Formation of the Solar System
 Lecture 18 -- Formation of the Solar System System
 

There are some obvious questions associated with the Solar System. The first might be ``how old is it?'' Stellar evolution theory says that Sun about 5 billion years old, but that depends on how well we understand how stars work. Is there an independent way of estimating the Solar System's age?

Yes, there is, and it has to do with nuclear fission. The metals in the solar system were formed from previous supernovae, and, included in those metals are certain radioactive elements, such potassium-40, rubidium-87, or uranium-238. (The number refers to the total number of protons and neutrons in the atomic nucleus. Different isotopes of an element have the same number of protons, but different numbers of neutrons.) Potassium-40 and uranium-238 are unstable -- left alone, they will spontaneously decay into other elements. (In the three examples above, potassium-40 will decay into calcuim-40 or argon-40, rubidium-87 will decay into strontium-87, and uranium-238 will decay into lead-206.)

Now radioactive decay proceeds in a very specific fashion. It is characterized by half-life. For example, the half-life of uranium-238 is 4.5 billion years. So, if you start with a block of uranium-238, then after 4.5 billion years, half of it will have turned into lead. If you wait another 4.5 billion years, then half of the remaining uranium-238 would also have turned into lead, so the ratio of uranium-238 to lead-206 will be 1-to-4. In another 4.5 billion years, the ratio would be 1-to-8 and so on.

Other radioactive decays proceed in a similar fashion; the half-life of potassium-40 is 1.3 billion years; that of rubidium-87 is 47 billion years. In their examination of meteorites and moon-rocks, geologists looks for inclusions of these radioactive elements. They then measure the ratio of the parent isotope to the daughter isotople. This defines the age of the rocks. Moon rocks and meteorites give an 4.6 billion years for the age of the solar system. (The oldest rocks on earth are a bit younger, 3.9 billion years, but the earth has been surfaced due to ancient lava flows.)

(While we're here, there is one other property of nuclear fission that is important. In general, when an atom heavier than iron undergoes fission, the mass of the two particles that are produced is less than the original particle. Thus, energy is produced. We'll come back to this later.)

The next question to ask is ``how did the Solar System form?'' Any theory of the solar system formation must account for the obvious features we see, such as 1) the fact that solar system is a fairly flat place, with all the planets within a few degrees of the ecliptic and revolving in roughly circular oribts that are all going in the same direction, 2) the division between the small, rocky terrestrial planets in the inner part of the solar system, and the hydrogen-rich Jovian planets in the outer solar system, 3) the decrease in average planet density from the inner part of the solar system to the outer part, and 4) the existence of Bodes law, with each planet roughly twice as far from the Sun as the previous planet.

The first property of the solar system, that of its flatness, is simple to understand in terms of the mechanisms we have already studied. The solar system probably began as a large gas cloud, which began collapsing due to gravity. Such a cloud would have had some rotation to start with: since all the gas in the Galaxy is rotating about the Galactic center and (thanks to Kepler's and Newton's laws) the rotational period for the gas further out is longer than that for the gas close in, any cloud of any size would have started with some rotation. As the collapse continued, centripetal force and the conservation of angular momentum would have caused the cloud to collapse to a disk, much like it caused the proto-galaxy to form a disk. The densest region of this disk (the center) became the Sun.

The composition of the solar nebula, like that of everything else in the galaxy, was mostly hydrogen and helium, with a few contaminants. In the disk of the early solar-system, the density would have been high enough for some molecules to form, for example water (or, more properly, ice), and, in time, small particles, called planetesimals would have condensed out of the gas. At first, these planetesimals (which may only be a centimeter or meter in size) would have grown by further condensation, where one atom or molecular attaches itself to the main body. After a while, accretion will take over, where two bodies collide and stick together. Note that this works because of Kepler's and Newton's laws. If a planetesimal forms on one side of the solar nebula, and another planetesimal forms on the other, unless the bodies happen to be exactly the same distance from the Sun, the difference in rotation speeds will guarantee that eventually the bodies will catch up to each other. Thus planetesimals will grow in size, and as they do, they will clear out spaces in the nebula. Note as the planetesimals grow, their gravitational attraction towards other planetesmals will increase as well, further helping them clear a path.

Eventually, the planetesimals reach a size that they can be called protoplanets. But note that not all protoplanets would be made of the same material. The inner solar system was probably very hot, due to the energy of the Sun. In this area, only elements with high melting temperatures (metals, etc.) could have condensed out, and the protoplanets would have a high density. Conversely, in the cold regions of the outer solar system, light ices could condense in the nebula. This explains the gradual change in planet density.

While planetary formation was going on, the Sun was moving towards the main sequence. In the early stages of the Sun's formation (as gravity was still condensing it down), its appearance would have been more like a red giant. The Sun would have be rotating faster then, and most of its outer portion would have been convecting. Convection in the outer portion of a star causes strong magnetic fields, which, in turn, cause sunspots and solar flares. As a consequence of all this, 1) the pre-main sequence Sun was brighter than it is now, and 2) the pre-main sequence Sun would have been ``active''.

This is important for it explains how most of the light gases got ejected from the inner part of the solar system. Think of the photons of light as little particles. When these photons collide with something light (like an atom), they impart momentum. This is radiation pressure. Now think of sunspots and solar flares. When this activity occurs, the Sun throws off into space many high energy particles, mostly protons and helium nuclei (called alpha particles). This is called the solar wind. Radiation pressure and the solar wind in the early solar system essentially blew all the excess gas out of the inner part of the solar system. That is why the terrestrial planets are so small -- the light gases were blown away.

Once the major planets were formed, the excess debris (extra proto-planets, asteroids, comets, etc.) couldn't stick around long. It turns out that while two bodies can go around each other in nice, stable orbits, the orbits of more than two bodies are chaotic. A body, say, in the orbit between Jupiter and Saturn, would occasionally pass (or be passed) by these planets (due to Kepler's and Newton's laws) and its orbit would be perturbed. After many years, centuries, the orbits would be affected so much that they might become highly elliptical, crossing the paths of other bodies. Eventually these objects will either crash into another planet, or be ejected completely from the solar system. Up until about 3 billion years ago, impacts in the solar system were common. However, as time as gone on, fewer and fewer of these excess bodies remain.

There is no easy explanation for Bode's law, other than to say that most computer simulations of the evolution of the Solar System create a Bode's law-type distribution of planets. Clearly, a small body can't exist in an orbit near Jupiter: Jupiter's gravitational pull would contort its orbit until it was ejected from the Solar System. (This is probably the same reason that no planet ever formed in the asteroid belt --- Jupiter never let it form itself.) Given the distribution of masses in the Solar System, it seems that Bode's law gives the minimum separation bodies could have without affecting each other's orbits.

While all this is going on, the terrestrial planets were forming. In the beginning all of these objects were molten. The continuous impacts of the debris from the solar system ensured this, and, if this weren't enough, the inside of these planets would have been heated to molten temperatures by the energy produced by the nuclear fission of radioactive materials. In a molten environment, differentiation occurs, where heavy metals sink, and lighter silicates (rocks) rise. (That's why the earth's core is mostly iron and nickel, while the surface is made of rocker substances.)

As the crust of the planet cooling, the age of cratering continued, as the Solar System slowly cleaned itself out. This was followed by flooding , not necessarily by water, but by molten lava from inside. (In time, the interior cools, as the amount of radioactivite materials on hand decreases, but at an age of 1-2 billion years, this source of energy was still very important.)

At the same time as this cratering and flooding was occuring, the planet was outgassing. Gases trapped inside the planet during formation (or possibly formed from radioactive decay) burst out, and form an atmosphere. Included in these gases is water vapor, carbon dioxide, hydrogen, helium, and probably methane and ammonia. As the planet cooled, the water vapor started to liquify and fall as rain. The first oceans were formed.

Finally, the process of surface erosion began. Included here are simple erosion due to water and the atmosphere, plus plate techtonics and geologic motions.

Planetary Atmospheres

The are some striking differences between the planetary atmospheres present in the solar system. The earth has an atmosphere that is about 3/4 nitrogen, 1/4 oxygen, and trace amounts of carbon dioxide and other gases. In contrast, our next-door neighbor, Venus, has a thick carbon-dioxide atmosphere with no oxygen, but with sulfuric acid clouds. Mars also has an atmosphere that is primarily carbon-dioxide, but on Mars, the atmosphere is extremely thin, and prone to high winds. The giant outer planets Jupiter, Saturn, Uranus, and Neptune have extremely thick atmospheres of hydrogen, helium, methane, and ammonia. Titan, the moon of Saturn also has a methane-ammonia atmosphere. For reference, Titan has roughly the mass as the planet Mercury (which doesn't have an atmosphere at all). We know that it is possible for planets to change their atmosphere over their existence: photographs of the Moon and Mars show dried river beds. Liquid water cannot exist on either of these bodies today, but at some point in the past, the conditions for liquid water must have existed.

Why all this diversity? The presence of hydrogen and hydrogen-rich molecules in the atmospheres of the outer planets is easy to rationalize. Most of the universe is hydrogen; the only reason hydrogen (and helium) are rare in the inner solar system is that these light gases were blown away in the early stages of the solar system via radiation pressure and the solar wind. Planets like Jupiter kept their hydrogen, and, since the hydrogen atom likes to combine with other atoms, you get things like methane (carbon with 4 hydrogens), and ammmonia (nitrogen with 3 hydrogens). Note that Jupiter is very much like the Sun in many respects. Of course, the Sun is more massive, so it has been able to fuse hydrogen in its core. Consequently, its surface is hotter, and most of its molecules have been torn apart by the heat.

One interesting feature of the atmosphere of Jupiter is its turbulence. Because Jupiter is rotating so rapidly, the gas around the material moves at extremely high speed. This causes wind patterns that are somewhat similar to the trade winds on earth, only much stronger; there is a band of rapidly moving air near the equator, followed by a calmer region, followed by another region of rapid atmospheric circulation, followed by another calm region near the planet's poles. In addition to these overall patterns, there are great storm systems on Jupiter (such as the Red Spot) that exist of for hundreds of years. (Galileo saw the Red Spot back in the 1600's.) Although the precise nature (and reason) for the longevity of the storms is not well known, at some level, such features are easy to understand. The cloud-tops of Jupiter are rather cold, since the planet is far from the Sun. On the other hand, the mass of Jupiter is large, so the inside of the planet is under great pressure. High pressure means high temperature, so down deep the in atmosphere, Jupiter is very hot. Just like on earth, when warm air hits cold air, you get storms.

Now let's contrast Titan with the planet Mercury. Both are roughly the same mass, but while Titan has an atmosphere, Mercury doesn't. Why? The answer lies in the planet's temperature. Mercury is close to the Sun, and is extremely hot. This high temperature means that the molecules and atoms in the planet's atmosphere are moving extremely rapidly. Occasionally, one of these atoms will reach a velocity such that Mercury's limited gravity will not be able to hold it. The atom will then be lost into space. The temperature on Titan, of course, is much lower, so the motions of the molecules are much less. Escape velocity is rarely attained, hence Titan can hold onto its atmosphere. For this same reason, Mars doesn't have much of an atmosphere -- its mass, though larger than Mercury's, is still rather low.

This same mechanism explains why there are no light gases (such as hydrogen) in the atmospheres of the Earth, Venus, Mars, and Titan. At a given temperature, heavy molecules move more slowly than light molecules. (Both have the same amount of energy, but just as a slowly-moving bowling ball carries the same amount of energy than a fast moving misquito, slowly moving heavy molecules carry the same energy as fast moving light molecules.) Now recall that the hydrogen molecule is made up of two hydrogen atoms, each of which has one proton. (Protons and neutrons weigh about 2000 times more than electrons, so we can ignore the electrons.) So the weight of a hydrogen molecule is 2. Helium (which doesn't form any molecules) has two protons and two neutrons, so its weight is 4. Methane is made up of one carbon (6 protons and 6 neutrons) and 4 hydrogens, so its weight is 16. Ammonia is nitrogen (7 protons plus 7 neutrons) with 3 hydrogens, so its weight is 17. Nitrogen gas is made up of two nitrogen atoms bonded together: its weight is 28. Similarly, oxygen gas has two oxygen atoms (each with 8 protons and 8 neutrons), so its weight is 32. Finally, carbon-dioxide is formed from 1 carbon (weight 12) and two oxygens (16 each), so its total weight is 44.

Molecules such as hydrogen and helium are extremely light, so they move very rapidly. Consequently, they often reach velocities that are too fast for the weak gravity of the terrestrial planets. These molecules escape into space. Hydrogenic molecules such as methane and ammonia are heavier, so their velocities are significantly less. These are trapped by the gravitational pull of Titan and the inner planets. That's why Titan has a methane and ammonia atmosphere.

Nitrogen and carbon-dioxide atmospheres are common in the inner part of the solar system. The reason for this is that ultraviolet photons from the Sun cause methane and ammonia to dissociate; when this happens, the results are nitrogen gas, carbon-dioxide, and hydrogen. The hydrogen is light, so it escapes into space, but the nitrogen and carbon-dioxide can be retained. Mars has only enough gravity to retain a little bit of carbon dioxide, while Venus can retain virtually all of its CO_2. Note that Mars is cold enough so that carbon-dioxide can freeze into solid form. (This is called ``dry ice.'') The Martian ice-caps are mostly dry ice with some water ice mixed in (most likely trapped below the dry ice). Since Mars' axis is tipped 23 degrees from the ecliptic plane (like the earth), Mars undergoes seasons, and each ``summer'', some of this ice (dry and water) evaporates into the atmosphere. Thus, parts of the Martian atmosphere are continually freezing out, and boiling in. This is what drives the Martian winds.

An intruiging mystery is why the Earth has a nitrogen-oxygen atmosphere, while Venus has a thick carbon-dioxide atmosphere. The answer is related to Venus' surface conditions, which are extremely hot --- Venus is, in fact, the hottest location in the Solar System. This difference is striking, especially when one considers that both planets have roughly the same mass, were formed roughly out of the same material, and are roughly the same distance from the Sun.

In fact, the atmospheres of Venus and Earth evolved along very different paths because of a slight difference in the beginning. Venus started out slightly closer to the Sun than the Earth. As a result, Venus' surface temperature started out a bit higher. This made the difference.

There are two interesting properties to carbon-dioxide. The first is that carbon-dioxide readily dissolves in liquid water. When you mix CO_2 with water (H_2O), the initial result is carbonic acid, (H_2CO_3). Carbonic acid then reacts with minerals to form rocks. For instance, when carbonic acid encounters calcium, it eats through it to form caclium-carbonate, CaCO_4 (otherwise known as limestone); when carbonic acid hits silicon, it forms silicon-dioxide (sand, quartz, etc.) So the net result is that, as long as there is water, carbon-dioxide can be taken out of the air, and deposited into rocks.

The second important property of carbon-dioxide is that it is a gas that is transparent to optical light, but opaque (i.e., it absorbs) infrared light. (That's one of the reasons that infrared telescopes are on top of high mountains, in airplanes, or even in space.) Carbon-dioxide acts like the glass sides of a greenhouse -- it allows the energy of optical light in, but none of the heat to get out.

Now, consider the early history of Venus. Since Venus was a bit closer to the Sun than the Earth, it started out with a slightly higher temperature; this caused most of the water to be in gaseous form (water vapor) rather than liquid. As the planet evolved, methane and ammonia were outgassed, and then dissociated by the Sun's UV light into carbon-dioxide. However, unlike the earth, there was little water around to dissolve the CO_2. Thus, the carbon-dioxide remained in the atmosphere to trap the Sun's heat. This, of course, warmed the planet even more, and evaporated whatever liquid water there was lying around. The greenhouse effect was increased, and, as more and more methane and ammonia were outgassed, the effects got even worse. In other words, a runaway greenhouse effect was the result.

In contrast, the Earth's liquid water enabled most of carbon-dioxide to condense out of the air and into rocks. With the carbon-dioxide gone, and the hydrogen and helium molecules lost to space, the remaining atmosphere on earth consisted mostly of nitrogen and some methane and ammonia. Eventually, however, photosynthetic plant life developed. These green plants worked to further remove carbon-dioxide from the air, and replace it with oxygen. Over the years, the precentage of oxygen in the air has gradually increased due to plants (it was only 5 to 10% in the days of the dinosaurs), while carbon-dioxide has decreased. (Without the plants, oxygen would disappear, as it would quickly react with the soil and get tied up in solids.)

Along with normal oxygen gas (which consists of 2 atoms of oxygen), some molecules consisting of 3 atoms of oxygen (ozone) are also formed. Ozone is unstable and quickly reacts with other molecules, but, what does exist in the air does a very good job at absorbing ultraviolet photons. Without ozone, this high energy light would penetrate alot further into the earth's atmosphere and destroy animal (and plant) cells.