# Why are Saturn s rings confined to a thin plane? 1. Tidal forces 2. Newton s 1st law 3. Conservation of energy 4. Conservation of angular momentum

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1 Announcements Astro 101, 12/2/08 Formation of the Solar System (text unit 33) Last OWL homework: late this week or early next week Final exam: Monday, Dec. 15, 10:30 AM, Hasbrouck 20 Saturn Moons Rings PRS Question: Look carefully at this picture. What might you conclude about the way that Saturn formed? 1. Tidal forces due to encounters between Saturn and comets/asteroids are the main origin of the rings 2. Saturn is a mini solar system. The physics that led to the formation of the rings are the same as those that formed the Sun and its planets, etc. Note: we didn t do the PRS question this semester, but it is a useful question to think about: PRS Question: Why are Saturn s rings confined to a thin plane? 1. Tidal forces 2. Newton s 1st law 3. Conservation of energy 4. Conservation of angular momentum angular momentum = m x v x r 1

2 SUMMARY: Collapse of the solar nebula into a disk Heating. Gravitational potential energy kinetic energy thermal energy. Temperature increases. Compaction. The mass of the cloud is packed into a smaller volume. Density increases. Spinning. Angular momentum is conserved. Rotation speed increases. Flattening. Angular momentum and collisions flatten the cloud. Disk emerges. Nebular Theory of Solar System Formation Gas cloud protosolar disk Sun & Patterns of motion. Orbits are planets 1) mostly circular 2) in the same direction (counterclockwise) 3) in (mostly) the same plane. 4) rotations are also (mostly) in counterclockwise direction Two classes of planets: terrestrial & jovian Asteroids & comets Weirdos (e.g., Uranus is tipped way over, Triton has a retrograde orbit) What happens next? Why does a stable disk turn into planets? PRS Question: Consider a balloon full of air. Inside that balloon, which of the following elements will move the slowest? 1. Hydrogen (atomic weight = 1) 2. Helium (atomic weight = 4) 3. Nitrogen (atomic weight = 14) 4. Oxygen (atomic weight = 16) Temperature is a measure of kinetic energy Kinetic energy = 1/2 mv 2 In a particular object, all elements are at the same temperature and have the same amount of kinetic energy Therefore, heavier elements must move more slowly (so that they have the same KE as the light elements). 2

3 What happens next? Kinetic energy = 1/2 mv 2 PRS Question: Consider a balloon full of air. Inside that balloon, which of the following elements will move the slowest? 1. Hydrogen (atomic weight = 1) 2. Helium (atomic weight = 4) 3. Nitrogen (atomic weight = 14) 4. Oxygen (atomic weight = 16) Why is this important? Answer: recall our discussion of the phases of matter. Particles can bond more easily at lower velocities. Therefore, at a high temperature, heavy particles can bond more easily than light particles. What happens next? Why does a stable disk turn into planets? Several processes play roles: Condensation: change from gas phase to liquid phase or solid phase. Particles bond and change phase. Different materials condense at different temperatures. Accretion: microscopic condensates collide and stick together and grow into planetesimals. Can grow to several hundred km across Planetesimal collisions: small ones shatter, big ones grow Condensation formed the seeds for planets, then accretion built them up. The seeds were in orbit just like planets, and nearby particles moved at nearly the same speed. Thus, they gently bumped together and were able to stick because of electrostatic force (opposite charges attract). As they grew larger, their gravitational forces grew stronger, and gravity started to hold the planetesimals together. 3

4 Materials in the protosolar nebula Metals Rock Hydrogen compounds Hydrogen and helium gas Iron, nickel Rock Water, methane, ammonia Hydrogen, Helium Condensation temperature 1600 K 1300 K < 150 K Cannot condense Relative abundance 1.4 % 98 % Examples 0.2 % 0.4 % Decreasing mass Increasing abundance The farther an The farther a gas object falls, the clump falls in a faster it goes: collapsing cloud, the hotter it gets: A longer fall converts more gravitational potential energy in heat. The purple ball has more gravitational potential energy to begin with. The temperature in the protosolar disk depended on distance from the Sun: hot at center, cold at periphery Only rocks & metals can condense in the hot region within 3.5 AU of the Sun the so-called frost line. Hydrogen compounds (ices) can condense beyond the frost line. Terrestrial vs. Jovian Planets Terrestrial planets are small because there was very little rock and metal in the protosolar disk to begin with. After the rock and metal in the protosolar nebula were used up, accretion had only managed to make small terrestrial planets. What about the jovian gas giants? HOT Temperature COLD These processes could form icy seed planetestimals, but not huge gas giants... How did the jovians grow so big? 4

5 Recall: Escape Velocity Recall: Escape Velocity The escape velocity of a microscopic particle is exactly the same as the escape velocity of a massive rocket! The escape velocity of a microscopic particle is exactly the same as the escape velocity of a massive rocket! At a given temperature, hydrogen moves more rapidly than, say, iron. Therefore, the velocity of hydrogen is more likely to exceed the escape velocity than the velocity of iron. Terrestrial vs. Jovian Planets Terrestrial planets are small because there was very little rock and metal in the protosolar disk to begin with. Escape velocity applies to particles in an atmosphere. Just like a rocket, a particle will escape from a planet if it is moving faster than the escape velocity. At the locations of the terrestrial planets, the temperatures made the hydrogen atoms and molecules all escape from the newly formed planetesimals. The gas giants captured huge amounts of hydrogen in their atmospheres. 98% of the protosolar nebula was H and He Hydrogen and helium escaped from the small planets in the hot inner protosolar nebula. Terrestrial planets. But in the outer nebula, cooler tempertures allowed the biggest planetesimals to capture and retain H and He, and these eventually gathered enough hydrogen and helium so that they no longer appeared anything like their icy seed planetesimals. Gas giants. 5

6 Observational clues Jovian moons and rings Gravity gathered a lot of gas around the Jovian planets Each gas (Jovian) planet formed its own miniature solar nebula. Moons and rings formed out of the jovian disks. protosolar disk Gas cloud Patterns of motion. Orbits are 1) 2) 3) 4) Sun & planets mostly circular in the same direction (counterclockwise) in (mostly) the same plane. rotations are also (mostly) in counterclockwise direction Two classes of planets: terrestrial & jovian Asteroids & comets Weirdos (e.g., Uranus is tipped way over, Triton has a retrograde orbit) Planet formation was not efficient. Most of the disk did not end up in a planet. Condensates planetesimals planets Gradually objects emerge from the protosolar disk and a few large ones settle out In the hot inner disk, only metallic/rocky planets can form. Past the frost line (beyond Mars), icy condensates/planetesimals. Most of these remained small: comets! Nov. 13, 2008 NASA press release: Hubble Space Telescope Directly Observes Planet Orbiting Fomalhaut Fomalhaut here (light blocked using a special technique) Ring of dust and asteroids surrounding Fomalhaut 6

7 Evidence of another directly observed planet, this time in the disk of the star Beta Pictoris Disk (edge-on) Possible planet Starlight blocked here In this case, the disk is viewed from the side (edge-on) Again, special techniques were used to block the overwhelming light from the star itself Disks around young stars are ubiquitous. Why don t we see a disk around our Sun? Well, we see the asteroid belt and the comets in the Kuiper belt. These are the remnants of the disk that once surrounded the Sun. But, a lot of the disk was cleared away. How? Composite image of the Sun. Main Sun Sun s corona (observed during eclipse) The Solar Wind Streamers affiliated with particles in the solar wind A spray of low-density, hot particles (mostly protons and electrons) flows away from the Sun all of the time, the solar wind The solar wind particles flow away from the Sun at km/s The solar wind has many important effects, e.g., likely played a major role in ruining Mars The Solar Wind At some point in the distant past, the solar wind started to blow Collisions and conservation of linear momentum swept out the gas and smaller planetesimals; the more massive planets remained behind Timing of solar wind turn on was important: If too early: no planets If too late: All planets icy and/or gas giants 7

8 Puzzle: why isn t the Sun spinning faster? Nebular theory predicts that the Sun should be rotating much more rapidly Angular momentum must be conserved, but it can be transferred from one thing to another How could the Sun give away some of its angular momentum? Consider a magnet Magnetic field lines show regions where the magnetic field is stronger Magnetic Fields Some objects, e.g., iron fileings, feel the magnetic force and reveal the field lines: Objects like the Sun and the Earth are effectively huge magnets with giant magnetic field lines The solar wind transfers angular momentum. How does this happen? Charged particles sort The Sun certainly has of stick to magnetic magnetic fields, and they fields: were probably much stronger when the Sun was young Electrons or protons follow a spiral path along magnetic field lines The solar wind transfers angular momentum. How does this happen? Charged particles The protosolar disk orbits in accordance with Kepler s stick to magnetic laws: P fields 2 = a 3 The Sun s magnetic field, and the charged particles it drags along with it, rotate more rapidly The Sun s magentic field transfers angular momentum to the charge particles farther out in the disk Eventually the solar wind evacuates the charged particles too and their angular momentum is carried away 8

9 But the Sun is not a solid bar of iron. How does it generate a magnetic field? An electromagnet also creates a magnetic field A battery connected to a simple coil of metal wire will generate a magnetic field The battery moves charges (electrons) through the wire Charges moving in a spiral pattern create a magnetic field Convection: a macroscopic energy transport process in which a blob/parcel of warm material expands and rises while other cool and fall Convection occurs in a pot of boiling water: The Earth is a giant electromagnet The rings of Uranus Three requirements for a substantial magnetic field Electrically conducting fluid region inside (metal conducts nicely) Convection in the fluid region Moderately rapid rotation Similar processes generate the Sun s magnetic field 9

10 Exceptions to the Rules So how does the nebular theory deal with exceptions, i.e. data which do not fit the model s predictions? There were many more leftover planetesimals than we see today. Most of them collided with the newly-formed planets & moons during the first few 10 8 years of the Solar System. We call this the heavy bombardment period. Exceptions to the Rules Close encounters with and impacts by planetesimals can explain: Why some moons orbit opposite their planet s rotation captured moons (e.g. Triton) Why rotation axes of some planets are tilted impacts knock them over (extreme example: Uranus) Why Earth is the only terrestrial planet with a large Moon giant impact 10

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