Astronomy 103

1. Lecturer: Prof. Alex Lazarian • Office Location: 4518 Sterling Hall • Email: lazarian@astro.wisc.edu • Website: http://www.astro.wisc.edu/~lazarian/ast103a/ • Office Hours: Tue. 1:15pm-3pm, Th. 1:15pm-3pm. Meetings at a different time can also be arranged. Course Reading: Pathways to Astronomy Schneider & Arny 1st edition Astronomy 103 Exams: 1st exam – 25% (Oct. 14) 2nd exam—25% (Nov. 11) final exam—30% (Dec. 16) total for homework, quizzes, participation in the work in class, presentations -- 20% Main Ideas to be covered: *Subject of astronomy (Units 1--4) *Observations of planets and stars (Units 5--12) *Laws of gravity, dark matter (Units 14-20) *Light, atoms, spectra (Units 21--30) *Stars: Sun as an example (Units 49--50) *Learning about stars (Units 52--55) *Birth and evolution of stars (Units 56—63, 69) *When the fuel begins to run out (Units 64--66) *Supernova, neutron stars and black holes (Units 67--68) *Galaxies and quasars (Units 74--77) *Our galaxy- Milky Way (Units 70--73) *The expanding Universe (Units 78--82) *Life in the Universe (Units 83--84) *Review of the course

2. During the winter the temperature is lower because the Sun • A. Stops moving • B. has lower temperature • C. is farther away from the Earth • D. does not rise as high in the sky

3. Figure 9.01 • Different Cultures record the passage of time in many ways. • These various ways may seem bewildering at first but they are based on just a few astronomical cycles

4. Figure 9.04 An ancient Roman calendar showing the first five months of the year. The Roman numerals at the bottom of each column indicate the number of days in each month. The letters A through H indicate the 8 days of the week.

5. Figure 9.05 A portion of a Mayan calendar which is broken up into 20 day “months.”

6. In addition, he noticed that stars were visible in some southern locations, while not visible in northern locations. Again, the Earth must be spherical for this to happen! Aristotle concluded from observations of the curved shadow of the Earth on the Moon during a lunar eclipse that the Earth was spherical. The Shape of the Earth

7. Distance and Size of the Moon • Aristarchus (~310-230 B.C.E.) • Used the relative sizes of the Moon and the Earth’s shadow during an eclipse to estimate the size of the Moon • He estimated that the Moon was 1/3 (0.33) as large as the Earth • Not too far off! (0.27) • Also estimated the distance to the Moon by timing how long it took the Moon to pass through the Earth’s shadow during an eclipse • Estimated a distance of 70 Earth radii • Pretty close! (~60 Earth radii)

8. Finally, he postulated that the Earth goes around the Sun, rather than the belief that everything revolves around the Earth His critics claimed that if this were true, they would see the positions of the stars change relative to each other. This is called parallax No parallax motion was visible, so Aristarchus must be wrong! Actually, there is parallax (and the Earth does indeed go around the Sun), but the motion was too small for the unaided eye to see – we need telescopes! Parallax Preview

9. Size of the Earth • Eratosthenes (296-195 b.c.e.) wanted to know the size of the Earth • He noted that the sun could be seen from the bottom of a well in Syene, so the Sun must be directly overhead • Then he measured the angle the Sun made with the horizon in Alexandria (7 degrees) • Calculated a diameter of 13,000 km, almost exactly correct!

10. In Astronomy, we will frequently estimate the sizes of planets, etc. To do this, we measure the angle that the object makes in the sky. We say that an object subtends an angle (A) in the sky For example, the moon subtends 0.5 degrees. The Sun also subtends 0.5 degrees, which is why solar eclipses are so beautiful! Measuring Angular Diameter

11. Measuring Linear Diameter • If we measure the angle subtended by an object in the sky (A), and we know the distance to it (d), we can calculate its actual, linear diameter (L)!

12. The Motion of the Planets • Because the planets’ orbits all lie in more or less the same plane, the paths of the planets through the sky all lie close to the ecliptic, appearing to move through the constellations of the zodiac • Only Pluto seems to move far from the ecliptic

13. Retrograde Motion • As the Earth catches up to the orbital position of another planet, that planet seems to move backwards through the sky. • This is called retrograde motion • Posed a frustrating problem to the ancients – if all planets moved in perfect circles, how could they move backwards, and why only occasionally?

14. Geocentric Models • Models in which everything revolves around the Earth are called Geocentric models. • From earliest Greek times, this kind of model was used to describe the heavens • Planets and stars resided on their own spheres, each tipped slightly relative to each other. This reproduced the motion of the planets and Sun through the sky. • Did not explain retrograde motion!

15. Ptolemy (100-170 C.E.) improved the geocentric models by including epicycles Planets were attached to small circles (epicycles) that rotated. These epicycles were attached to a larger circle, centered on Earth This can be visualized as a planet attached to a Frisbee, attached to a bicycle wheel with the Earth at the center. Did a fair job of reproducing retrograde motion. Epicycles

16. Heliocentric Models • Nicolas Copernicus devised a heliocentric (Sun-centered) model in which everything, including the Earth, revolves around the Sun • Retrograde motion is a natural result of these models! • Copernicus was also able to measure the relative distances between the Sun and the planets

17. It was found that Mercury and Venus were closer to the Sun than the Earth, as they were never found very far from the Sun in the sky Mercury’s greatest elongation, or angular separation from the Sun, is never more than 28 degrees Venus’s greatest elongation is never more than 47 degrees Mercury is therefore closer to the Sun than Venus Mercury and Venus

18. Built instruments to measure the positions of planets very accurately (~1 arc minute) Found that comets moved outside of the Earth’s atmosphere Witnessed a supernova and concluded that it was much farther away than any celestial sphere As he could detect no parallax motion in the stars, he held that the planets go around the Sun, but the Sun, in turn, orbits around the Earth Tycho Brahe (1546-1601 C.E.)

19. Using Tycho Brahe’s data, discovered that planets do not move in circles around the Sun, rather, they follow ellipses with the Sun located at one of the two foci! Johannes Kepler (1571-1630

20. Kepler’s First Law • Planets move in elliptical orbits with the Sun at one focus of the ellipse • Developed a heliocentric (Sun-centered) model • Did not agree with the ancients (or Brahe!) • The shape of the ellipse is described by its semi-major and semi-minor axes.

21. Kepler’s Second Law • The orbital speed of a planet varies so that a line joining the Sun and the planet will sweep out equal areas in equal time intervals • That is, planets move faster when near the Sun, and slower when farther from the Sun • Explained the non-circular behavior of the planets!

22. Kepler’s Third Law • The amount of time a planet takes to orbit the Sun (its period) P is related to its orbit’s size, a, by P2 = a3 • Kepler’s Laws describe the shape of a planet’s orbit, its orbital period, and how far from the Sun the planet is positioned. • These were empirical relationships, found from observation rather than the logic of the ancients.