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Formation of the Solar System. (a) A rotating interstellar cloud. (b) The cloud begins to contract. Since the angular momentum is conserved, the rotation becomes faster. (c) The rotation is fast enough to slow the collapse perpendicular to the axis of rotation, so a disk forms.The center is collapsing fastest, forming a denser concentration that will eventually become the Sun. (d) When the rotation prevents farther collapse of the disk, it breaks up into smaller clumps, so that some of the angular momentum is taken up by the orbital motion of the clumps.The clumps can then collapse. (e) Clumps of material gather together, forming planets, as the proto-Sun begins to radiate, and generate a large wind. (f) The wind clears debris from the Solar System.

In following the evolution of the solar nebula, we must keep track of three types of materials: gases, ices and rocks. Most of the mass was in the gas (as most of the mass of the interstellar medium is in gas). However, gas cannot be held to a growing planet by gravity, so it escapes from all but the largest objects. The ices are water (H2O), carbon dioxide (CO2) and nitrogen (N2), along with some ammonia (NH3) and methane (CH4). These make up 1.4% of the mass of the Solar System. The rocks are iron oxides and silicates of magnesium, aluminum and calcium. Some of the iron was metallic and some of it was in iron sulfide (FeS). They can only be destroyed at high temperatures, in excess of 2000 K. They make up 0.44% of the mass (not including the Sun) in the Solar System. They are particularly prominent in the inner planets, while the ices are prominent in the outer planets. Comets provide us with the best clues on the initial composition of the rocks and ices.

The accretion of the nebula probably took place over 10 000 to 100 000 years. The first step in the process was for small grains to clump together. The grains collided, sometimes making larger ones, and sometimes breaking into smaller ones. The process produced many grains about 1 cm in size. These grains were large enough to settle through the gas in the plane of the nebula. This brought the clumps closer together, and allowed for even more collisions. Calculations indicate that the thin sheet of grains could then clump into objects with sizes of a few kilometers (essentially asteroid sized objects). About 1000 of these could then form a group held together by their own gravity. At that point, the groups were spinning too fast to collapse completely. Eventually these groups served as the cores for farther condensation of bodies orbiting at the same distance from the Sun.

Different parts of the Solar System then evolved differently because of the fall-off in solar radiation with distance from the Sun. The collapsing nebula had a higher temperature in the center (near the forming Sun) than at the edge. In equation (23.4) we found the equilibrium temperature of a planet as a function of the solar luminosity and its distance from the Sun. This expression works as well for dust particles. (Indeed, the calculation that led to equation (23.4) was essentially the same as that which we used to calculate the temperature of interstellar grains, in Chapter 14.) So, from equation (23.4), we see that the temperature falls off as the square root of the distance from the Sun. When the temperature was about 3000 K near the center, it was a few hundred kelvin in the regions of planetary formation. It also falls by a factor of about five between the orbits of Venus and Neptune. Therefore, different materials condensed at different distances from the center.

Another factor affecting the nature of forming planets was a fall-off in the density of material as one goes farther from the Sun. As we saw in Chapter 15, when even a uniform interstellar cloud collapses, it develops a higher density in the center than at the outside. In fact, ultimately the highest density center becomes the star. In the higher density regions near the center, the material is also moving faster, as a result of infall, converting gravitational potential energy into kinetic energy. The higher density and higher speeds near the center meant that collisions also played an important role in shaping the gas. As a result of the temperature and density variations, we can think of planetary formation as occurring in three zones: (1) the terrestrial planets, (2) the giant planets, and (3) comets.

Near the Sun, the temperature was too high for most of the gas (especially the H2 ) to have survived the star formation process. So solid materials had to be involved. We think that the original building blocks for the terrestrial planets where chondrules (discussed in Chapters 23 and 26). These were heated to temperatures of 1500 to 1900 K, and then cooled. Chondrules that we can study in meteors suggest that, to give their particular structure, the heating and cooling took place very quickly, possibly over a few hours. This would mean that the early solar nebula was rocked with energetic events. These chondrules would have had a range of sizes, but typical sizes might have been a few millimeters. There were so many of these chondrules, and their relative speeds were so low (about 1 m/s), that they eventually began to stick together. We don't know what provided the attractive force. It has been speculated that the so-called van der Waals force could have been involved. This is a very weak electrical attraction between neutral objects when the charges can move so that the centers of positive and negative charge are in different places. This created small aggregates of chondrules, which could also grow by sweeping up dust. Eventually they grew to sizes of about 1 km. At that point, we call them planitesimals.

Even though there were many planitesimals, they were distributed over a large volume of space, so encounters between planitesimals were rare, maybe once per thousand years. Computer simulations show that these collisions eventually made larger objects, and after about 20 000 years several Moon-sized objects should have appeared. After about ten million years, these objects collected to form most of the four terrestrial planets, though these planets probably continued to sweep up planitesimals for 100 million years. These collisions were constantly reforming the surfaces of the planets through violent events.

The outer edge of the inner zone is the asteroid belt. There is a large gap between Mars and Jupiter suggesting that there was room for another planet to form. It is the one gap in Bode's law (discussed in Chapter 22). We don't expect a gap, since we expect that the material in the solar nebula would have been falling off gradually in abundance, and we know there was enough material farther out to form the giant planets. The most likely explanation is that the early formation of the very massive Jupiter prevented the formation of a planet. This could have been either by Jupiter somehow preventing the formation of the more massive planitesimals, or by Jupiter somehow removing them after they had formed. We do know that Jupiter has been effective at removing objects from certain resonant orbits, e.g. the Kirkwood gaps discussed in Chapter 26.

In the second zone, material was far enough out for water ice to exist. Since O is more abundant than the elements that are important in dust grains (e.g. Si, Mg, Fe), particles of water ice (essentially snowflakes) would have been more abundant than dust particles in the second zone. It is thought that Jupiter and Saturn formed initially from planitesimals made up primarily of water ice. These planitesimals would have formed in a manner similar to those for the rocky planitesimals that formed the terrestrial planets. However, once Jupiter and Saturn had enough material to exert strong gravitational forces, then they would have collected all of the interstellar material (mostly gas and a little dust) that was near them. This resulted in two very massive planets. Also, the planets had compositions reflected in the interstellar medium 4.5 billion years ago. So the compositions of Jupiter and Saturn are essentially the same as that of the Sun, meaning that they have primarily hydrogen.

Uranus and Neptune formed in the outer parts of the second zone. The icy planitesimals would have filled a larger volume of space, meaning fewer collisions, and less chance for growth than the ones that started Jupiter and Saturn. There would therefore have been less gravity to hold interstellar gas in. Furthermore, the density of interstellar gas was lower the farther one got from the center of the solar nebula. So, Uranus and Neptune are just the result of the buildup of icy planitesimals, and are dominated by ices. Their compositions are therefore different from those of Jupiter and Saturn. (Fig. 25.13 illustrates some of the differences in composition between Jupiter and Saturn and Uranus and Neptune.)

Most of the satellite systems probably grew from a disk forming around the planet. This process repeated the formation of the rocky planets on a smaller scale. The satellites whose orbits are close to the ecliptic and are not too eccentric were probably made in this way. Satellites with very inclined or eccentric orbits may have been captured.

In the third zone, beyond Neptune, ice/rock planitesimals were formed. However, they fill such a large volume of space that gravitational encounters are very rare. This means that they cannot collect into a planet. The ones from Neptune's orbit out to 50 AU formed the Kuiper Belt. Those farther out formed the Oort cloud. As we discussed in Chapter 26, occasionally one of these objects has its orbit perturbed, and enters the inner Solar System as a visible comet.

The scenario that we have discussed probably left a large amount of debris around the planets. However, the Solar System is now relatively clean. Where did the leftover material go? We think that the Sun went through a stage when its wind was much stronger than it is now, much like the winds in T Tauri stars. The peak mass loss rate may have been 1 M0/1O6 yr. The wind carried sufficient energy and momentum to sweep out the debris and stop the infall into the solar nebula.

Collisions among the particles also helped to clear the Solar System. Some of the debris crashed directly into planets, leaving the craters that we still see on Mercury, Mars and the Moon. Other collisions led to ejection of bodies from the Solar System. Finally, the momentum carried by the sunlight itself may have helped clear the

Solar System. The momentum carried by the light is the energy, divided by the speed of light. That is, p = E/c

The radiation would have been able to sweep out small dust particles, and also carry away the orbital angular momentum of the dust. Finally, some of the collisions could also reduce the orbital energy of the dust, allowing it to fall into the Sun. This is known as the Poynting-Robertson effect. In these collisions, aberration of light, discussed in Chapter 7, makes it appear to the dust particle that the light from the Sun is coming from slightly ahead in the orbit. Thus, the particles lose energy, and eventually spiral into the Sun.

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