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CORNELL ASTRO 202 - Study Notes

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Tips for Writing in Astro 202In this class, you will have the opportunity to integrate what you’re learning aboutour Solar System with your skills in writing. This can be a great chance to show yourcreativity and make connections with the ideas you encounter during lectures andreadings. However, science writing is more than likely a little different than the writingyou’re accustomed to, and thus will probably take some time to “master”. Therefore, thefollowing are some tips that might help you as you tackle your papers:- Read and try to understand the material BEFORE you start to write! You don’thave to know exactly where you are going in terms of organization, etc., on a firstdraft, but the fastest way to write a meandering, bloated paper is starting withouthaving a good grasp of the topic. Please take advantage of office hours to clearup anything you’re uncertain about—we’re happy to help.- Clearly define technical terms before you use them. Also, avoid “listing” factsinstead of explaining them in your own words (see additional handouts forexamples). Having a friend unfamiliar with the material read your papers to makesure that they “make sense” is a good way to ensure you’ve achieved theappropriate level of clarity.- Check carefully before submitting an assignment that you have addressed thequestion(s) posed. My suggestion (note: suggestion only… everyone has his/herown style) is to write a first draft focusing on the science content and then workfrom there to add your creativity and style. This can help you avoid gettingsidetracked.- Always thoroughly proofread your papers to guard against silly typos. I find thebest way to do this is to read your work aloud. It sounds silly, but it really doeswork. Plus, hearing the words spoken can help you get a feel for the phrasing ofyour writing and may help you identify everything from missed commas to run-onsentences. Along those same lines, good grammar makes for clear, functionalwriting. Thus, be sure that you are using the formal rules of written English(avoid contractions, no prepositions at the end of sentences, etc.) for the formalwriting you submit.- Do not plagiarize, it will not be tolerated. Thus, make sure you give credit whereit is due in terms of citations. The exact method that you use for citation is not asimportant to me as the fact that a citation has been given. Just be consistent withyour style and make sure enough information is given that I could find the workyou used if I went looking for it.Part I: What is the ultraviolet catastrophe? Approach I: The ultraviolet catastrophe results from the equipartition theorem of classical statistical mechanics which states that all modes (degrees of freedom) of a system at equilibrium have an average energy of kT / 2. According to classical electromagnetism, the number of electromagnetic modes in a 3-dimensional cavity, per unit frequency, is proportional to the square of the frequency. This therefore implies that the radiated power per unit frequency should follow the Rayleigh-Jeans law, and be proportional to frequency squared. Thus, both the power at a given frequency and the total radiated power approach infinity as higher and higher frequencies are considered: this is clearly an impossibility, a point that was made independently by Einstein and by Lord Rayleigh and Sir James Jeans in the year 1905. -Wikipedia, “Ultraviolet Catastrophe”Part I: What is the ultraviolet catastrophe? Approach II: The road to quantum mechanics began with a puzzling problem. Imagine that your oven at home is perfectly insulated, that you set it to some temperature, say 400 degrees Fahrenheit, and you give it enough time to heat up. Even if you had sucked all the air from the oven before turning it one, by heating its walls you generate waves of radiation in its interior. This is the same kind of radiation—heat and light in the form of electromagnetic waves—that is emitted by the surface of the sun, or a glowing-hot iron poker. Here’s the problem. Electromagnetic waves carry energy—life on earth, for example, relies crucially on solar energy transmitted from the sun to the earth by electromagnetic waves. At the beginning of the twentieth century, physicists calculated the total energy carried by all of the electromagnetic radiation inside an oven at a chosen temperature. Using well-established calculational procedures they came up with a ridiculous answer: For any chosen temperature, the total energy in the oven is infinite. It was clear to everyone that this was nonsense—a hot oven can embody significant energy but surely not an infinite amount. To understand the resolution proposed by Planck it is worth understanding the problem in a bit more detail. It turns out that when Maxwell’s electromagnetic theory is applied to the radiation in an oven it shows that the waves generated by the hot walls must have a whole number of peaks and troughs that fit perfectly between opposite surfaces. …By making use of nineteenth-century thermodynamics, physicists were able to determine how much energy the hot wall of the oven would pump into electromagnetic waves of each allowed wavelength… The result they found is simple to state: Each of the allowed waves—regardless of its wavelength—carries the same amount of energy (with the precise amount determined by the temperature of the oven). In other words, all of the possible wave patterns within the oven are on completely equal footing when it comes to the amount of energy they embody. At first this seems like an interesting, albeit innocuous, result. It isn’t. It spells the downfall of what has come to be known as classical physics. The reason is this: Even though requiring that all waves have a whole number of peaks and troughs rules out an enormous variety of conceivable wave patterns in the oven, there are still an infinite number that are possible—those with ever more peaks and troughs. Since each wave pattern carries the same amount of energy, an infinite number of them translates into an infinite amount of energy. At the turn of the century, there was a gargantuan fly in the theoretical ointment. -Brian Greene, The Elegant UniversePart II: How does


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