Published on March 20, 2008
COSMOS – Cluster 6: The physics of Waves and Stars – July 9, 2007: COSMOS – Cluster 6: The physics of Waves and Stars – July 9, 2007 Tycho Brahe and two competing models of the universe Johannes Kepler discovers the correct mathematical description of planetary motion Tycho Brahe: Tycho Brahe 1546 – 1601 Danish nobleman Discovered a supernova in 1572 Most importantly, he was an excellent observer of stellar and planetary positions. Introduced observational errors Competing cosmological systems: Competing cosmological systems Tycho learned two cosmological systems The Ptolemaic system held that the Earth was at the center of the Universe. The Copernican system placed the Sun at the center of the Universe. Portrait of Tycho Brahe Socrates, Plato, and Aristotle: Socrates, Plato, and Aristotle Socrates 469-399 B.C. Plato 427-347 B.C. Aristotle 384-322 B.C. Pictures from: School of Mathematics and Statistics, University of St. Andrews, Scotland Slide5: Raphael – School of Athens 1510-1511 Aristotle’s universe: Aristotle’s universe The entire Universe was centered on the Earth. Spheres of ether (translucent spheres – no vacuum) carried the Moon, the planets and the Sun. The outermost sphere rotated daily and carried the stars. Aristotle’s universe Claudius Ptolemy: Claudius Ptolemy Ptolemy wrote the Almagest (“The Great System” in Arabic) that provided a mathematical method to predict the location of planets. Ptolemy’s universe was Aristotle’s with the addition of the trigonometry and math needed to make predictions The planets and the Sun moved along small circles (epicycles) guided by large circles with the Earth stationary. About 85 A.D. to about 165 A.D. Alexandria, Egypt Nicolaus Copernicus: Nicolaus Copernicus 1473 – 1543 Canon of the Catholic church. Doctorate in canon law at University of Ferrara 1503. Proposed the first detailed (mathematical) heliocentric model. His model was published in 1543. Disadvantages of the Copernican Model: Disadvantages of the Copernican Model Copernicus used circles and circles guided by circles (epicycles). The model was very complex mathematically. More circles were needed than in Ptolemy’s model. The accuracy of the predictions was less than the accuracy of Ptolemy’s model for predicting most phenomena. Slide11: De Revolutionibus Was published in 1543, the year that Copernicus died. Georg Joachim von Lauchen Rheticus (1514-1574) Obtained permission From Duke Albert of Prussia to publish Copernicus’s De Revolutionibus in 1541 Nicolaus Copernicus 1473-1543 The Copernican Model: The Copernican Model Competing cosmological systems: Competing cosmological systems The Ptolemaic system could be used to predict astronomical events but the accuracy was not very good. The Copernican system with the Sun at the center of the Universe explained the motions of planets in a more intuitive way. The Copernican system often had worse accuracy than the Ptolemaic system for predicting astronomical events. What could Tycho Brahe do to resolve these conflicts? Portrait of Tycho Brahe Uraniborg on the Island of Hven– Tycho’s Observatory: Uraniborg on the Island of Hven– Tycho’s Observatory Tycho’s Measurements of Stars and Planets: Tycho’s Measurements of Stars and Planets Tycho used instruments like quadrants and sextants to measure angles on the sky. Tycho’s goal was to measure the position of stars and planets to an accuracy of one arc-minute. Tycho recorded not just the measurement, but also an estimate of the accuracy of his measurements. Angles on the sky: Angles on the sky When objects are far away and we don’t know the distance we can only measure an angular size or angular separation. 360° is a full circle. 60′ (60 arc minutes) in each degree 60″ ( 60 arc seconds) in each arc minute Johannes Kepler: Johannes Kepler 1571-1630 Imperial Mathematician of the Holy Roman Empire. Inherited the observational data from Tycho Brahe who died in 1601. Interpreted the data by formulating three laws for the motions of the planets around the Sun. Kepler’s Laws: Kepler’s Laws The orbits of the planets are ellipses with the Sun at one of the two foci. The line connecting the Sun and a planet sweeps out an equal area in each equal time The square of the period is proportional to the cube of the semi major axis Slide20: Kepler’s First Law: The orbit of a planet is an ellipse with the Sun at One of the two foci. The eccentricity of an ellipse: The eccentricity of an ellipse A circle is an ellipse with an eccentricity of 0.00. A line is an ellipse with an eccentricity of 1.000. Slide22: A recently discovered extrasolar planet with an eccentric orbit - Slide23: Kepler’s Second Law: A line that connects the Sun and a planet sweeps out an equal area in equal intervals of time. Planets move with a higher speed along their orbits when they are near the Sun. Kepler’s first two laws: Kepler’s first two laws Kepler published his first two laws in 1609 in a book called New Astronomy. The elliptical shape was a departure from the circles of Aristotle, Ptolemy, and the circles in the heliocentric model of Copernicus. The model now had the Sun as the center (at one of the two foci) Kepler’s third law: Kepler’s third law Kepler found a mathematical relationship between the sidereal period of a planet and its semimajor axis. Kepler published this result in 1619. With the period measured in Earth years and the semimajor axis in astronomical units, then we can write P is the sidereal period in Earth years a is the semi-major axis in astronomical-units Notes on Kepler’s Laws: Notes on Kepler’s Laws Matched the observations within the observational errors. Provided a simpler system for predicting events in the solar system. Marked the end of the Earth centered models. Provided a system with more predictive power than Ptolemy’s system. Provided no explanation of why the orbits were ellipses.