Final Exam Notes [COMPLETE] for Astronomical Universe -- 4.0ed this final exam

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Department
Astronomy and Astrophysics
Course
ASTRO 001
Professor
All Professors
Semester
Summer

Description
ASTRO 001.3 NOTES for FINAL EXAM! 1 8-28-12 INTRODUCTION TO THE CLASS A. Astronomy has been around for a very long time. 1. Stonehenge was early astronomy. 2. Ancients concerned themselves with astronomy for spiritual reasons, navigation, farming, etc. B. Stimulating questions in Astronomy 1. What is the closest planet to Earth? How do we know? 2. Are black holes really like cosmic vacuum cleaners? 3. What are stars? What are they made of? 4. Are dark energy and dark matter real? 5. What is the Milky Way? 6. Are there other Milky Ways? Other universes? 7. What is the farthest thing we can see? Is it really the farthest thing? C. Disclaimer about the class 1. This class does not focus on: a. astrology, zodiac signs, horoscopes b. learning constellations c. memorizing facts d. endlessly plugging numbers into equations e. staring at pretty pictures for hours on end 2. This class will make you: a. think! b. use arithmetic, compute ratios, etc. c. understand how scientists draw certain conclusions 8-30-12 I. TO UNDERSTAND THE UNIVERSE: A. Astronomers use the laws of physics to construct testable theories and models. 1. Scientific method: a. based on observation, logic, and skepticism (will be explained in a bit) 2. Hypothesis a. a collection of ideas (or guesses) concocted to explain a phenomenon 3. Models a. sophisticated set of hypotheses, usually mixing tested and untested ideas 4. Theory a. a succinctly stated description of a model, self consistent, compact, and easily testable. 5. Laws of Physics a. theories that accurately describe the workings of physical reality, have stood the test of time and have been shown to have great and general validity. ASTRO 001.3 NOTES for FINAL EXAM! 2 B. “Scientific Method” 1. First, we must observe, study, and research what we want to find the answer to. 2. Next, we formulate a hypothesis. a. Must be testable (able to be tested) i. must be testable because you must be able to TEST it in order to determine if it is accurate, otherwise once can never determine how good or accurate of a hypothesis it is. b. Must be falsifiable (never provable) i. It must be falsifiable because the hypothesis could be right 99% of the time, but it's the 1% chance that it is wrong that makes it truly a hypothesis. 3. After, we must test the hypothesis by experiment. 4. If needed, we can reject the hypothesis if contradicted by data that we receive from the experiment. C. Objectivity and the Role of the Skeptic 1. Mother Nature tells us what naturally occurring science is. 2. Natural scientific phenomenons cannot be created. 3. To uncover scientific truths, we must be as objective as possible. 4. Are scientific results ever affected by: a. fake data that is published? Such as the case with elements 116 & 118 which were originally real elements proven by a lab, but that lab then came out with the truth which was that these elements were lab-created and actually not true elements. b. observational biases? (e.g.: ratemyprofessor.com) c. and most importantly, personal biases? (e.g.: personal opinion) D. Example: Global Warming 1. Hypothesis: Carbon dioxide emissions and human activity are warming the planet. II. CATCHING UP TO MEDIEVAL TIMES A. In medieval universities... 1. Students began with the trivium level of schooling. a. consisted of grammar, logic (also known as dialectic), and rhetoric. 2. The quadrivium was the next level. a. considered preparatory work for philosophy and theology. b. consisted of arithmetic, geometry, music, and astronomy. 3. Thus, astronomy has been an integral part of a well-rounded education for centuries. ASTRO 001.3 NOTES for FINAL EXAM! 3 B. Facts that MUST be memorized! (What the Ancients always knew.) 1. Simple motions as viewed from the ground: a. Stars circle to same location every 23 h, 56 m, 04 s (stars move east to west) b. Sun returns to same approximate location every 24 h. c. Motion of sun and moon is East with respect to stars. d. Mars, Jupiter, and Saturn also move Eastward most of the time, but Westward when opposite the sun. e. Mercury and Venus move Eastward most of the time, but Westward after maximum Eastward elongation (ie: as far East as they are going to go) III. CELESTIAL MOTIONS A. Basic Concepts of Celestial Motions 1. Angles a. We measure the separation of things in the sky using angles, not distances, for obvious reasons. (Distances are very large.) b. The whole sky is marked out in a grid like latitude and longitude, but called Right Ascension and Declination. 2. Angular separation: a. The angle between a line drawn from an observer to an object and a second line drawn from the observer to a different object is the angular separation of those objects. 3. Angular size: a. The angle between a line drawn from an observer to one end of an object and a second line drawn from the observer to the other end of the object is the angular size of the object. B. Stellar (Star) Motions 1. Stars move so slowly with respect to each other that naked-eye measurements cannot detect the motion. 2. They appear to circle the pole star (polaris) in 23 h, 56 m, and 4 s, one sidereal day. 3. This means if we pick a spot on the horizon in the East, say the tip of a mountain peak, a star rising at the point will rise there again 23 h, 56 m, 4 s later. 4. The stars rise and set at an angle with the horizon that depends on the latitude of the observer. C. Solar and Lunar Motions 1. The Sun and Moon generally appear to circle the Earth along with the stars, but in a time longer than the sidereal day. a. 4 minutes longer for the Sun, 50 minutes for the Moon. ASTRO 001.3 NOTES for FINAL EXAM! 4 2. This implies that their motion with respect to the stars is Eastward. 3. This also means that the sun does not return to the same position after one sidereal day. 4. The sun's motion and the planets' motion follows a path among the stars called the ecliptic. 5. An entire circuit around the ecliptic takes 1 year for the sun. 6. The moon follows a different path near the ecliptic. a. This path takes about 27 days to make an entire trip, with respect to the stars. 7. Solar eclipses occur when the sun and moon align and the moon is on the ecliptic. 8. Lunar eclipses occur when the sun and moon are opposite and the moon is near the ecliptic. 9-4-12 I. THE SOLAR SYSTEM’S COMPONENTS A. Gas Retention Plot 1. Hydrogen can escape Earth’s atmosphere much more easily than carbon dioxide. 2. For anything to escape Earth’s atmosphere, the object must be traveling 11 km/s.. 3. For anything to hypothetically escape the Sun’s atmosphere, it must be traveling 617.7 km/s. B. Trans-Neptunian Objects 1. Surrounding the entire galaxy is a cloud called the Oort Cloud. 2. The Oort Cloud is quite possibly where comets come from. a. This fact has not been proven, but is very likely. 3. Comets a. They are simply rocky balls filled with ice and gases b. Once they get closer to the sun, the “tail” on a comet gets brighter and brighter because they begin to “melt”. c. Comets leave behind small pieces of material called meteors. 4. The average size of the shooting star is about the size of a grain of sand. C. The Giant Impact Hypothesis 1. Also known as the “Big Splash”. 2. States the Moon formed from debris leftover from collision between Earth and a Mars-sized object. a. This happened approximately 4.5 billion years ago. 3. If this Mars-sized object hit the Earth, then that’s how the Earth got it’s severe tilt. 4. Before the impact, the Earth was straight up and down. ASTRO 001.3 NOTES for FINAL EXAM! 5 II. METHODS OF DETECTING EXTRASOLAR PLANETS A. The Transit Method 1. Transit: when one body passes in front of another. 2. When the planet transits, it blocks out part of the star’s visible light. 3. Which planets are generally the easiest to find with the transit method? a. Larger planets close to the their host stars. 4. The more light blocked by the planet, the easier it is to find. B. The Doppler Method 1. Also known as the radial velocity method. 2. Which planets are generally the easiest to find using the radial velocity method? a. High mass planets close to their host stars. 3. The planets easiest to find are the ones with the most force on the star. b. The more force = the more wobble the planet has. C. “PSR B1257+12” 1. The first confirmed exoplanet. a. Discovered in 1992. 2. Alex Wolszczan discovered it. a. He was a PSU astronomer. 3. He is Polish, and was awarded his face on a stamp in Poland. 9-6-12 I. MATH CONCEPTS IN ASTRONOMY A. Angular Speed 1. Definition: the change in angular position with respect to time. 2. If you make an assumption about the motion of the planets, namely that they all move with the same speed, then ranking them by angular speed also puts them in order of distance. 3. The assumption of the planets having the same velocities is wrong, but not so wrong that it gives the wrong order. This allowed the ancient Greeks to correctly infer the relative distances to the planets. B. Small Angle Approximation 1. If the angle is small, and you want to know the tangent of the angle, it’s just the measurement of the angle. 2. There is no “small” angle limit, because in astronomy, nothing is really close to us, relatively. The angles are quite small. a. In this class, we will only be dealing with angles that are a couple of degrees. 3. We will not be using trigonometry: e.g.: sin, cos, tan. 4. ANGLE: SIZE/DISTANCE (small angle formula) 5. Units: The units in the formula stated in number 4 are meters/meters or ASTRO 001.3 NOTES for FINAL EXAM! 6 miles/miles or feet/feet etc. The units will cancel out and leave us with simply radians. 6. Small angle formula will only ever give us radians. 7. 2 pi radians equals 360 degrees. 8. To convert from radians to degrees, multiply by 360 degrees over 2 pi radians. The radians cancel out and leave you with degrees. II. HOW DID THE ANCIENTS KNOW EARTH WAS SPHERICAL? A. Proven Theories 1. If you were to see a ship on the edge of the horizon, the top of the mast appears first, then the middle, then the rest of the ship. This implies a curved surface. 2. During lunar eclipses, one can see that the shadow of the Earth is curved. B. Eratosthenes (276 BC-195 BC) 1. Mathematician, poet, athlete, geographer, astronomer. 2. Nicknamed “Beta” because he was the second best at everything. 3. A few of his accomplishments: a. Created leap day b. Developed system of latitude/longitude c. Created map of the world d. Proposed system for finding prime numbers e. Discovered that the Earth is not flat 9-11-12 I. “FIXED EARTH” MODEL A. Aristotle (384-322 BC) 1. He was an influential Greek philosopher. 2. He also learned from Plato. 3. Taught Alexander the Great. B. What is the Fixed Earth model? 1. The model describes that the Earth is stationary and the celestial sphere rotates around it. C. Evidence for the “Fixed Earth” Model 1. We throw something up, it comes back down in the same place. a. Aristotle taught that motion must be caused for earthly objects, and with no cause the motion of the object would stop, while the natural motion of the heavenly sphere would continue. 2. The stars do not show visible parallax. b. e.g.: changing apparent position due to our changing point of view. D. Other Aristotelian Premises ASTRO 001.3 NOTES for FINAL EXAM! 7 1. Uniform circular motion a. Otherwise a void is opened, which is impossible. 2. Perfectly spherical bodies 3. So if Earth is “fixed” and motions are circular, what are we left with? E. The models of Hipparchus (150 BC) 1. Immobile Earth near center (but not exactly at center) 2. Planets move on “deferents” 3. To explain retrograde motion, there were “epicycles” 4. The epicycles of Venus and Mercury were attached to a line connecting Earth and Sun. 5. To explain the varying speed of the Sun, the Earth was offset from the center of the Sun’s orbit. 6. All of this was still not adequate to explain the naked-eye positions of the planets. F. Ptolemy’s Almagest 1. Introduced the Equant, a point from which the motion would appear uniform even though it was not uniform at the center or from the Earth. 2. This violated the precept of uniform circular motion, quietly. II. GEOCENTRIC MODEL A. Predictions of the Geocentric Model 1. Mars, Jupiter, and Saturn should be brighter during retrograde, since they are closer at that time. 2. Mercury and Venus, if illuminated by the sun, should always appear in crescent phase. 3. Stars should show no parallax. B. Ancient Mechanics 1. Aristotle’s Law (in modern notation) a. “That which moves is moved by another” 2. Objects fall because of their “gravitas” or “weight” b. Rate of descent (ascent) depends upon composition. c. “air” + “fire” + “earth” + water” d. Each has a natural place to which it moves. III. CHURCH CONDEMNATIONS OF 1210-1277 A. These banned propositions helped scholars to break from Aristotelian science’s restrictions. 1. That the First Cause could not make several worlds. a. The condemnation of this proposition opened the way to consider the planets to be worlds like ours. 2. That God could not move the heavens with rectilinear motion. ASTRO 001.3 NOTES for FINAL EXAM! 8 b. The condemnation of this notion allowed Medieval Scholastics to consider a void or vacuum in which planets move. 3. That celestial bodies are moved by an internal principle, which is soul; and that they are moved by a soul and by an appetitive power just as an animal; for just as an animal is moved by desire, so is the sky. 4. That it is not true that something could be made from nothing. 9-13-12 I. THE BIRTH OF HELIOCENTRIC MODELS A. Mars, Jupiter, and Saturn 1. Those three planets should be brighter during retrograde. 2. Mercury and Venus should always appear crescent-shaped from Earth. They will never appear in the full phase. B. The Heliocentric Model 1. So far, we have been describing the motions as seen from the surface of Earth, and trying to fit them into a model that has the Earth at the center. 2. In its ability to predict planetary positions, Ptolemy’s model was the best of the geocentric or Earth centered models. It was so good that no refinements were needed until the precise observations of Tycho Brahe. Which raises the interesting question of why Copernicus would try to “improve” it using a model with the sun at the center. 3. Perhaps Copernicus was inspired by Aristarchus (280 BC) who proposed a sun-centered model with planets orbiting in a single plane. Perhaps he was motivated by aesthetics. Whatever his reasons, Copernicus’s Heliocentric model was published in 1543, the year of his death. It did not gain instant acceptance, but generated lively debate. 4. “But since for one and the same movement varying hypotheses are proposed from time to time, as eccentricity or epicycle for the movement of the sun, the astronomer much prefers to take the one which is easiest to grasp.” - Nicolaus Copernicus C. Copernicus (De Revolutionibus orbium coelestium) 1. Objected to Equant (violated precept of uniform circular motion) 2. Constructed Heliocentric model with the following properties: a. Sun at center, heavenly spheres go around it. b. Stars are very far away relative to sun. c. Daily motions are due to rotation of the earth. d. Sun’s motion is apparent, due only to Earth’s motion e. Retrograde is explained by Earth passing the other planets in their orbits (or them passing us in the case of the inner planets Venus and Mercury) D. Difficulties with the Copernican model 1. The moon still went around the Earth, requiring two centers of motion. 2. It didn’t work as well as Ptolemy’s model, because it used perfect circles. ASTRO 001.3 NOTES for FINAL EXAM! 9 3. Whether it was “pleasing to the mind” was a matter of opinion. It still had multiple circles to get positions right. E. Triumphs of the Copernican model 1. Naturally explained the timing of retrograde motions 2. Allowed the computation of sidereal periods from synodic a. Synodic period: The time required for the angle between the sun and a planet in the sky to return to some fixed value (usually 0 or 180). b. Sidereal period: the time required for the planet’s position with respect to the stars to return to a fixed value, as viewed from the sun. 3. This showed the presence of a harmony not known before, the planets closest to the sun have shortest sidereal periods. This understanding laid the groundwork for Kepler’s third law. F. Tycho Brahe 1. Nova of 1572 showed heavens were not immutable (Siderius Nuncius introduction discusses comet of 1577 as well. 2. Built an observatory on Hven, which he used to measure planetary positions to better accuracy than ever before. (1 arcminute=60 arcseconds) 3. Arcminutes and arcseconds were a new way of describing angle measurements. 4. Parallaxes were not measurable with his equipment, so he rejected Copernicus and made a hybrid model. 5. He measured positions very accurately. G. Johannes Kepler 1. Around 1590, while lecturing, Kepler had an insight relating planetary orbits to geometric solids. This is an accident, but a fortunate one, for it caused Kepler to pursue Heliocentric models. 2. Mysterium Cosmographicum (1594) told of this insight and introduced the concept of a “force” emitted by the sun which propels the planets. 3. He did not get along with Brahe, but he did eventually get permission to use the data to “find the thickness of the shells” 4. Kepler’s Laws a. To place this in perspective, Kepler approached the observations of Brahe with a particular model in mind: That of Copernicus. b. First Law: (1609) The orbit of each planet is an ellipse, with the sun at one focus. c. Second Law: (1609) A line drawn from a planet to the sun sweeps out equal areas in equal times. d. Third Law: (1618) The square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun. ASTRO 001.3 NOTES for FINAL EXAM! 10 9-18-12 NOTES ARE IN A PDF 9-27-12 I. LIGHT A. Doppler Shift 1. Wavelength x frequency = c (speed of light) 2. If you drive a certain speed towards a red light, it will appear green. 3. However, one would have to drive approx. 18k miles per hour to see green.
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