The Science of Astronomy - Copernicus, Tycho, and Kepler Reminder to take out your clicker and turn it on!
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Today s Topics Ancient Astronomy Greek Astronomy Models & Theories Ptolemaic (Earth-centered) model of solar system Copernicus, Tycho, & Kepler Problems with Ptolemaic system Copernican (Sun-centered) solar system Tycho & Kepler Kepler s Laws of Orbits
Ancient Astronomy Astronomy is the oldest science, stretching thousands of years into prehistory All humans are scientific thinkers Choosing apples in the store Astronomy was important to ancient people Determining time of day Predicting seasons & rainfall patterns Important for development of agriculture At right are Stonehenge (constructed between 3100-1550 BCE) and Templo Mayor (Aztec temple, built between 1325-1519) both of which can be used to mark the equinoxes
Greek Astronomy Greeks were the first to create models or theories of nature Models (or theories) are conceptual representations which can explain and predict observable phenomena Theories can never be proven - only disproven A successful theory incorporates many observations and can predict testable observations correctly Examples of successful theories Plate tectonics Special and General Relativity Biological Evolution by Natural Selection Genetics and Heredity (DNA) Sun-centered Solar System (Kepler) Earth-centered model of the Solar System (c. 400 BCE)
Ptolemy (c. 100-170 CE) Ptolemy was a Greek astronomer who created an Earth-centered model The model correctly predicted the positions of the Sun and planets to the accuracy of the time (a few degrees - the width of your hand at arms length) The theory explained retrograde motion (the apparent backtracking of planets) using epicycles (circles on circles) - Interactive Figure 3.15 This theory was far and away the best of its day and lasted 1500 years (until better observations came along)
Copernicus, Tycho, & Kepler By the time of Copernicus (1473-1543), the predictions of the Ptolemaic model were noticeably inaccurate Copernicus argued for a Sun-centered system, based on a more natural explanation of retrograde motion (when you pass a car on the inside of a track, it seems to be going backwards) However, he kept the idea of circular orbits (which is incorrect), so his model also required epicycles and was no more simple or accurate than Ptolemy s Many supporters preferred the aesthetic advantages of the Copernican model
Tycho Brahe Born in 1546 to Danish noble family Flamboyant and arrogant When 20 yrs old, had duel over who was the best mathematician and lost part of his nose, which he replaced with a gold nose! Over 35 years he made astronomical observations using instruments of his own design He measured the positions of objects with unprecedented accuracy (less than 1/60 th of a degree; the width of a fingernail at arm s length)
Johannes Kepler Kepler was born in 1571 in southwest Germany Had a religious training leading him to a mystical view of the Universe In 1595 he was a high school math teacher in Austria and had a revelation there were 6 known planets and five perfect Platonic solids Maybe he could explain the orbits of the planets! He entitled his theory The Sacred Mystery of the Cosmos
Tycho and Kepler together Problem his beautiful theory didn t fit the observations! However, the observations (before Tycho) weren t that good, so he doubted the observations In 1600, Kepler joined Tycho in Prague (Tycho had left Denmark due to quarrels with the King) Tycho died in 1601 and bequeathed his data to Kepler
Triumph of Observation over Theory 8 years and 900 pages of calculations later, Kepler had solved the problem If you are wearied by this tedious procedure, take pity on me Kepler tried seventy circular orbits to try to explain the motion of Mars! Kepler s genius is that he gave up his cherished theory for the correct description of Nature
Kepler s Laws 1st Law - The Planets move in elliptical orbits with the Sun at one focus 2nd Law - Orbits sweep out equal areas in equal times 3rd Law - More distant planets orbit at slower average speeds, obeying a simple mathematical relationship p 2 a 3 where p is the period of an orbit, and a is the average distance of the planet from the Sun
Ellipses An ellipse is a special type of oval that can be constructed using a pencil, a string, and two tacks (Interactive Figure 3.18a) The eccentricity is a measure of how squashed the ellipse is A circle has an eccentricity of zero, and a very flat ellipse has an eccentricity that approaches one The size of an ellipse is measured by its semi-major axis (Interactive Figure - Eccentricity and semi-major axis of an ellipse)
Kepler s 2nd Law Equal areas in equal times In a given time, a line connecting the Sun to the planet will sweep out an area that is the same in all parts of the orbit (Int. Fig. 3.20) Thus, the planet moves faster when it is closer to the Sun (Int. Fig. Kepler II)
Kepler s 2nd Law B C A D E
Lecture Tutorials 1. Get right to work! You typically have 10-15 minutes to complete these activities. That is plenty of time, if you don t mess around. 2. The questions go from easier to harder. Don t spend a long time agonizing over the early questions; they are generally pretty straightforward. If there is a very simple answer that makes sense, that is probably correct. 3. Most of the questions on the exams are like those in the Lecture Tutorials, so you are writing your own textbook! If you don t write complete clear explanations of your answers now, you are going to be mad at the author of your textbook (yourself!) when you go to study for the exam! :) 4. If you feel pressured for time, at least write enough so that you can go back later to write a more detailed explanation (aka, leaving bread crumbs) don t write nothing! 5. It is OK to change groups around to find people you work well with
Lecture Tutorial: Kepler s 2nd Law pp. 21-24 Work with one or more partners - not alone! Get right to work - you have 15 minutes Read the instructions and questions carefully. Discuss the concepts and your answers with one another. Take time to understand it now!!!! Come to a consensus answer you all agree on. Write clear explanations for your answers. If you get stuck or are not sure of your answer, ask another group. If you get really stuck or don t understand what the Lecture Tutorial is asking, ask me for help.
Kepler s 2nd Law Quiz I The planet shown in the drawing obeys Kepler s Second Law. At which lettered position is the planet speeding up? B C A D E
Kepler s 2nd Law Quiz II The planet shown in the drawing obeys Kepler s Second Law. Each lettered position represents a particular day during the year. During which day (at which lettered position) will the planet move the shortest distance? B C A D E
Kepler s 2nd Law Quiz III Which of the three planet orbits shown below (a, b or c) would you say most closely matches the shape of Earth s orbit around the Sun? a b c
Kepler s 3rd Law Kepler s 3rd Law concerns the relationship between the average distance of a planet from the Sun and its orbital period The closer a planet is to the Sun, the shorter its period This is both because the distance travelled each period is shorter and because the closer planets move faster (Interactive Figure 7.1) Kepler s 3rd Law can be expressed mathematically as Period 2 Distance 3 Note that the period (and speed) do not depend on the planet s mass
Kepler s 3nd Law Period 2 Distance 3
Planetary Data (including Eris) Name Orbital Elements Orbital Period p 2 /a 3 Semimajor Axis Eccentricity (years) (yr 2 /AU 3 ) (AU) Mercury 0.3870989 0.206 0.2408467 0.9996 Venus 0.72333199 0.007 0.61519726 1.0002 Earth 1.0000001 0.017 1.0000174 1.0000 Mars 1.5236623 0.093 1.8808476 1.0000 Jupiter 5.2033630 0.048 11.862615 0.9988 Saturn 9.5370703 0.054 29.447498 0.9996 Uranus 19.191264 0.047 84.016846 0.9987 Neptune 30.068963 0.0086 164.79132 0.9989 Pluto 39.481687 0.249 247.92065 0.9987 Eris 67.5 0.437 560 1.0197 Note that if a is measured in astronomical units (AU), and p is measured in years, then Kepler s 3rd Law can be written p 2 = a 3
Lecture Tutorial: Kepler s 3rd Law pp. 25-28 Work with one or more partners - not alone! Get right to work - you have 15 minutes Read the instructions and questions carefully. Discuss the concepts and your answers with one another. Take time to understand it now!!!! Come to a consensus answer you all agree on. Write clear explanations for your answers. If you get stuck or are not sure of your answer, ask another group. If you get really stuck or don t understand what the Lecture Tutorial is asking, ask me for help.
Homework For homework Complete the Lecture Tutorials Kepler s 2nd Law and Kepler s 3rd Law (if necessary) Complete the ranking tasks, Kepler Orbital Motion #1, 2, 5 (download from class website)
Kepler s 3rd Law Quiz I If a small chunk of rock and the large International Space Station are orbiting Earth at the same altitude above Earth s surface, which object takes longer to orbit once around Earth? a) the large space station b) the small chunk of rock c) they would take the same amount of time
Kepler s 3rd Law Quiz II Consider a planet orbiting the Sun. If the orbital distance of the planet doubled, then the planet would take a) More than twice as long to orbit the Sun b) Exactly twice as long to orbit the Sun c) The same amount of time to orbit the Sun d) Exactly half as long to orbit the Sun e) Less than half as long to orbit the Sun