Test 2: Oct. 12

1. Test 2: Oct. 12 • Test covers Chapters 4-7 and sections 8.1,8.3 • Section 5.3, and part of Ch. 7 (Doppler effect) are excluded • Show your work everywhere • Don’t forget to prepare formula sheet • Bring your calculator • Textbook and lecture notes are not allowed

2. Help sessions • Today, 6:00-7:30 pm, room 213 ENPH (teaching wing) • Tomorrow, 5:10-5:55 pm, room 213 ENPH

3. Your test survival kit: • Formula sheet • Formula sheet • Formula sheet

4. How to prepare: • Read chapters and lecture notes • Pay extra attention to chapter summary • Answer review questions • Solve homework problems

5. Remember and check UNITS for all terms in the formulas!!! Indicate units on your formula sheet Express all terms in correct units before plugging in the formula Check your answer for right unit

6. History • Geocentric Universe; epicycles • Copernicus and his model • What Galileo did • What Kepler proposed • Newton and his achievements

7. Chapters 4,5 • Milestones in the history of astronomy • Kepler’s laws • Newton’s accomplishments • Gravity force • Application to the orbital motion

9. Elliptical orbits Remember parameters: perihelion, aphelion, semimajor axis, eccentricity Ra - Rp e = Ra + Rp a = (Rp + Ra)/2

10. LAW 2: A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time The closer to the sun, the larger the orbital velocity

11. LAW 3: The squares of the periods of the planets are proportional to the cubes of their semimajor axes: For the Earth P2 = 1 yr, a2 = 1 AU Note units!!

12. Gravity: by far the most important force in the Universe m1 m2

13. m r M Uniform circular motion On the Earth’s surface r = R = 6400 km; M = 6x1024 kg; Acceleration of gravity does not depend on a body’s mass!

14. m r M Uniform circular motion - continued III Kepler’s law:

15. Escape condition: Kinetic Energy K  Gravitational Potential Energy U At threshold: Note: total energy E = K + U; E < 0 for bound orbits E  0 for unbound trajectories

16. Chapters 6,7 • Telescope powers • Different types of telescopes • Electromagnetic spectrum • Black body radiation • Quantized states in an atom • Radiative transitions • Origin of the discrete spectrum • Spectral classes of stars

19. Photons

20. Dual, wave-particle nature of light 1 eV = 1.6x10-19 J c = 3x108 m/s 1 Angstrom = 10-10 m 1 nm = 10-9 m 1 m = 10-6 m

21. Refracting/Reflecting Telescopes Refracting Telescope: Lens focuses light onto the focal plane Focal length Reflecting Telescope: Concave Mirror focuses light onto the focal plane Focal length Almost all modern telescopes are reflecting telescopes.

22. Telescope parameters • Light-gathering power (ability to see faint objects) • Resolving power (ability to see fine details) • Magnification (least important)

23. The Powers of a Telescope:Size Does Matter 1. Light-gathering power: Depends on the surface area A of the primary lens / mirror, proportional to diameter squared: D A = p (D/2)2

24. The Powers of a Telescope (2) 2. Resolving power: Wave nature of light => The telescope aperture produces fringe rings that set a limit to the resolution of the telescope. Resolving power = minimum angular distance amin between two objects that can be separated. amin = 1.22 (l/D) amin For optical wavelengths, this gives amin = 11.6 arcsec / D[cm]

25. Two Laws of Black Body Radiation 1. The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases. Wien’s displacement law: lmax≈ 3x106 nm / T(K) (where T(K) is the temperature in Kelvin).

26. L = A*s*T4 Two Laws of Black Body Radiation 2. The hotter an object is, the more luminous it is. The Stefan-Boltzmann law: Radiation Flux, or power emitted by unit area of a black-body emitter, is proportional to the fourth power of its surface temperature: s = Stefan-Boltzmann constant Luminosity, or total power: whereA = surface area

27. Note units!! Wien’s law: The Stefan-Boltzmann law

28. Luminosity Surface area of the star = 4R2 Luminosity, or total radiated power L = T4 4R2 J/s Intensity, or radiation flux on the Earth: R d

29. Comparing radiation fluxes and luminosities from two sources A and B:

30. Atomic Transitions • An electron can be kicked into a higher orbit when it absorbs a photon with exactly the right energy. Eph = E3 – E1 Eph = E4 – E1 Wrong energy • The photon is absorbed, and the electron is in an excited state. (Remember that Eph = h*f) • All other photons pass by the atom unabsorbed.

32. Kirchhoff’s Laws (SLIDESHOW MODE ONLY)

33. Lines of Hydrogen Most prominent lines in many astronomical objects:Balmer lines of hydrogen

34. Spectral Classification of Stars (1) Different types of stars show different characteristic sets of absorption lines. Temperature

35. Spectral Classification of Stars (2) Mnemonics to remember the spectral sequence:

36. Sun - basic facts • What is the Sun • Internal structure and composition • Source of energy • Lifetime • Sun’s activity and variability Spectral class: G2 Surface temperature: 5800 K Lifespan: 10 billion years Composition by mass: ~ 71% Hydrogen, 27% Helium

37. The Composition of Stars From the relative strength of absorption lines one can infer the composition of stars.

38. Stellar Structure Energy transport via convection Sun Energy transport via radiation Flow of energy Energy generation via nuclear fusion Basically the same structure for all stars with approx. 1 solar mass or less. Temperature, density and pressure decreasing

39. Energy Transport in the Sun Energy generated in the star’s center must be transported to the surface. Outer layers (including photosphere): Convection Inner layers: Radiative energy transport Bubbles of hot gas rising up Cool gas sinking down Gas particles of solar interior g-rays

40. Conduction, Convection, and Radiation (SLIDESHOW MODE ONLY)

41. The Sun (SLIDESHOW MODE ONLY)

42. 11-year period of solar activity (Solar cycle)