Unit 3: The Science of Astronomy PDF

ASTR 205 Unit 3 Dr. Bryan Rowsell Unit 3: The Science of Astronomy 3.1 The Ancient Roots of Science Humans have been making observatio ns about the stars for millenia, humans love patterns! Home reading…some interesting historical information here! 3.2...

ASTR 205 Unit 3 Dr. Bryan Rowsell Unit 3: The Science of Astronomy 3.1 The Ancient Roots of Science Humans have been making observatio ns about the stars for millenia, humans love patterns! Home reading…some interesting historical information here! 3.2 Ancient Greek Science Why is so much attention given to the ancient Greeks with respect to science and astronomy? − Worked to understand nature without relying on supernatural explanations − Debated and challenged each other’s ideas − Used mathematics to give precision to their ideas − Understood that an explanation could not be right if it disagreed with observed facts − Developed scientific models of nature What is a scientific model of nature exactly? The Science of Astronomy ·3−1· 3.2: Ancient Greek Science ASTR 205 Unit 3 Dr. Bryan Rowsell In everyday language, a model is a miniature representation of a physical object, i.e. a model airplane (a miniature, perhaps buildable representation of a real object) In science, a model is a physical, mathematical, or conceptual representation of some aspect of nature that aims to both explain observed phenomena and predict future phenomena. A scientific model never invokes myth, magic, or the supernatural. All of modern science can be thought of as the continual refinement of current models, and the development of new models. A few historical figures in ancient Greek astronomy: Aristarchus of Samos (c. 310 – 230 BC) Greek astronomer and mathematician Proposed the first known heliocentric model of the Solar System (but this model didn’t gain popularity at this time) Thought the stars were the same as the Sun, just much farther away Used observations of a lunar eclipse to deduce the relative sizes of Earth and the Moon Eratosthenes of Cyrene (c. 279 − 194 BC) Greek astronomer, mathematician, geographer, and poet Chief Librarian at the Library of Alexandria First person to calculate Earth’s circumference and rotation axis tilt The Science of Astronomy ·3−2· 3.2: Ancient Greek Science ASTR 205 Unit 3 Dr. Bryan Rowsell Although the Greeks made many advancements and worked to find natural explanations for observed phenomena, they still had an underlying assumption of perfection in the heavens: The planets, Sun, Moon, and stars move in perfectly circular orbits. The speed of the planets, Sun, Moon, and stars is uniform. The Earth is at the exact center of the motion of the bodies. Is this model heliocentric or geocentric? Claudius Ptolemy (c. 100 – 170 AD) Greek astronomer, astrologer, mathematician, and geographer Wrote The Amalgest, in which he describes the motion and position of the Moon, Sun and planets and explains his model of the Solar System The Science of Astronomy ·3−3· 3.2: Ancient Greek Science ASTR 205 Unit 3 Dr. Bryan Rowsell To account for retrograde motion (see Unit 2), Ptolemy made planets move on small circles (called epicycles) who’s centre moves around the Earth on a larger scale. Very mathematically−complex model, but it accurately forecast planetary positions for more than 1000 years. Is this model heliocentric or geocentric? 3.3 The Copernican Revolution Nicolaus Copernicus (1472 – 1543 AD) Polish astronomer and mathematician Published On the Revolutions of the Heavenly Spheres posthumously to avoid objections The Science of Astronomy ·3−4· 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell The Copernican model was much simpler than the Ptolemic model, but no more accurate (still used perfect circular orbits). If the Copernican Model was no more accurate than the Ptolemic model, is the Copernican Model a better scientific model? Yes, it requires less mathematics and is simpler to explain. Science is all about efficient predictions! But what is “accuracy”? Does it differ from “precise”? In everyday language, these terms are synonyms. In science, they are not! accuracy the “closeness” of an experimental value to the actual value the “closeness” of all your experimental values precision to each other, related to error As a scientist, of course our goal is to be both accurate and precise. If we can’t do that for some reason, what’s the next best option? Staying accurate, but losing some precision is okay (when the target is known). Getting a very precise wrong (inaccurate) answer isn’t helpful, however if the target isn’t known, precision at least tells you your experiment isn’t completely flawed. The Science of Astronomy ·3−5· 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell Tycho Brahe (1546 – 1601 AD) Danish astronomer and alchemist In 1566, lost part of his nose in a sword duel with his third cousin; wore a prosthetic nose for the rest of his life) In 1572, discovered a “new star” or “nova” With his younger sister, Sophie, compiled extensive high accuracy and high precision (~1 arcminute) observations without the use of a telescope Tycho’s equipment and observations made for a slight improvement in the Copernican Model, but never solved the planetary motion problems that plagued the other models. Image Credit: Vitold Muratov The Science of Astronomy ·3−6· 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell Johannes Kepler (1571 − 1630 AD) German astronomer and mathematician, student/apprentice of Tyco Used Tycho’s data of planetary positions to develop his three laws of motion Kepler’s First Law of Planetary Motion 1. The orbit of each planet about the Sun is an ellipse with the Sun at one focus. At first, Kepler tried to match Tycho's observations with circular orbits, but was out by 8 arcminutes or 0.133°. An arcminute is 1/60th of a degree (a degree is like an hour, so arcminutes are 1/60th of a degree, arcseconds are 1/3600th of a degree). Circle vs. Ellipse Elliptical orbits are non−symmetric. The Science of Astronomy ·3−7· 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell Ellipses have eccentricity, i.e. essentially how different the ellipse is from a perfect circle. (𝑠𝑒𝑚𝑖 − 𝑚𝑖𝑛𝑜𝑟 𝑎𝑥𝑖𝑠)2 𝑒 = √1 − (𝑠𝑒𝑚𝑖 − 𝑚𝑎𝑗𝑜𝑟 𝑎𝑥𝑖𝑠)2 For the Earth−Sun Orbit: 0.99986 𝐴𝑈 𝑒 = √1 − = 0.012 1.0000 𝐴𝑈 More “squished” = more eccentric The Science of Astronomy ·3−8· 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell Consider a comet that goes inside Mercury’s orbit when it’s at perihelion and goes beyond Neptune’s orbit when it’s at aphelion. How would you describe this comet’s orbital eccentricity? (a) negative eccentricity (c) low eccentricity (b) zero eccentricity (d) high eccentricity Kepler’s Second Law of Planetary Motion 2. A planet moves faster in the part of its orbit nearer the Sun and slower when farther from the Sun, sweeping out equal areas in equal times. What does this “sweeping” mean, exactly? Imagine a line that connects the planet to the Sun. That line sweeps out equal areas in equal intervals of time. Which of these three “cones” contains the largest area? none, they are all the same The time t is also the same…so what is different about the orbiting body? Do planets move faster at aphelion or perihelion? (a) aphelion (c) same speed at either (b) perihelion position The Science of Astronomy ·3−9· 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell All those t values are the same, so the highest velocity occurs when the distance covered in that time is maximized. 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝑡𝑖𝑚𝑒 Not surprising, the greatest gravitational effect occurs when the two bodies are closer together. 𝐺𝑚1 𝑚2 𝐹= 𝑑2 m1 and m2 are the masses of the objects, d is the distance. As mass increases (or d decreases) the force of attraction increases. Consider a comet with a highly eccentric orbit. Its perihelion is at about 1 AU and its aphelion is at about 100 AU. Of the following choices, where does it spend the longest amount of time? (a) Less than 10 AU from the Sun (b) Between 45 and 55 AU from the Sun (c) More than 90 AU from the Sun (d) It spends an equal amount of time at all of the above The Science of Astronomy · 3 − 10 · 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell What would be the semi−major axis of that comet? (a) 1 AU (d) 90 AU (b) 10 AU (e) 100 AU (c) 50.5 AU Kepler’s Third Law of Planetary Motion 3. More distant planets orbit the Sun at slower average speeds, obeying the relationship 𝑃2 = 𝑎3. P is the orbital period (how long one orbit takes), and it must be in units of years, a is the semi-major axis of the orbit, units of AU. Think of Earth. What is P for Earth and what is a for Earth? Kepler’s 3rd Law equation is only true in the Solar System, or in another star system where the star has the same mass as the Sun. Kepler didn’t know this at the time, but this simple equation is true for everything in our Solar System, not just planets. And since it doesn’t depend on anything to do with the orbiting object, all objects in the Solar System with a given semi-major axis will take the same amount of time to orbit the Sun. Consider a house-sized space rock (asteroid) in our Solar System on an orbit with semi-major axis equal to 1 AU. How long does it take this asteroid to orbit the Sun? (a) Less than 1 year (c) more than 1 year (b) Exactly 1 year (d) not enough info given The Science of Astronomy · 3 − 11 · 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell The Earth is instantly replaced in its orbit by a speck of dust. Which statement best describes the subsequent orbital motion of that piece of dust? (a) The dust particle will spiral into the Sun (b) The dust particle will be ejected from the Solar System. (c) The dust particle will move to a smaller orbit and orbit the Sun in less than 1 year. (d) The dust particle will move to a larger orbit and orbit the Sun in more than 1 year. (e) The dust particle will continue in the same orbit as the Earth did, orbiting the Sun in 1 year. An asteroid’s orbit has semi-major axis 7.2 AU. Find the asteroid’s orbital period. An asteroid takes 12.85 years to orbit the Sun. Find the semi-major axis of the asteroid’s orbit in AU. The heliocentric model (with Kepler’s Laws) had excellent agreement with observations, but that didn’t change everyone’s minds overnight… It went against the well accepted beliefs of the day: The heavens are perfect and unchanging. The Sun and planets follow perfect circular paths with fixed speeds. The Earth is unmoving at the centre of the Celestial Sphere. The Science of Astronomy · 3 − 12 · 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell Galileo Galilei (1564 − 1642 AD) Italian astronomer and physicist Advocate of the Heliocentric Model of the Solar System Improvements to the telescope lead to observations that gave clear evidence in favour of the heliocentric model Galileo’s Telescopic Evidence for Heliocentrism: 1. There are many more stars than we can see with the naked eye and they are much farther away than previously thought. This is why they don’t appear to change position as the Earth orbits the Sun. 2. The heavens are not perfect—the Moon and the Sun both have imperfections (craters, mountains, sunspots) 3. Galileo observed four moons orbiting Jupiter, thereby showing that not every celestial object in the heavens orbits Earth. [image credit: Jan Sandberg] The Science of Astronomy · 3 − 13 · 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell Galileo also observed a complete set of phases of Venus (similar to phases of the Moon from Earth). This is not possible in the Ptolemaic View of Venus. In the Ptolemaic View, quarter phases would not be present, but they are clearly visible. Which phase of Venus should appear largest to an observer on Earth? (a) Crescent (b) Gibbous (c) Full (d) All phases appear nearly the same size The Science of Astronomy · 3 − 14 · 3.3: The Copernican Revolution ASTR 205 Unit 3 Dr. Bryan Rowsell The heliocentric model (with Kepler’s Laws) slowly took over as the predominant model of the Solar System. The reason why Kepler’s Three Laws of Planetary Motion were true remained unexplained until Isaac Newton (Unit 4). The Copernican Revolution a demonstration of the scientific method in action! 3.4 The Nature of Science You might already be a bit familiar with the scientific method. Choose the answer that shows the correct steps in the correct order. (a) Question, Observe, Experiment, Analyze, Hypothesize, Share Results (b) Experiment, Hypothesize, Analyze, Question, Observe, Share Results (c) Hypothesize, Question, Experiment, Observe, Keep Results Secret (d) Question, Hypothesize, Experiment, Observe, Analyze, Share Results Is science more about having all the answers, or about the process of how to find and test possible answers? (a) More about having all the answers (b) More about the process of how to find and test possible answers The Science of Astronomy · 3 − 15 · 3.4: The Nature of Science ASTR 205 Unit 3 Dr. Bryan Rowsell Hallmarks of Science Let’s go over these one−by−one. In today’s age of “fake news”, the concept of science and the scientific method is even MORE important than ever. 1. Science seeks explanations for observed phenomena that rely solely on natural causes. Science aims to explain observations of natural phenomena without relying on myth, magic, or the supernatural. No invocation of the supernatural is accepted in science. Science progresses through the creation and testing of models of nature that explain observations as simply as possible. “We should not use more things than are necessary.” What it means: When presented with two explanations for the same set of observations, choose the simpler one because it is more likely to be the correct explanation. Occam’s Razor: when there are multiple explanations, choose the simpler one. Thinking back to the Copernican Revolution, what’s an example of Occam’s Razor in action? (a) Choosing Eratosthenes’ calculation of the circumference of the Earth instead of relying on myth or magic. (b) Choosing the Ptolemy’s model of the Solar System instead of Copernicus’ model. (c) Choosing Galileo’s telescopic observations instead of Tycho Brahe’s quadrant observations. The Science of Astronomy · 3 − 16 · 3.4: The Nature of Science ASTR 205 Unit 3 Dr. Bryan Rowsell (d) Choosing a heliocentric model with elliptical orbits instead of a geocentric model with circular orbits and epicycles. 2. Science makes testable and falsifiable predictions about natural phenomena If a prediction is testable, then it can be tested. In other words, can you design an experiment where observations of the natural world would be collected, and these observations would either support or refute the prediction? Examples of testable predictions: Examples of untestable predictions: Consider the following two statements. 1. Biology is more fun than chemistry. 2. More RDP students are enrolled in biology courses than chemistry courses in the Winter 2023 term. Which statements, if any, are testable? If a prediction is falsifiable, then it can be proven false. In other words, no matter how convinced you are that a hypothesis, model, or The Science of Astronomy · 3 − 17 · 3.4: The Nature of Science ASTR 205 Unit 3 Dr. Bryan Rowsell theory is correct, you should always be able to come up with some theoretical evidence that would change your mind. Example of falsifiable prediction: Do you believe vaccines cause autism? (a) Yes (b) No No matter which answer you chose, identify what evidence could come to light that would cause you to rethink your belief. 3. Science is adaptable, tentative, and cumulative. If predictions do not agree with observations, the model must be revised or abandoned. Scientists changing their views is a feature of the scientific methodology, not a bug! Can you think of an example in real life where a widely held belief was later changed after new information came to light? Everyday Language vs. Scientific Vernacular Scientists use some words very differently than the public uses them. This has caused a lot of confusion and misinterpretation of science. For example, think of the word “theory”. What does that word mean to you? When a scientific model both explains a wide variety of observations in just a few general principles, and correctly predicts the results of The Science of Astronomy · 3 − 18 · 3.4: The Nature of Science ASTR 205 Unit 3 Dr. Bryan Rowsell a wide variety of different tests over and over again, then scientists promote its status from scientific model to scientific theory. A scientific theory can never be promoted to “scientific fact” because in science, there is only evidence−not proof−and there is no threshold for “enough” evidence to “prove” something. All scientific models and theories are falsifiable, so even though they can’t be proven, they can be disproven. Bias Scientists are human and all humans have biases. Can you think of some biases in everyday life? The effect of bias can be minimized but never fully eliminated. Stay open−minded (but not so open−minded your brain falls out!). Science Goal: By following the scientific method, we remove as many implicit biases introduced by the human scientists as possible. Experimental procedures and results are openly shared with other scientists, who then scrutinize the work and look for sources of bias. Multiple scientists from different countries, cultures, backgrounds recreate experiments to verify results and eliminate bias. A scientific experiment is biased if there is a systematic tendency to obtain a particular result (due to limitations in technology, methodology, funding, time, etc.). Example: We’ve discovered many more large planets orbiting other stars than small planets orbiting other stars because it’s hard to find The Science of Astronomy · 3 − 19 · 3.4: The Nature of Science ASTR 205 Unit 3 Dr. Bryan Rowsell small planets—(presumably) not because there are actually significantly fewer small planets in the Milky Way Galaxy. Pseudoscience A collection of beliefs or practices that are commonly mistaken to be scientific or that claim to be scientific (science-ploitation), but that do not rely on the scientific method and do not adhere to the hallmarks of science. Which of the following statements describe a pseudoscience? (a) Something that often uses scientific words, but doesn’t follow the hallmarks of science. (b) Something that may want the respectability of science, but doesn’t use the method of science. (c) Something that usually doesn’t really work, or doesn’t work the way claimed. (d) All of the above. (e) None of the above. The Science of Astronomy · 3 − 20 · 3.4: The Nature of Science ASTR 205 Unit 3 Dr. Bryan Rowsell What are some common characteristics of pseudoscience? (a) It explains things people care about that may not have other explanations. (b) It explains after the fact—it’s based on post−diction instead of prediction. (c) If it fails, there is always an excuse—the theory is not revised or abandoned. (d) It uses scientific-sounding jargon incorrectly (e.g., energy flows) (e) All of the above. The Science of Astronomy · 3 − 21 · 3.4: The Nature of Science ASTR 205 Unit 3 Dr. Bryan Rowsell Chapter 3: The Essential Cosmic Perspective End−of−Chapter Questions: 1−36 (skip 33), 38 (ans. 68 AU), 39a (ans. 17.9 AU). Solutions are found on Bb. Extra Resources: Watch the following Crash Course History of Science videos: The Scientific Revolution [13 min]: https://www.youtube.com/watch?v=vzo8vnxSARg The New Astronomy [13 min]: https://www.youtube.com/watch?v=-FYvy3_egHw The Scientific Methods [13 min]: https://www.youtube.com/watch?v=UdQreBq6MOY Watch any or all of the following videos from Spahn's Science Lectures: [26 min] https://www.youtube.com/watch?v=dN-qpLV97ro [23 min] https://www.youtube.com/watch?v=2Pt4mX9lgN4 [41 min] https://www.youtube.com/watch?v=1d8UuFJ25BQ (This video covers a mixture of ASTR 205 Units 3 and 4) Watch Carl Sagan succinctly explain how Eratosthenes accurately measured the Earth's circumference: https://www.youtube.com/watch?v=f-ppBtuc_wQ Read this blog post that has some nice visualizations of the Ptolemaic model: https://blog.richmond.edu/physicsbunn/2012/09/13/ptolemy-and-copernicus/ Watch this video that summarizes the change from a geocentric to heliocentric model of the Solar System [5 min]: https://www.youtube.com/watch?v=khIzr6610cQ Watch this video if you’re struggling to understand Kepler’s Laws [19 min]: https://www.youtube.com/watch?v=kyR6EO_RMKE Experiment using different parameters on this interactive website to gain a better understanding of elliptical orbits and Kepler’s 2nd Law: https://ophysics.com/f6.html Read about the Hallmarks of Science: https://scienceornot.net/hallmarks-of-science/ Read about Cognitive Biases: https://www.mindtools.com/pages/article/avoiding- psychological-bias.htm Watch this Veritasium video about cognitive biases [5 min]: https://www.youtube.com/watch?v=vKA4w2O61Xo Watch this video for an easy-to-understand example of a common implicit bias [4 min]: https://www.youtube.com/watch?v=b9mMLmJskzs Test yourself to determine your own implicit biases: https://implicit.harvard.edu/implicit/selectatest.html Watch Richard Feynman discuss the scientific method [10 min]: https://www.youtube.com/watch?v=0KmimDq4cSU Watch Neil deGrasse Tyson discuss bias and science [2 min]: https://www.youtube.com/watch?v=pYPgi1oUqXA Watch Adam Savage tell the story of how simple ideas lead to scientific discoveries [8 min]: https://www.youtube.com/watch?v=F8UFGu2M2gM Watch this Smart By Design video about why people believe in astrology [6 min]: https://www.youtube.com/watch?v=NBXRzdzFnHk Read about Logical Fallacies:https://www.mindtools.com/pages/article/newTMC_81.htm Interact with the Thou Shalt Not Commit Logical Fallacies website: https://yourlogicalfallacyis.com/ The Science of Astronomy · 3 − 22 · Questions and Resources