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Name: ____________________ Partner(s): ________________ ________________ AST 111: Lab #9 The Structure of the Solar System Objectives To explore the general characteristics of the solar system To analyze possible relationships between object density, distance from the Sun, diameter, and composition To discuss the most important physical factors that determine the scope and composition of a planetary atmosphere To relate specific observations of planets and moons to their actual atmospheres References Exploring the Planets, Hamblin & Christiansen, 1990 Materials Ruler Calculator Introduction How did the solar system form? When did this happen? Why are objects in the solar system arranged in the particular order we find them in? Although it is difficult to interpret events that occurred billions of years ago, it can be done. A combination of careful observations of present conditions and knowledge of physical principles allows us to reconstruct the history of the solar system. Observations of variables such as temperature or mass density are crucial to our understanding of how the solar system works. We will use these variables to build a storyline of the solar system’s formation and evolution. First we will examine the densities of objects and compare them to the densities of known materials. Then we will relate this to the temperature structure of the solar system. Finally, we will attempt to draw some basic conclusions about the solar system and its history. Activity #1: The Mass Density Profile of the Solar System It is well established that different objects in the solar system are made from different materials. Is this due to random causes, or is there a reason for this? We will explore this issue by plotting the density of objects as a function of two different variables. 87 (a) Table 9-1 contains density data from selected objects (planets, moons, & asteroids) in the solar system. Plot density as a function of distance from the Sun on the first sheet of graph paper. (b) Next, plot density as a function of the diameter of the object on the second sheet of graph paper. (c) Is there a dependence of density vs. distance from the Sun? If so, what is it? How strong is it? (d) Is there a dependence of density vs. object diameter? If so, what is it? How strong is it? Table 9-1. Density Gradient Data for the Solar System. Name of Object Distance from Sun (AU) Density (g/cm3) Diameter (km) Name of Object Distance from Sun (AU) Density (g/cm3) Diameter (km) Mercury 0.387 5.44 4880 Tethys 9.54 1.2 1060 Venus 0.723 5.25 12,104 Dione 9.54 1.43 1120 Earth 1.000 5.52 12,576 Rhea 9.54 1.33 1530 Moon 1.000 3.34 3476 Titan 9.54 1.88 5150 Mars 1.524 3.93 6787 Iapetus 9.54 1.16 1460 Vesta 2.362 ? 549 Uranus 19.18 1.28 51,120 Ceres 2.768 ? 1020 Miranda 19.18 1.35 470 Pallas 2.773 ? 538 Ariel 19.18 1.66 1150 Jupiter 5.203 1.3 143,800 Umbriel 19.18 1.51 1170 Io 5.203 3.50 3640 Titania 19.18 1.68 1580 Europa 5.203 3.03 3130 Oberon 19.18 1.58 1520 Ganymede 5.203 1.93 5280 Neptune 30.07 1.64 49,560 Callisto 5.203 1.79 4840 Triton 30.07 1.64 2700 Saturn 9.54 0.69 120,660 Nereid 30.07 ? 340 Mimas 9.54 1.4 392 Pluto 39.44 2.06 2284 Enceladus 9.54 1.2 500 Charon 39.44 2.06 1192 88 89 90 91 92 Activity #2: The Temperature Profile of the Solar System That temperatures of objects change with distance from the Sun is perhaps obvious. A more specific question to ask is how the temperature of the original solar nebula behaved vs. distance from the forming Sun (“protosun”). This is a more fundamental question, as it addresses why different objects are made of different materials in the solar system. Astronomers assume that the composition of the original nebular disk was the same as the present-day Sun. The Sun consists mostly of hydrogen and helium gas, but only the jovian planets have similar compositions. All other objects in the solar system are made up of various combinations of solid (rarely fluid) materials. Why are small objects not made of hydrogen and helium? In this activity we will look at the effects of temperature on composition. Activity #3 will look at the effects of the masses of objects on their compositions. (a) Table 9-2 contains density data from selected materials common in the solar system. Plot density as a function of condensation temperature 1 from the Sun on the third sheet of graph paper. (b) Next, plot condensation temperature as a function of condensation distance2 on the fourth sheet of graph paper. (c) Is there a dependence of density vs. condensation temperature? If so, what is it? How strong is it? (d) What is the dependence of condensation temperature vs. condensation distance? (e) Did either of the graphs from Activity #1 resemble either of these graphs from Activity #2? If so, why? “Condensation temperature” refers to the when a substance sifts out of gas and condenses into liquid or solid form. These temperatures are approximations only. 2 Distances were calculated from a simple power law, assuming that the primordial temperatures at the distance of Mercury (0.39 AU) and Jupiter (5.2 AU) were 1400 K and 200 K, respectively. 1 93 Table 9-2. Physical Properties of Various Substances. Substance Density (g/cm3) Condensation Temperature (K) Condensation Distance (AU) Iron-Nickel Alloy 7.9 1470 0.36 Oxide minerals 3.2 1450 0.37 Feldspars 2.8 1000 0.61 Troilite 4.6 700 0.98 Carbonates 2.9 400 2.07 Water ice 0.92 273 3.44 Carbon Dioxide ice 1.56 216 4.70 Ammonia ice 0.82 195 5.39 Methane ice 0.53 91 14.9 Nitrogen ice 0.88 63 24.3 (f) Today, the temperature decreases rapidly as one moves further from the Sun. What was it like during the formation of the solar system – i.e. as one moved further from the protosun? (g) Suppose an object made of a variety of ices moved closer to the Sun than the Earth. What would happen to it? (h) The original solar nebula was in the shape of a thin disk. How is it similar today? How is it different? (i) The Sun today is far hotter than the protosun, yet the temperatures in the rest of the solar system are much cooler today (see Activity #3). Why is this so? 94 95 96 97 98 Activity #3: Atmospheres of Objects in the Solar System The ability of an object to hold on to an atmosphere depends primarily on three characteristics: its escape velocity, as determined by its gravity; its surface temperature, as influenced by its distance from the Sun; and the potential components of its atmosphere. In contrast, the average speed of a gas particle (atom or molecule) is determined from the mass of the molecule and the temperature of the atmosphere: v 3kT m where k is a quantity known as Boltzman’s constant (1.38 x 10-23 J/K), T is the temperature of the gas, and m is the mass of the gas particle. Any gas molecule traveling faster than an object’s escape velocity cannot be held by that object. Because individual particles have a wide range of speeds for any given temperature, a planet’s atmosphere may leak away to space even if its escape velocity appears to be large enough. In practice, to hold on to a specific type of gas molecule requires that the escape velocity be about six or more times greater than the average molecular speed. Table 9-3 lists several solar system objects with their escape velocities and average temperatures (due to the Sun). Table 9-4 lists various gases popular in the solar system with their average speeds at various temperatures. Some of the substances are liquids at low enough temperatures, so they will not have speeds listed. Hydrogen and helium are the most common gases. (a) Determine from these tables which gases can be retained by an object and record those gases in Table 9-3. If an object can retain more than three gases, list only the three lightest gases. (b) Molecular hydrogen gas will leak away to space from the Earth within a million years. Does this statement agree with the results in Table 9-3? Briefly describe why or why not. (c) Earth has a warmer average atmospheric temperature (295 K) than its solar temperature of 235 K. Why is this so? 99 Table 9-3. Average Temperatures and Escape Velocities of Various Objects. Object Solar Temperature (K) Escape Velocity (km/s) Mercury 385 4.3 Venus 285 10.4 Earth 235 11.2 Moon 235 2.38 Mars 190 5.0 Jupiter 100 60 Ganymede 100 1.9 Saturn 75 36 Titan 75 1.9 Uranus 55 21 Titania 55 0.54 Neptune 40 24 Triton 40 1.0 Pluto 35 0.07 Possible Atmospheric Constituents (d) Oxygen is actually only found on Earth in significant amounts. Why is oxygen popular on Earth but on no other object? (Hint: could there be other reasons besides the ones studied above?) (e) Mercury has a daytime temperature of 700 K and a nighttime temperature of 100 K. How can this be reconciled with its solar temperature of 385 K? (The Moon behaves in a similar fashion) (f) Venus has an extremely thick atmosphere and very high temperatures (its actual temperature is 750 K, not 285 K). What is its atmosphere made of – molecular hydrogen or carbon dioxide? 100 (g) Even though the atmosphere of Mars is very thin, many astronomers believe most of the carbon dioxide of Mars is still there. In what phase (gas or solid) might it exist? (h) Jupiter’s escape velocity allows it to hold on to any gas. Why then is Jupiter primarily made of hydrogen and helium? (i) Titan and Ganymede have the same escape velocity. Why then does Titan have a thick atmosphere (thicker than Earth’s, by the way) whereas Ganymede has no atmosphere? (j) Triton has a thin atmosphere of nitrogen and Titan has a thick atmosphere of methane. Why do these substances dominate their respective atmospheres? Hint: Consider the various phases in which water can be found on Earth. (k) Finally, objects in the solar system are split into a variety of categories. In (rough) order from the Sun, they are terrestrial planets, asteroids, jovian planets, jovian moons, icy dwarfs and comets. Fill in Table 9-5 below. Indicate the two or three most likely popular substances to be found in each category. (Notes: “jovian planets” are a special case, being made primarily of gas, so the answer is given for them. All other objects will be solid. “Jovian moons” are simply the moons that orbit jovian planets and “icy dwarfs” are objects like Pluto. Consult your textbook for more information if necessary.) 101 Table 9-4. Average Speeds for Gases Found in the Solar System. (All speeds in kilometers per second) Gas Temperature (K) Name Molecular Formula 400 350 300 250 200 150 100 75 50 Hydrogen H2 2.2 2.1 1.9 1.8 1.6 1.4 1.1 0.97 0.79 Helium He 1.6 1.5 1.4 1.2 1.1 0.97 0.79 0.69 0.56 Methane CH4 0.79 0.73 0.68 0.63 0.56 0.48 0.39 * * Ammonia NH3 0.77 0.71 0.66 0.60 0.54 * * * * Water H2O 0.74 0.69 0.64 * * * * * * Nitrogen N2 0.60 0.56 0.52 0.47 0.42 0.37 0.30 0.26 * Oxygen O2 0.56 0.52 0.48 0.44 0.39 0.34 0.28 0.24 * Carbon Dioxide CO2 0.48 0.44 0.41 0.38 0.34 * * * * Notes: * = exists as liquid or solid at this temperature. Calculations assume one Earth atmosphere of pressure. Table 9-5. Categories of Objects in the Solar System. Category Likely to be made of these substances Terrestrial Planets Asteroids Jovian Planets Jovian Moons Icy Dwarfs Comets 102 Hydrogen, helium