1. © 2007 Jones and Bartlett Publishers Chapter 2 2-6 thru 2-10 From an Earth-Centered to a Sun-Centered System Courtesy of NASA/JPL-Caltech

2. © 2007 Jones and Bartlett Publishers 2-6 Nicolaus Copernicus and the Heliocentric Model 1. Copernicus, a contemporary of Columbus, worked for 40 years on a heliocentric—Sun-centered—model for two reasons. –Ptolemy’s predicted positions for celestial objects had become less accurate over time. –The Ptolemaic model was not aesthetically pleasing enough.

3. © 2007 Jones and Bartlett Publishers The Copernican System 1.Copernicus’ system revived many of the ideas of Aristarchus. –An Earth that rotates from west to east under a stationary sky produces the same observations as a rotating celestial sphere from east to west around a stationary Earth. 2.Copernicus’ system is heliocentric with the Earth being just another one of the planets, all of them revolving around the Sun.

4. © 2007 Jones and Bartlett Publishers 3.As seen from high above the Earth’s North Pole, all planets move in a counterclockwise direction, with the planets closer to the Sun moving faster than those farther away. 4.To explain the apparent motion of the Sun in the sky, Copernicus’ model had the plane of the Earth’s equator tilted with respect to the plane of its orbit around the Sun. Fig. 2-15

5. © 2007 Jones and Bartlett Publishers 5. Copernicus’ model explains the generally west to east motion of the planets, as does Ptolemy’s. However, the observed retrograde motion of planets such as Mars is explained more simply in the Copernican system. Retrograde motion is a natural result in a heliocentric system. 6. Copernicus had the Moon revolving around the Earth and all the planets circling the Sun. Figure 2.19c: Copernicus’s Sun- centered theory of the layout of the universe

6. © 2007 Jones and Bartlett Publishers Question 1 How does Copernicus explain retrograde motion in his model?

7. © 2007 Jones and Bartlett Publishers 2-7 Comparing the Two Models 1. Accuracy in Fitting the Data ( a) Copernicus’ model was not accurate enough to account for all observed planetary motions. Copernicus’ assumption of uniform motion (like Ptolemy) forced him to add small epicycles of his own to improve accuracy. (b) Copernicus did not abandon the circle as the preferred planetary orbit. He considered circles the best representative of the heavens’ repetitive motions.

8. © 2007 Jones and Bartlett Publishers (c) Once parallax was observed (in 1838), it provided obvious evidence that the heliocentric model is the better one. Stellar parallaxes prove the Earth moves. Parallax also provided evidence that stars are not all at the same distance from Earth, which was assumed in both the Copernican model and the Ptolemaic model. (d)Using the evidence available in the 1500s, both models had about the same errors.

9. © 2007 Jones and Bartlett Publishers 2. Predictive Power (a)A good theory (or model) must make testable predictions that might allow the theory (or model) to be disproved. (b) Both the Copernican and Ptolemaic models made predictions about parallax. When parallax was finally observed, it proved that the Ptolemaic model was wrong. (c) The Copernican model also made predictions about relative distances of the then known planets from the Sun; these predictions were (much) later confirmed.

10. © 2007 Jones and Bartlett Publishers 3. Simplicity: Mercury and Venu s (a) Copernicus liked his model because it was aesthetically more pleasing than the Ptolemaic model. A good model is nearly always simple and elegant in its power to explain and predict. (b) The Copernican model could explain the motions of Mercury and Venus without resorting to special rules needed by the Ptolemaic model.

11. © 2007 Jones and Bartlett Publishers (c) Copernicus offered a simpler explanation for retrograde motion that required no use of epicycles. He did use epicycles, however, in order to make his model fit as accurate as possible. (d) Copernicus, who died in 1543 just as his book De Revolutionibus was published, started such an upheaval in people’s thinking that the word “revolution” took on a second meaning that is so familiar to us today.

12. © 2007 Jones and Bartlett Publishers Question 2 Discuss how stellar parallax affected the geocentric and heliocentric models and their places among science.

13. © 2007 Jones and Bartlett Publishers 2-8 Tycho Brahe The Importance of Accurate Observations 1. Tycho (1546–1601) was born 3 years after Copernicus died. After learning that the Ptolemaic and Copernican models were based on inaccurate recorded data, he decided to obtain more accurate observations of planetary positions. 2. Tycho built the largest and most accurate naked-eye instruments yet constructed. (The telescope had not yet been invented.) They allowed him to measure angles to within 0.1º, close to the limit the human eye can observe. 3. He not only made careful measurements, but he recorded the accuracy of each measurement. The inclusion of an error in a measurement is now a common practice in science.

14. © 2007 Jones and Bartlett Publishers Tycho’s Model 1. The quality of his observations led Tycho to reject the Copernican model because he could not observe parallax for the distant stars. –His observations of a “new” star (a supernova) and a bright comet led him to conclude that these objects were far away from the Earth because he could not measure their parallax. 2.Tycho’s model of the heavens was a mix between the Ptolemaic and Copernican models. –He positioned the Earth at the center with the Sun revolving around it, but he argued that the other planets were revolving around the Sun.

15. © 2007 Jones and Bartlett Publishers Figure 2.19d: Tycho Brahe’s Earth-centered model of the universe

16. © 2007 Jones and Bartlett Publishers 2-9 Johannes Kepler and the Laws of Planetary Motion 1. In 1600, a year before Tycho died, he hired Johaness Kepler as his assistant. Tycho’s accurate measurements of planetary positions (especially for Mars) proved invaluable for Kepler. 2. After 4 years and 70 combinations of circles and epicycles, Kepler devised a combination that would predict Mars’ position when compared to Tycho’s data to within 0.13º. –Knowing the quality of Tycho’s work, Kepler decided to abandon the circle as the basic motion of the planets. 3. The shape that worked not only for Mars but for every planet Kepler had data was the ellipse.

17. © 2007 Jones and Bartlett Publishers The Ellipse 1.The ellipse is a geometrical shape of which every point is the same total distance from two fixed points (the foci). PF 1 + PF 2 = constant +major axis. 2.Eccentricity is the ratio of the distance between the foci divided by the longest distance across the ellipse (major axis).

18. © 2007 Jones and Bartlett Publishers Kepler’s First Two Laws of Planetary Motion First Law Each planet’s path around the Sun is an ellipse, with the Sun at one focus of the ellipse (there is nothing at the other focus). Fig. 2-23a

19. © 2007 Jones and Bartlett Publishers Second Law A planet moves along its elliptical path with a speed that changes in such a way that a line from the planet to the Sun sweeps out equal areas in equal intervals of time. The second law implies that a planet moves fastest when it is at the nearest point to the Sun (the perihelion) while it moves most slowly at its farthest point from the Sun (the aphelion). Figure 2.23b: Kepler’s second law

20. © 2007 Jones and Bartlett Publishers Kepler’s Third Law 1.The ratio of the cube of a planet’s semimajor axis (the average distance a from the Sun) to the square of its sidereal period P is the same for each planet: a 3 / P 2 = constant. 2.A planet’s sidereal period is the time the planet takes to complete a full orbit around the Sun, relative to the stars. This differs from the synodic period, which is the time between two successive identical configurations between a planet and the Sun, as seen from Earth.

21. © 2007 Jones and Bartlett Publishers 2-10 Kepler's Contribution 1. Kepler’s modification to the Copernican model brought it into conformity with the data. Finally, the heliocentric theory worked better than the old geocentric theory. 2. Kepler’s breakthrough choice of ellipses to explain planetary motion was empirical—ellipses worked but he did not know why they worked. © North Wind Picture Archives

22. © 2007 Jones and Bartlett Publishers 3.Models of the universe have changed over the past 4000 years, with most of the changes coming in the last 500 years. Fig. 2-24

23. © 2007 Jones and Bartlett Publishers Question 3 Why do you think a perfect circle is unrealistic as an orbital path?