AT 9th Ed. Ch. 2 Homework Assigned: Disc 2,4,6-15 M-C 2-6,8-10 (Other answers are also shown in brackets.) [1. What contributions were made to astronomy by Chinese and Islamic astronomers during the Dark Ages in Europe? The Chinese contributed a calendar and records of celestial events like comets and novae which are still used today. The Islamic culture built on the Almagest by Ptolemy during the dark ages. They gave most stars the names we use today. They established trigonometric and algebraic methods (to, e.g., find the direction to Mecca from any place on Earth) important in astronomy.] 2. Briefly describe the geocentric model of the universe and explain why it was accepted for so long. The geocentric model has the Earth at rest at the center with the Sun and Moon orbitting it. The inferior planets moved on epicycles which were centered on a bar between the Earth and the Sun. The superior planets were also modelled as moving on epicycles which moved on deferents, but the deferents were beyond the Sun. The stars were on the most distant "sphere". It was accepted well into the European rennaissance because it was adopted by the Catholic Church who saw it as consistent with the Bible. [3. The benefit of our current knowledge lets us see flaws in the Ptolemaic model of the universe. What is its basic flaw? The basic flaw of the Ptolemaic model is that the Earth is fixed at the center. It is also complex, but that is not so much a flaw as an undesireable quality in a theory.] 4. What was the great contribution of Copernicus to our knowledge of the solar system? How was his model still flawed? He did not contribute much knowledge in the sense of new discoveries (like Galileo could with the telescope), but he put together a heliocentric (sun-centered) model of the solar system that was much more comprehensive than our records of Aristarchus' model. He explained how the Earth rotated to explain daily motions and the Earth orbited the Sun to explain annual motions of the Sun. The planets no longer had to move in loops, but only appear to because of the Earth's motion. It was still flawed in that it insisted on circular motions. [5. What is a scientific theory? Can a theory ever be proved to be true? A theory, in its weakest definition, is just a hypothesis. For its stronger definition, it is a set of related ideas which describe a large collection of observations. A theory cannot be proved to be true, only disproved.] 6. What discoveries of Galileo helped confirm the views of Copernicus and how did they do so? Since a theory cannot be proved, only disproved, Galileo's observations confirmed the Copernican view by discrediting the Ptolemaic model. A gibbous phase of Venus was not allowed in the Ptolemaic model (which always had Venus between Earth and then Sun) but was allowed by the Copernican model. Thus, the discovery of a gibbous Venus disproved the Ptolemaic model while leaving the Copernican unscathed. Galileo also made several discoveries which contradicted the philosophical underpinnings of the Ptolemaic model, which originated with Plato, Aristotle and the like. These include: the moons orbitting Jupiter (Earth was supposed to be the center of all motions), and sunspots on the Sun (the Sun was supposed to be perfect and unblemished). In addition, experiments studying falling and rolling bodies on Earth disproved Aristotle's notions that heavier objects fall faster. [ Old#6. What is the Copernican Principle? The Copernican Principle is, most generally, that we are not special. Originally, this meant that the Earth is not at the center of the solar system. Since then it has been extended to include our Galaxy, our local group of galaxies, our local supercluster, and the universe. It is also cited when considering life in the universe - we may not be the only place with life or even intelligent life. ] 7. How did Tycho Brahe contribute to the development of Kepler's Laws? Tycho made meticulous observations of the positions of planets over many years. Kepler then analyzed this data and determined the true orbits of the planets around the Sun. 8. Briefly describe Kepler's three laws of planetary motion. First Law: the orbits of planets are in the shape of an ellipse with the Sun at one focus. Second Law: a line connecting the Sun and a planet sweeps out equal areas in equal time intervals. Third Law: the square of the orbital period is proportional to the cube of the semi-major axis. 9. If radio waves cannot be reflected from the Sun, how can radar be used to find the distance from Earth to the Sun? When Venus is near inferior conjunction, it is possible to bounce radar waves off of it and measure the time for radar to make the trip to Venus and back to Earth. The relative size (0.7 AU) and shape of Venus's orbit were known, so the distance to Venus during inferior conjunction (about 28 million miles) could be used to calculate the distance to the Sun (the AU). Specifically, if the distance from Earth to Venus is 28 million miles and this is 3/10 of 1 AU, then you can solve 1 AU * 0.3 = 28,000,000 to find 1 AU = 93,000,000. 10. What does it mean that Kepler's laws are empirical? Kepler's laws are empirical because they were based on analysis of observational data rather then deriving from some theoretical premise. They are descriptive laws which don't explain why the planets move as they do. 11. What are Newton's laws of motion and gravity? 1st law: every body continues in a state of rest or in uniform motion in a straight line unless it experiences some net force. 2nd law: when a force F acts on a body of mass m it causes the body to accelerate at a rate a=F/m 3rd law: for every force there is an equal but opposite force. 12. How do Newton's laws account for Kepler's laws? It is beyond the scope of this class to prove, but the Law of Universal Gravitation naturally leads to orbital paths that are conic sections like the ellipse. Universal Gravitation, F=G(Mm/r^2), says that the force of gravity varies inversely as the distance between the two bodies squared and points along a line between the two bodies. Newton used these facts to show that the planets should have elliptical orbits around the Sun, which was Kepler's 1st law. He actually found that Kepler was wrong in saying that the focus of the ellipse was centered on the Sun and that it was actually centered on the center of mass of the solar system. 13. Why do we say that a baseball falls toward Earth, and not Earth toward the baseball? The Earth moves in response to the baseball but its motion is not noticeable because it is so slight. From Newton's 3rd law, both the baseball and the Earth feel the same attractive force. However, Newton's 2nd law states that an object's acceleration is inversely proportional to its own mass (a=F/m). Thus, the smaller mass (baseball) will accelerate/move much more than the larger mass (Earth). 14. In what sense is the Moon falling toward Earth? How can we use this fact to measure Earth's mass? When the force of gravity pulls an object toward the Earth, the object is said to be "falling". The Moon is being pulled continuously toward the Earth by gravity, sometimes it moves toward Earth and sometimes it moves away, but continuously falling. Whether it is moving toward or away from the Earth, it is ALWAYS ACCELERATING towards the Earth since it is moving in a curved orbit. From the acceleration we can calculate the force of gravity and thus the mass of the Earth-moon system. F_g = G(M*m/r^2). 15. What is the meaning of the term escape speed? If body 1 orbits body 2 at the escape speed, its orbit will be open instead of closed. That is, body 1 will leave the vicinity of body 2 and never return (unless influenced by some 3rd body). [ Important OLD EDITION QUESTION: 15. What were the modifications made by Newton to Kepler's laws? The two modification by Newton to Kepler's laws: 1) For the first law, one focus of an elliptical orbit was located at the center-of-mass of the solar system rather than on the Sun itself. 2) For the 3rd law, the mass of the system should be taken into account to make it more widely applicable ... P^2 = R^3/M_tot ] Mult Choice [ 1. a ] 2. d 3. b 4. c ----- 5. c 6. a [ 7. c ] ------ 8. b 9. c 10. a