MCC PHS 142 M01 Astronomy Homework Ch.12-13 Adj Prof Astronomy: Sam Wormley <email@example.com> Web: edu-observatory.org Background Material Textbook - Read Chapters 12-13 Textbook - http://highered.mcgraw-hill.com/sites/0073512184/student_view0/chapter12/ Textbook - http://highered.mcgraw-hill.com/sites/0073512184/student_view0/chapter13/ (take the Multiple Choice Quiz for for each chapter) Web - http://janus.astro.umd.edu/SolarSystems/ Web - http://edu-observatory.org/swormley/eo/planets.html Web - http://edu-observatory.org/swormley/eo/solar_system.html Web - http://edu-observatory.org/swormley/eo/science.html Web - http://antwrp.gsfc.nasa.gov/apod/archivepix.html Jupiter, its closest Galilean satellite, Io, and Io's shadow on the "surface" of Jupiter. The Laws of Nature: A Skeptic's Guide by Zoran Pazamet Awareness of the fundamental laws of nature is essential to any skeptical endeavor. These principles are presented so they can be understood, and explained to others, without assuming specialized prior knowledge. Anyone who has studied physics (the science of the laws of nature) knows how daunting the task is of learning the philosophical and mathematical formalisms needed to fully comprehend, express, and apply natural laws. Complicating this situation is the fact that some of these laws are still "under construction"-being debated by the scientific community. Moreover, today we have two fundamental approaches to studying the natural world (quantum theory and Einsteinian physics), built from completely different basic assumptions (Sachs 1988). Fortunately, in the macroscopic ("real") world, the subject of this article, physics has revealed to us definite rules by which nature always operates-rules for establishing what is physically possible and for eliminating the impossible. We have confidence in these laws because with all the observations and experiments that have been (and continue to be) performed, no exception to them has yet come to light; that is, they constitute the best explanation of the natural world available to us today. At this point, one could ask: Why do these laws exist in the first place? The answer to this question is beyond the reach of science; all we know is that we can identify natural laws, observe them in action, and use them to explain and predict natural phenomena. This is what Einstein meant with his famous statement, "To me, the most incomprehensible thing about the universe is that it is comprehensible" (my emphasis). Arguably the most fundamental of these laws is one due to Einstein himself, though it isn't a law about the behavior of nature but, rather, a law about natural laws themselves. Principle of Universality The Principle of Universality says that all laws of nature must work the same way everywhere. That is, the laws are objective; it doesn't matter who does the experiment or where, the same results should be produced under the same conditions. This is why knowledge of, say, biology, chemistry, and the forces of nature in our part of the universe allows us to outline the potentialities and limitations of life and space travel in other regions. Since the speed of light (c in the equation E=mc2) is the speed limit for travel and signal propagation here, it is also the (extensively verified) limit everywhere else; no matter how advanced spacefaring technology may be on other worlds, their inhabitants are still condemned to travel the vast reaches of interstellar space, for many thousands or millions of years, at speeds below c. (And as for "wormholes," those hypothetical shortcuts through space, they are pure theoretical abstractions possessing serious conceptual difficulties-including violation of several of the laws outlined below-as well as insurmountable practical ones.) Principle of Causality Causality states that causes must exist for all effects, and must come before the effects they produce. Parents must be born before their children; they cannot be born after them. In Einstein's physics causality holds in all domains of the natural world, but quantum theory allows for violation of microcausality at the (microscopic) quantum level. In our macroscopic world, however, causality holds absolutely. This is one important reason why time travel is impossible; to go backwards in time means reversing every cause-and-effect event in the entire universe between then and now. Apart from the obvious practical difficulties, this would entail violations of other fundamental natural laws-such as conservation (see below)-if the traveler's own birth (or other specific event) was not to be reversed! (True, solutions of certain equations for travel at speeds exceeding c do allow a reversal of the direction of time, but this is physically meaningless because the particles which could exist in such a world-named tachyons-would not be real; they have imaginary masses!) It is also important to remember that the connection between a cause and its effect must be a legitimate consequence of natural laws. Pseudoscience frequently misapplies irrelevancies (such as simple coincidence) to imply such a connection, then brings in untestable (therefore scientifically meaningless) supernatural agents to connect cause and effect. I should also mention that a system that is too complex for us to model with cause-and-effect relations (for example, a roomful of air molecules) is usually studied using statistics and probability. This approach has been called the "mathematical theory of ignorance" (Kline 1964) because we use it where we can't follow (are ignorant of) the physical behavior of every specimen in the system. The statistical treatment bypasses the details of how the natural laws affect each individual particle, and instead gives us information about the state of the whole system; it's therefore descriptive rather than explanatory. However we investigate it, though, the behavior of every component of our system is still governed by the same natural laws as the rest of the universe. Law of Extrema Simply put, the Law of Extrema states that all natural processes act to extremize (maximize or minimize) a physical quantity. (In mathematics, an extremum-plural, extrema-is the maximum or minimum of a function.) An especially important instance of this (related to the Law of Entropy, below) is the principle that all systems, by themselves, tend toward a state of minimum energy. This explains many phenomena in nature including the deaths of all organisms as well as of stars, water running downhill by itself but not uphill, the temperature of a hot object decreasing to that of its surroundings, and all possible chemical reactions-from the formation of atoms into molecules and molecules into matter, to combustion of fuels, to metal rusting, to metabolism in living beings. This is why the dead do not spontaneously come back to life, and why one cannot make an engine that uses water (the "ashes" from combustion of hydrogen and oxygen) as fuel. A further example comes from Einstein's theory of general relativity, where all bodies influenced by gravity move along paths of maximum or minimum length, called geodesics. And all of geometrical optics (the study of light moving through macroscopic media) derives from Fermat's principle: Light follows the path for which time is a minimum. Conservation of Matter and Energy In general, conservation means that in an isolated system a given physical quantity does not change with time. (If you do have outside interference, it can be included by extending the definition of the "system" and conservation will still hold.) An especially important and useful conservation law is that matter and/or energy are neither created nor destroyed over time; they merely change form, and their sum total always remains the same. For example, the chemical energy of a quantity of gasoline is changed into the same amount of kinetic energy in a moving car. Braking to a stop converts this kinetic energy into the same amount of heat energy in the brakes, and this increases the heat of the ambient air by, again, the same amount. You can of course add in external effects of air resistance, friction with the road, and so on; the grand total will still equal the initial energy released by the gasoline. And the total mass of air and gasoline ingested by the engine equals the total mass of the exhaust products. Consider now the erroneous belief that electric automobiles run on "free" energy. The vehicle's kinetic energy comes from electrical energy made elsewhere, predominantly from conversion of chemical energy in fossil fuels or thermal energy from a nuclear reactor. And these processes produce waste, so cars (and other devices) running on electrical energy usually aren't truly "pollution free," either! Many people claim that ghosts from time to time leave their nonphysical realm to appear here in ours. If they can interact with our material environment (by becoming visible to human eyes or cameras, causing objects to move, and so on), they must be at least partially composed of matter themselves (since it's observational fact that only matter produces the radiation, gravity, and mechanical forces that affect other matter). Therefore, by disappearing from their domain and appearing in ours, they violate conservation of matter (and energy) in both worlds! And in ours, this simply cannot occur. Law of Entropy The concept of entropy is still being actively debated by philosophers of science and is difficult to convey, so what follows is my own working definition. I find it useful to define an increase or decrease in entropy as a loss or gain in any one, two, or all three of these properties of a system: order, information, and available energy. The Law of Entropy then states that, in any real-world situation, entropy irreversibly increases for an isolated system. Consider an ordinary piece of photocopy paper. There is a certain amount of order to it (its geometric shape, uniform thickness, and so on). It also contains information, since all of its particles reside within its clearly defined form and have definite locations within it. It also has some available energy, since we can burn it to produce heat and light. Suppose we now do ignite this piece of paper and let it burn completely. Order has been lost because there is no longer a nice rectangular shape to the material, and the particles have dispersed. Information is lost because we no longer know where a given particle is; most have in fact broken up into smoke and ashes. And available energy is lost too, because the heat and light have dissipated into the environment and the burnt remains possess far less available energy than the paper did. In sum, entropy has increased. But can we "recombine" the fire, smoke, and ashes by reversing every microscopic process involved in the combustion and reconstitute the paper? In theory, yes-but only through external efforts; one consequence of the Law of Entropy is that the paper (like any isolated system) will not spontaneously regenerate itself. In practice, of course, this would be an unfeasible task, so the burning of the paper remains an irreversible process. The same holds, for example, for the death of any living being. All living creatures take in energy from their surroundings to offset the natural tendency toward increasing entropy (and its ultimate consequences, death and total decomposition). But while this allows for small-scale, individual growth in size and complexity (increasing order, information, and available energy, meaning a local decrease in entropy), the entropy of the ambient as a whole increases. As the Sun emits energy into space, its entropy increases irreversibly. A plant uses a tiny fraction of this energy, and chemicals from its environment, to decrease its own entropy as it grows. Put the plant in an airtight, lightproof container, though, and this now-isolated system will quickly succumb to the Law of Entropy: It will die and decompose as it approaches its maximum entropy state. Another consequence of the Law of Entropy is that all real-world processes, biological or otherwise, must produce some waste in the form of cast-off energy (and, often, matter also). However small this waste may be, it is never zero-that is, no natural or man-made process can ever be 100 percent efficient. The human metabolism, for example, is only about 50 percent efficient; half of the energy we derive from food and oxygen intake becomes waste heat. Clearly, the Law of Entropy rules out practical perpetual-motion machines whose efficiency is by definition 100 percent, not to mention those miraculous "free-energy" machines that, on their own, produce more energy than they consume (thus exceeding 100 percent efficiency). We conclude by noting that the Law of Entropy can be stated in terms of the Law of Extremes: All natural processes act to maximize the entropy of a system. As we have seen, any such system can temporarily sustain itself from the energy cast off by another system as it progresses towards its own state of maximum entropy, but ultimately the entropy of the entire ambient must irreversibly increase. This offers another argument against time travel (as well as, for example, resurrection of the dead), since all of the myriad processes and events that elapse between any two dates (such as the beginning and end of the dying process) are, for all practical purposes, irreversible. (Some philosophers connect this with the concept of the arrow of time.) It indeed appears that the ancient Greek thinker Heraclitus was right: You can never step into the same river twice. References Kline, M. 1964, Mathematics in Western Culture, New York: Oxford University Press. Sachs, M. 1988, Einstein versus Bohr: The continuing controversies in physics, La Salle, Ill.: Open Court. About the Author Zoran Pazameta teaches astronomy and physics at Eastern Connecticut State University. His research interests include relativity, cosmology, and the philosophy of science. Address: Physical Sciences Department, Eastern Connecticut State University, Willimantic CT 06226. E-mail: firstname.lastname@example.org. How do You Know What to Believe? "In the macroscopic "real" world, the subject of the above article, physics has revealed to us definite rules by which nature always operates--rules for establishing what is physically possible and for eliminating the impossible. We have confidence in these laws because with all the observations and experiments that have been (and continue to be) performed, no exception to them has yet come to light; that is, they constitute the best explanation of the natural world available to us today". The same is true for the two great pillars of 20th century physics, the Quantum Mechanics dealing with the world of the atom, and General Relativity dealing with the Universe as a whole. Was Einstein right? Without a doubt! These theories have been tested for almost a century and have never failed to be in agreement with observation and experiment. What about Darwinian Evolution? Darwinian Evolution is very often misquoted and misunderstood. Indeed Evolution correctly accounts for much of the observation and experimental result in the biological world. For life, there are limited resources. Species compete for those resources. Random mutations occur (minor as they may be) in reproduction of life forms from generation to generation. On the whole, it is "the survival of the fittest" that produce the most offspring and generations adapt to the changing environment. When resources are plentiful, diversity tends to take place often accompanied by the proliferation of new species. When resources are scarce, whole lines of species die out, become extinct. This is the basic mechanism that Darwin observed and understood. Was Darwin right? Without a doubt! Evolution is certainly tied to astronomy. There is evolution of the Universe, evolution of the galaxies and stars, evolution of the Earth, its atmosphere, its contents, its geology, its life forms, and, of us. All of these are in a continual state of change and on the grand scale it is all intertwined. The iron in your blood was made in the cores of very massive stars. The evolution of mammals and eventually us, came about after the mass extinction 65 million years ago, thought to be brought about by a cosmic impact on the Earth. Darwinian Evolution, like Special and General Relativity and the Quantum Mechanics, although historically called theories, are all elevated to scientific fact, supported by decades of observation and experiment. I see no need of religious conflict. God seems to work with all the mechanisms that humans are discovering. Science is not a set of "facts", but a process in which we understand nature about us, how it works, how it evolves... The mechanisms of how we know things are: observation and experiment. Models and theories are tools to help us understand. They are revised and corrected with new and changing evidence... rarely are they over-thrown, but usually always refined as we converge toward a better understanding of the Universe and our place in it. I bought an astronomy textbook some years ago, "The Physical Universe" by Frank H. Shu. I liked this textbook because Dr. Shu describes all the physical processes in the Universe as a battle between Gravity and the 2nd Law of Thermodynamics, Entropy. Gravity is trying to collapse stars, the thermonuclear fusion holds the star up against gravity. The 2nd Law says that systems tend toward decay and tearing down, yet on the Earth, life tends evolve to form greater complexity. A contradiction? No, the energy for building on the Earth comes from the Sun. As long as the Sun provides the Earth with energy, Entropy is held at bay. "We conclude by noting that the Law of Entropy can be stated in terms of the Law of Extremes: All natural processes act to maximize the entropy of a system. As we have seen, any such system can temporarily sustain itself from the energy cast off by another system as it progresses toward its own state of maximum entropy, but ultimately the entropy of the entire ambient must irreversibly increase. This offers another argument against time travel (as well as, for example, resurrection of the dead), since all of the myriad processes and events that elapse between any two dates (such as the beginning and end of the dying process) are, for all practical purposes, irreversible. (Some philosophers connect this with the concept of the arrow of time.) It indeed appears that the ancient Greek thinker Heraclitus was right: You can never step onto the same river twice". Homework Problems Note the answers to the odd (Conceptual Questions, Problems and Figure-Based Questions) are in the back of your textbook. It is strongly suggested that you do some of those in every chapter so you have immediate feedback as how well you are understanding the material. There are online multiple choice quizzes for each chapter of your textbook. Goto http://www.mhhe.com/fix then click on Your book Student Edition Choose a chapter Multiple Choice Quiz You are expected to do all of your own homework. Statistical patterns showing copying or collaboration will result in no credit for the homework assignment for all participants involved. The Code of Academic Conduct for Iowa Valley Community College District is found in the Student Handbook. Physical Science classes require the use of mathematics. If you don't know algebra, you sould NOT be taking this class. If you need to review, look at Introduction to Algebra http://www.math.armstrong.edu/MathTutorial/ WolframAlpha is way faster than a scientific calculator. http://www.wolframalpha.com There is little excuse for turning homework in late. You have a whole week between classes to read the chapters and do the homework. Homework one week late - half credit. Two or more weeks late - no credit. Do the homework during the week, not in class! You got homework questions, email me 24/7. email@example.com Even if you don't have a homework question, email me anyway! Problem 1: Use figure 13.5 to estimate the pressure at the depths in the atmospheres of Uranus and Neptune where ammonia (NH3) clouds lie. Hint: Regardless of the cloud labels in the diagram, ammonia clouds form at a temperature of 140 K. Problem 2: Using your Planisphere (starwheel), in what constellation is the Sun on your birthday? Hint: The Sun transits at Noon on your Birthday. Problem 3: Using your Planisphere (starwheel), how long is the day in hours and minutes (sunrise to sunset) on your birthday? Alternate resource: http://edu-observatory.org/mcc/syllabus/skycalendar.html Problem 4: How many distinct "ringlets" can be identified in Figure 12.32 between 113,000 km and 113,200 km from Saturn? Takes a little work! Problem 5: Describe what forms (physical states) hydrogen takes in Jupiter from the surface to the center of the planet. Problem 6: How does the size and shape of Jupiter's magnetosphere compare to the Earth's magnetosphere? Be specific. Problem 7: What evidence do we have that Saturn's rings aren't solid disks? Problem 8: What was the reason that, after the discovery of Uranus, astronomers began to believe that there was a planet beyond Uranus? Problem 9: Pluto has a temperature of about 50° K. Use Wien's law (Chapter 7) to calculate the wavelength at which Pluto is brightest. Problem 10: How were the ring systems of Uranus and Neptune detected before they were actually seen in Voyager 2 images?