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- Title: Lecture01-08-29-2006-ASTR111-Weigel-Revised
- Type: Notes
- School: George Mason
- Course: ASTR 111
- Term: Fall
for Outline 29 August (Tuesday) Course Outline and Syllabus ( ~15 minutes) Lecture Outline Course Outline and Syllabus ( ~15 minutes) Introduction to ASTR 111 (~30 minutes) Introduction to ASTR 111 (~30 minutes) Review of Math that is used in Astronomy (~30 minutes) Review of Math that is used in Astronomy (~30 minutes) Lecture Outline Course Outline and Syllabus ( ~15 minutes) Introduction to ASTR 111 What does an astronomer do? The Pluto Problem Estimation of angles Astronomical distances Introduction to ASTR 111 (~30 minutes) Review of Math that is used in Astronomy (~30 minutes) By observing galaxies, astronomers learn about the origin and fate of the universe By exploring the planets, astronomers uncover clues about the formation of the solar system The star we call the Sun and all the celestial bodies that orbit the Sun including Earth the other eight planets all their various moons smaller bodies such as asteroids and comets (and dwarf planets such as Pluto) 1 What does an astronomer see in this picture? To understand the universe, astronomers use the laws of physics to construct testable theories and models Scientific Method based on observation, logic, and skepticism Hypothesis a collection of ideas that seems to explain a phenomenon Model hypotheses that have withstood observational or experimental tests Theory a body of related hypotheses can be pieced together into a self consistent description of nature Laws of Physics theories that accurately describe the workings of physical reality, have stood the test of time and been shown to have great and general validity Introduction to ASTR 111 What does an astronomer do? The Pluto Problem Estimation of angles Astronomical distances Pluto: Problem Planet We almost had 12 planets a planet is any body that orbits a star, is neither a star nor a satellite of a planet, and has gravity strong enough to pull it into a rounded shape and a planet must be heavy enough to clear other objects from its path http://www.space.com/scienceastronomy/060819_new_proposal.html This serves as a reminder that we are still learning about places nearby in the universe but 2 My Very Educated Mother Just Served Us Nine Pizzas My Very Educated Mother Just Said Uh-oh No Pluto My Very Educated Mother Just Served Us Nine Pizzas My Very Educated Mother Just Said Uh-oh No Pluto My Very Educated Mother Just Served Us Ninjas? Pluto: Problem Planet Introduction to ASTR 111 What does an astronomer do? The Pluto Problem Estimation of angles Astronomical distances Astronomers use angles to denote the positions and apparent sizes of objects in the sky = Observer s Zenith The basic unit of angular measure is the degree ( ). Astronomers use angular measure to describe the apparent size of a celestial object what fraction of the sky that object seems to cover The angular diameter (or angular size) of the Moon is or the Moon subtends an angle of . If you draw lines from your eye to each of two stars, the angle between these lines is the angular distance between these two stars 3 Angular Measurements Subdivide one degree into 60 arcminutes minutes of arc abbreviated as 60 arcmin or 60 Subdivide one arcminute into 60 arcseconds seconds of arc abbreviated as 60 arcsec or 60 The adult human hand held at arm s length provides a means of estimating angles 1 = 60 arcmin = 60 1 = 60 arcsec = 60 A B Group Questions Form groups of 2 or 3 Write your answers on a sheet of paper to be turned in at the end of class Write your row number on the sheet (not name or G#) 1. What is the angular distance between points A and B on this slide? In degrees? In arcseconds? 2. Student X is in the middle of the room. Student Y is in the same row as X but next to the wall. Should X s angular measure from Question 1 be greater, less than, or equal to Y? 3. Next week you come sit in the same chair but weigh 30 pounds less. Will your (angular) measurements change? 4. What equation was used to determine the finger-length-to-degree relationship? Answers 1. What is the angular distance between points A and B on this slide? Depends on where you are sitting. If you hold out your hand and both dots are (barely) obscured, the angular distance is 10 degrees (=600 arcminutes=36,000 arcseconds). Answers 1. 2. Student X is in the middle of the room. Student Y is in the same row as X but next to the wall. Should X s angular measure from Question 1 be greater, less than, or equal to Y? X should be less. To see this, think about what would happen if you moved the walls out very far. 3. 4. 4 1. 2. 3. Next week you come sit in the same chair but weigh 30 pounds less. Will your (angular) measurements change? Yes. Increase. The length of your arm would not change, but the width of your hand would decrease. Instead of needing one hand width to obscure the dots you would need one plus, say, a finger to cover them. 4. Answers Answers 1. 2. 3. 4. What equation was used to determine the finger-length-to-degree relationship? The small angle formula (Chapter 1, page 8). d is the length of your arm and D is the length between points on your hand (for example, the width of your index finger or width of your hand). Introduction to ASTR 111 What does an astronomer do? The Pluto Problem Estimation angles of Astronomical distances Astronomical distances are often measured in astronomical units, parsecs, or light-years Astronomical Unit (AU) One AU is the average distance between Earth and the Sun 1.496 X 108 km or 92.96 million miles Light Year (ly) One ly is the distance light can travel in one year at a speed of about 3 x 105 km/s or 186,000 miles/s Parsec (pc) the distance at which 1 AU subtends an angle of 1 arcsec or the distance from which Earth would appear to be one arcsecond from the Sun Group Questions 1. How many meters are in a ly? (The speed of light is 3x10^8 m/s) 2. How long does it take light to reach Earth from the sun? (1 AU = 1.5x10^8 km) Note: 10^8 means the same thing as 1E8 on your calculator or 108. The ^ is used in text editors and email clients where you can t create subscripts. 5 Group Questions 1. How many meters are in a ly? (The speed of light is 3x10^8 m/s). 1 ly = 1 light-year, which is the distance that light travels in one year. Using the formula distance = rate x time, with rate = 3x10^8 m/s and time = the number of seconds in a year = 365 days x (24 hr/day) x (60 min/hr) x (60 sec/min), Group Questions 1. 2. How long does it take light to reach Earth from the sun? (1 AU = 1.5x10^8 km) About 8 minutes. gives distance = 1.5E15 = 1.5x1015 meters Lecture Outline Course Outline and Syllabus ( ~15 minutes) Review of Math that is used in Astronomy Powers of 10 notation (1E8 =10^8 =108) Powers of 10 words (from nano to peta) How to "derive" rules for manipulating numbers in scientific notation How to make an educated guess about a formula given only units Introduction to ASTR 111 (~30 minutes) Review of Math that is used in Astronomy (~30 minutes) Powers-of-ten notation is a useful shorthand system for writing numbers which was coined by Milton Sirotta, nephew of American mathematician Edward Kasner, and was popularized in the book, Mathematics and the Imagination by Kasner and James Newman. It refers to the number represented by the numeral 1 followed by 100 zeros. Google's use of the term reflects the company's mission to organize the immense, seemingly infinite amount of information available on the web. [http://www.google.com/corporate/history.html] Google is a play on the word googol, 6 Review of Math that is used in Astronomy Powers of 10 notation Powers of 10 prefixes (from nano to peta) How to "derive" rules for manipulating numbers in scientific notation How to make an educated guess about a formula given only units Common prefixes you must know Factor (tera) (billion) (million) (thousand) 1012 109 106 103 Name TeraGigaMegakilocentimillimicronanoSymbol T G M k c m n (hundredth) 10-2 (thousandth) 10-3 (millionth) (billionth) 10-6 10-9 Review of Math that is used in Astronomy Powers of 10 notation Powers of 10 words (from nano to peta) How to "derive" rules for manipulating numbers in scientific notation How to make an educated guess about a formula given only units How to "derive" rules for manipulating numbers in scientific notation You should know that when you multiply numbers in powers of ten notation you need to do something with the exponents. So make up problems you know how to answer: 102 x 101 = 100x10 = 1000 = 103 = 102+1 102 x 10-1 = 100x0.1 = 10 = 102+(-1) Looks like adding the exponents should work. You should always remember that if you forget something, you may still know enough to reason things out. Review of Math that is used in Astronomy Powers of 10 notation Powers of 10 words (from nano to peta) How to "derive" rules for manipulating numbers in scientific notation How to make an educated guess about a formula given only units How to make an educated guess about a formula given only units Reason it out: If you are asked the circumference of a circle given a radius in meters a good guess is the circumference will have units of meters and will be proportional to the radius. Draw a circle; if it looks like it would take more string to cover the radius line than the circumference line, you should make a visual guess how much more string would be required and eliminate any multiple choice answers accordingly. (Answer: requires 2*pi times more string since C = 2*pi*radius.) Think about how you would get an approximation to the volume of a sphere given its radius. Think of volume formulas that you know and build on them. 7 You should already know: The formulas for the volume of a sphere, the surface area of a sphere, and the circumference of a circle (see Appendix A-8) Powers of 10 notation (practice: Chapter 1, problems 10-12, 22-23) Powers of 10 words including nano, milli, micro, kilo, mega, giga, tera Unit conversion (Chapter 1, page 13-14) The planets Questions Why are there many units for distance in astronomy? What are three units of distance in astronomy? How to convert from one unit to another, Chapter 1, questions 10-18. Why Pluto is not considered a planet How to estimate angular distances (Chapter 1, page 6; question 9). Definition of an arcminute and arcsecond (Chapter 1, question 7-8). The meaning of angular distance and subtends . The difference between angular distance and actual distance. What happens to angular measure when things change (as covered in the group question, for example). Quiz yourself using questions 10-24 of the textbook Chapter 1 Quiz at http://bcs.whfreeman.com/universe7e. 8
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