heated more strongly at higher altitudes.
At the 100 km level, the air becomes hotter as absorption of solar UV and soft x-rays heats the air, and the very low density means that the air cools very inefficiently.
Above the thermosphere is the exosphere (not shown on diagram), extending up to 500 km altitude (and perhaps beyond). In this region, the particle density is so low that high speed particles can simply fly away from the Earth without bumping into any other particle. Lower in the atmosphere, even a very high speed particle (with speed higher than escape speed) could NOT fly away from the Earth because it would soon bump into another particle and give up some of its kinetic energy. The average distance a particle in a gas can move before colliding with another particle is called the mean free path. In the air near sea level, the mean free path is microscopic (about 300 nanometers) in the exosphere the mean free path it is many kilometers.
Temperature vs depth in ocean There is a common misconception that the decrease in temperature as one goes to higher altitude is somehow CAUSED by the decreased pressure. This is not correct. In the ocean, we see the exact opposite effect- as we go down (increasing depth) the pressure rises, but the temperature falls- opposite what happens in the troposphere.
So "higher pressure" does NOT automatically mean "hotter". In a lab where one has, say, gas in a thermally isolated (no external heat flow) piston, increasing the pressure WILL increase the temperature. (As can be seen from the Ideal Gas Law). But in the atmosphere, or inside a planet, or inside a star, one doesn't have a thermally isolated system, and the details of heat flows and cooling mechanisms must be understood to understand the temperature of a system.
P and S Earthquake waves There are 2 different types of waves produced by earthquakes. P (pressure) waves and S (shear) waves. P waves can travel through a liquid- S waves cannot.
Earthquake waves The chief tool to study the Earth's interior are waves from earthquakes.
Simplified internal structure of Earth Using earthquakes to make a type of "CAT scan" of the Earth, we surmise this structure of crust (thin layer of brittle rock), mantle (large volume of "plastic" rock which can flow VERY slowly), outer liquid iron core, and inner solid iron core.
Earth interior: density vs. depth This gives a schematic idea of the way the local density changes with depth as we go deeper and deeper into the Earth. The laboratory density of iron is about 7874 kg per cubic meter. Note that the density of the iron core of the Earth ranges from 10,000 to over 12,000 kg per cubic meter. This is because the iron in the core is greatly compressed by the gravity of the overlying material. The affect of the compression on the density of the material in a planet must be taken into account if we are to use the average planet density (which is easy to measure) as a guide to the amount of different materials that make up the planet.
The sharp discontinuity in density at about 3000 km depth marks the mantle-core (or rock - iron) interface. The Earth is clearly very well differentiated- almost all the high density iron sank to the center during formation of the Earth (except for the iron used to make SUVs).
Compressed vs. Uncompressed density It is easy to find the average observed or compressed density of a planet- just divide mass by volume. However, the observed density is NOT equal to the average "lab" density of the stuff that makes up the planet! This is because the gravity of a planet compresses that material and makes the density higher than it would be in the lab. For planets the size of Venus or Earth (but not so much for Mars or Mercury) there is a sizable difference between the compress and uncompressed density.
To find the uncompressed density, one could imagine pulling the planet apart, small block by small block. As you did this, the blocks would expand in volume (no longer being compressed by the planets gravity) so the total volume of the blocks would be significantly larger than the volume of the spherical planet!
Preliminary Reference Earth Model (PREM) Combining what we know of physics (equation of hydrostatic equilibrium, equation of state of materials at various pressure etc) with what we know from observations (mass and radius of Earth, behavior of seismic waves etc) we can try to produce a self-consistent model of physical conditions inside the Earth. (Stellar astronomers use very similar ideas to make models of stars.)
This table shows some results of one such model. One striking number is the central density of 13000 kg/m**3. This is about 1.7 the lab density of iron, and shows the effects of compression by the bulk of the Earth. Iron may seem incompressible in a lab, but with enough pressure, its density will increase, like air in a bicycle pump.
Note too the central pressure - 3.64E11 Pa. The atmospheric pressure at sea level- 1 atmosphere of pressure- is about 1.01E5 Pa. The central pressure is thus 3.6E6 atm!
Temperature vs depth in Earth The temperature structure reveals some interesting structure. Near the surface (top 100 km or so) there is a large temperature gradient, with T changing by 5-20 degrees every km you go down. At around 100 km depth, the gradient quickly drops to something like 0.5 degree per km, which holds more or less all the way to the mantle- outer core boundary.
The low temperature gradient in the mantle is due to tranport of heat by convection, which is an efficient heat transport mechanism. In the top 100 km, the rock is "brittle", and convection is not possible- rather, heat transport is by conduction.
Mercury core I won't say much about the internal structure of the other inner planets- we don't have much definite detail. However, even with the most basic info, Mercury stands out as being made (on average) of denser stuff than the other inner planets. On the previous slide about densities, note that the uncompressed density of Mercury is about 5300 compared to 4400 for the Earth. Mercury must have a significantly larger fraction of its mass in its iron core than does the Earth. In this simple cartoon, we see the iron core of Mercury extending almost 74% of the diameter of the planet, as opposed to Terra, where the iron core extends about 55% of the planets diameter. Why? Nobody knows for sure, but the leading idea is that Mercury was hit by a Giant Impact after it differentiated. This impact knocked off a significant fraction of the rocky mantle, but didn't knock off much of the iron core.
*****M**E**S**S**E**N**G**E**R***** to the Winged Messenger
MESSENGER: MErcury Surface, Space ENvironment, GEochemistry and Ranging. This spacecraft is on its way to orbit around Mercury in 2011. If all goes well, it will orbit Mercury for one Earth year. On its way to Mercury (via a complicated multiple-gravity assist orbit, as shown a few weeks ago) MESSENGER has already made several quick Mercury flybys and learned some interesting things. Just think what we will learn as the data from the orbital phase starts coming in! If you want to learn more about MESSENGER see http://messenger.jhuapl.edu
Caloris Basin A quick glance shows that the surface of Mercury appears somewhat like that our Moon- an old, geologically dead surface dominated by many many impact craters. This is one of the MESSENGER "flyby" images, taken on its way to orbiting Mercury. This image is made from several different colors of light. The orange spots at the edge of the large Caloris Basin are said to be volcanoes. So Mercury may be somewhat more active than the Moon. I will say no more about Mercury, as MESSENGER should return a wealth of new data after it starts orbiting the planet (in March 2011, assuming all goes as planned).
Venera color Most of what we know about atmosphere and detail of surface of Venus comes from Russian spacecraft. The Russians landed a number of spacecraft on Venus, floated instrumented balloons in the atmosphere.
Venus global topography This shows "elevation" of Venus on a global scale. Note the two large "continents"- Aphrodite Terra (roughly size of Africa) and Ishtar Terra (roughly size of Australia). About 80% of surface of Venus is within a kilometer of the average altitude.
Magellan in orbit around Venus Almost everything we know about the large-scale surface features on Venus comes from the US Magellan mission. This spacecraft orbited Venus from about 1990 to 1994, and used synthetic aperture radar to make a map of almost the entire surface of Venus at about 60 meter resolution.
*********** The next half-dozen images are all from Magellan and illustrate some of the geological features on Venus. Now, the surface area of Venus is almost *3 times* the land area of the Earth, so this is only a tiny, tiny slice of the vast Magellan dataset. The official Magellan web site is at www2.jpl.nasa.gov/magellan , where you can find links to vast quantities of data from Magellan.***********
Three impact craters on Venus Magellan "image" of 3 impact craters. For scale, the rim of the one in the upper left (Danilova) is about 50 km in diameter.
Large shield volcanos on Venus and Mars These large shield volcanoes are roughly analogous to the Big Island of Hawaii, but on a larger scale.
Arachnoid An arachnoid is a large structure of unknown origin, found only on the surface of the planet Venus. Arachnoids get their name from their resemblance to spider webs. They appear as concentric ovals surrounded by a complex network of fractures, and can span 200 kilometers. Over thirty arachnoids have been identified on Venus, so far. The arachnoid might be a strange relative to the volcano, but possibly different arachnoids are formed by different processes.
Pancake dome volcano A pancake dome is an unusual type of volcano found on the planet Venus. Pancake domes have a broad, flat profile similar to shield volcanos and are thought to form from one large, slow eruption of viscous silica-rich lava.
Fotla Corona On Venus, coronae are large (typically several hundred kilometres across), crown-like, volcanic features. It is believed that coronae are formed when plumes of rising hot material in the mantle push the crust upwards into a dome shape, which then collapses in the centre as the molten magma cools and leaks out at the sides, leaving a crown-like structure: the corona.
Lava carved channels? Hope the Venusians had titanium inner tubes to go tubing when these puppies were flowing!
Impact craters on Venus- global view Experts have identified over 900 impact craters on Venus. There are very few "small" craters, say as big as the Arizona Meteor Crater. This is understandable, as the very dense atmosphere of Venus breaks up much bigger rocks than does Earth's atmosphere. However, rocks that make bigger craters (say 1 km rocks that make 10 km craters) are NOT stopped by the atmosphere. There are several important properties of the Venusian impact craters: (1) there are only ~900 or so of them (2) they are randomly distributed over the surface and (3) they look surprisingly "fresh"- few have, for example, lava flows in them. 900 may sound like a lot of craters, but if Venus had a "dead" surface, like Moon or Mecury, we would expect many times as many impact craters to be visible. These facts have lead to a hypothesis called the "global resurfacing of Venus". The idea is that about 0.5 to 1 billion years ago, pretty much the entire surface of Venus melted (wiping out any older craters), then rather quickly cooled and solidified (so that new craters were not filled in with lava). Venus does have numerous old volcanoes, but does not appear to have plate tectonics, like the Earth. Perhaps the "resurfacing event" was Venus's way of getting rid of excess internal heat??? We really need seismometers on Venus to start to map out its internal structure, but such devices would have to operate in the extreme heat on the surface.
(1) Activity (earthquakes, volcanoes) on Earth (2) Tectonic plates The Earths outer shell is divided into a dozen or so "plates" that move around. The plate boundaries are outlined by earthquakes and volcanoes.
Earthquakes on Earth Same idea as previous, but with lots more real data! This shows position of over *1/3 of a Million different earthquakes** over 35 years.
(1) Plate boundaries (2) Plate boundaries - spreading ocean floor to subduction zone (3) Subduction zone, ocean trench and orogeny - west coast of South America (4) San Andreas transform (slip fault) boundary There are 3 kinds of plate boundaries- converging, diverging and transform. At diverging boundaries (in oceans) "new" sea floor is made, which is then "lost" at converging boundary (subduction zone). By the way, "orogeny" has nothing to do with erogenous or orgy- orogeny means the process of mountain formation.
Age of sea floor This color- coded map of the ages of sea floor rock shows the spectacular success of the idea of sea floor spreading- you can clearly see the long linear "sources" of the sea floor rocks as the youngest rock (coded as red- make sure you look at the color-age bar in lower left).
(1) Continental drift (2) Pangea breakup animation The continents are lighter rock (mostly granite- about 2700 kg/m**3) that "float" on the denser sea floor (basaltic rock- about 3300 kg/m**3). The continents move about slowly.
Fossil map evidence of continental breakup Maps of fossils of ancient creatures show that the ranges of some creatures, presumably once contiguous land, are now split onto two continents- just what you would expect from continental breakup and drift.
Earthquakes in Fiji Sea and plate subduction By plotting position and depth of earthquakes in the Fiji Sea, we can "see" a subducting plate. This drawing shows the relationship between ocean trench, volcano and subducting plate.
Earth impact sites As we discussed earlier, we have identified fewer than 200 impact structures on the Earth- far fewer than the other inner planets. The primary reason for this is, of course, that the Earth is much more geologically active than the other planets. Many Terran craters presumably were formed in the oceans, and have been destroyed by seafloor spreading. On land, small to medium sized craters are quickly erased by geological processes- remember the image of the Roter Kamm crater in Namibia being filled with sand. Most very large, old craters have been filled in, but can sometimes be found by studying buried rocks. Certainly more impact craters remain to be found on Terra. It seems iromic that it is easier to see the impact craters on the Moon or Mercury than the ones on our own planet!
Near side of Moon Our old friend (actually, the astronomers enemy, due to it lighting up the sky!) the Moon. The surface is covered by some 30,000 impact craters larger than 1 km in diameter, as well as "billions and billions" of smaller ones (well, no one has counted them all!). As Shoemaker said in the DVD "The Moon is a slate that no one has been erasing". The large dark areas are called maria. These are really "super craters". These very large impacts broke through the lunar crust and the craters were flooded by lava. As discussed earlier, these maria may have been created in the "Late Heavy Bombardment" period about 3.9 Ga ago.
Far side of Moon The far side of the Moon has lots of impact craters, but only a few small maria. The reason is shown in the following slide.
Schematic Moon structure The Moon has a much thicker crust on the far side than on the near side. (We know something about the Moon's interior because of seismometers left on the Moon by Apollo astronuts.) The large impacts that punched through the crust to create the maria on the near side seem not to have been able to penetrate the thicker crust on the far side.
Giant Impact Theory of Moon formation. How did our Moon form? Over the past century or so, there have been several theories: (1) formation somewhere else and then capture by Earth, (2) fission from the forming Earth and (3) separate formation alongside the Earth. In the 1970s, using chemical and isotopic data from Apollo moon rocks, a new theory was proposed: the Giant Impact theory. In the GIT, the Moon formed as the result of a collision between the forming Earth and a Mars sized body (often called Theia) in the early solar system. This theory comes closest to explaining what we know of the Earth-Moon system: angular momentum, orbit of Moon, differences in chemical and isotopic compostion between the Earth and Moon.
Several groups have done detailed computer simulations of the GI. One short "movie" derived from one such simulation can be found here .
Tidal bulge. The tidal bulge is dragged around by rotation of Earth, so that it "leads" the Moon slightly. This has all sorts of interesting results, including lengthening of the Earths day and lengthening of the orbital period of the Moon around the Earth.
This happens because of conservation of angular momentum (AM). The Earth-Moon system AM consists of the rotational (spin) AM of Earth and Moon and the orbital AM of Earth and Moon around their center of mass. For purposes of AM, we can consider the Earth-Moon system an isolated system (no external torques)- thus the total AM of the Earth-Moon system is conserved. The near tidal bulge pulls the Moon just a little bit along its direction of motion (see right hand part of figure). The far bulge tends to cancel this, but it can't quite do so because it is farther from the Moon than the near bulge. This results in the Earth produces a torque on the Moon- an off-center force. Now, from physics you should know that a torque on a body changes the bodies AM. In the Earth-Moon system, tidal friction (of tides with coastline) cause the Earth to spin more slowly as time goes on, and thus to lose spin AM. The AM the Earth loses goes to increase the orbital AM of the Moon (through the physical mechanism of the not-quite balanced tidal bulges pulling on Moon!). As the Moon gains orbital AM, it slowly spirals away from Earth and the length of the "month" increases. The change in Earth-Moon distance is about 4 centimeters/year. We can actually measure the increase in Earth-Moon distance by timing laser pulses sent from the Earth that are reflected from corner reflectors the Apollo astronauts left on the Moon. Mind-boggling!!!
Corner reflector A corner reflector (here in 2dim- real ones are in 3dim of course) returns light rays in a direction *parallel* to the incident direction, unlike a flat mirror, where the angle of incidence equals the angle of reflection.
Lunar corner reflector array Apollo astronauts and Russian robotic lunar landers have left several corner refectors on the Lunar surface. By shooting laser beams at these, and measuring the time to get an "echo" precise measurements of the Earth- Moon distance have been made for the past 40 years.
Detail of lunar corner reflector Looking like a thing for the astronauts to store their empty soda bottles in, each "hole" is actually a glass corner reflector like the one I passed around in class. These reflect laser beams sent through a telescope from Earth directly back to that telescope.
