1. “I always wanted to be somebody, but I should have been more specific.” Lilly Tomlin Any late HW2 are due before class on Wednesday. HW2 solutions posted after class on Wednesday. You will want to bring a calculator to class. This next part is math-rich, but we will do many sample problems in class.

2. Test 1 is Friday- be sure to bring a pencil and a calculator. There is a study guide and sample test on the course web page.

3. Next section:The power of light!

4. We want to know: How hot are stars? How BIG are stars (size)? How massive are stars? What are stars made of? How far away are stars? Are they in motion? How much energy do stars emit? Where does that energy come from?

5. A spectrum

6. Blue light has more energy (is hotter) than red light.

8. Quiz 8: Which light has the most energy? A) X-raysB) Green lightC) MicrowavesD) Radio waves

9. Temperatures given in Kelvins T=2.9x10 6 / max for in nm. Shorter wavelengths = hotter object. Objects glowing blue are hotter then objects glowing red.

10. Stefan-Boltzmann Law Can determine energy per square meter from the temperature. E/m 2 =  T 4 Where  = 5.67x10 -8 W/m 2 K 4

11. Example: Our Sun looks yellow. So from the chart below, let's assume the peak of the continuous spectrum is at 575nm. What are the temperature and energy per square meter of our Sun? 400 575 700 nm

12. Example: our Sun First find the temperature: T=2.9x10 6 / = ? =575 Now find the energy associated with that temperature. E /m 2 =  T 4 =(5.67x10 -8 )(T 4 )=?

13. Example: our Sun First find the temperature: T=2.9x10 6 / = 2.9x10 6 /575 = 5043K Now find the energy associated with that temperature. E =  T 4 =  (5043 4 )= (5.67x10 -8 )(6.47x10 14 ) =3.7x10 7 W/m 2 That's 37 million watts for each square meter at the surface of the Sun!

14. Example: our Sun T=2.9x10 6 / = 2.9x10 6 /575 = 5043K E =  T 4 =  (5043 4 )=3.7x10 7 W/m 2 That's 37 million watts for each square meter at the surface of the Sun! But it's not the total energy of the Sun. How do we find the total energy of the Sun?

15. Example: our Sun T= 5043K E/m 2 =3.7x10 7 W/m 2 To get the total energy, multiply by the surface area of the Sun: A=4 p R 2 where R is the radius of the Sun: 6.96x10 8 m.

16. Example: our Sun T=2.9x10 6 / = 2.9x10 6 /575 = 5043K E =  T 4 =  (5043 4 )=3.7x10 7 W/m 2 To get the total energy, multiply by the surface area of the Sun: A=4 p R 2 where R is the radius of the Sun: 6.96x10 8 m. E tot = 2.25x10 26 watts. This energy has a special name: Luminosity

17. Luminosity: The total energy emitted by a star: L=4 p R 2  T 4

18. We want to know: How hot are stars? How BIG are stars (size)? How massive are stars? What are stars made of? How much energy do stars emit? Where does that energy come from? How far away are stars? Are they in motion?

19. INVERSE SQUARE LAW Light drops off as the square of the distance (1/d 2 ) The light received at 2m is ¼ the light received at 1m. The light received at 3m is 1/9 the light received at 1m and so on. This is called the apparent luminosity (L ap ). So L ap at 3m is 1/9L.

20. Put it all together: Apparent Luminosity Include distance into the calculation. L ap = 4 p R 2  T4/d 2 This is how bright stars appear to us when we look up into the sky at night. Units: Temperature must be in Kelvin, size and distance must be in meters.

21. How to make a star brighter Make it hotter: E~T 4 Make it b i g g e r : E~R 2 Make it closer: E~1/d 2 Hotter is most powerful.

22. The motions of stars. Parallax

24. From parallax we can determine distances to nearby stars. This is the first step in determining the distances in our Universe. This method is only good for nearby stars.

25. Parallax From parallax we can determine distances to nearby stars. This method is only good for nearby stars. The closest star to us is 4 light years away (~25,000 AU) Most stars we see are tens to thousands of light years away.

26. We want to know: How hot are stars? How BIG are stars (size)? How massive are stars? What are stars made of? How much energy do stars emit? Where does that energy come from? How far away are stars? Are they in motion?

27. Parallax is due to the motion of Earth around the Sun. But stars are in motion too! (everything in the Universe is)

29. Parallax is due to the motion of Earth around the Sun. Proper motion is a stars motion across the sky. (not towards or away from us) Again, closer stars will have larger proper motion, and faster stars will have larger proper motion.

30. Radial velocity But stars are also moving towards and away from us. To measure this motion, we use the Doppler shift.

32. Parallax is due to the motion of Earth around the Sun. Proper motion is a stars motion across the sky. (not towards or away from us) Radial velocity uses the Doppler shift to measure a star's motion towards or away from us.

33. The complete picture. Arrow shows true motion of star

34. We want to know: How hot are stars? How BIG are stars (size)? How massive are stars? What are stars made of? How much energy do stars emit? Where does that energy come from? How far away are stars? Are they in motion? Yes!

35. Luminosity (brightness) When we look at a star from Earth, we measure its APPARENT LUMINOSITY (BRIGHTNESS): L ap We call the TOTAL energy emitted from a star its LUMINOSITY: L We also have a standard called ABSOLUTE LUMINOSITY: L abs which is how bright a star would appear if it were at 10 parsecs (pc) from us.

36. Parsecs 1pc=3.1x10 16 m 1pc = 206,667 AU 1pc = 3.26 light years (ly)

37. Kirchoff In the 1850s, Gustav Kirchhoff took another look at Wien's work.

38. He also heated ceramics and got the spectrum on the left. Then he put a cool gas in front of the ceramic and got the center spectrum. Then he just heated the gas (with electricity) and got the spectrum on the right. He discovered 3 types of spectra

39. So now we have 3 types of spectra Continuous spectra are made by objects under high pressure (like solids) Absorption line spectra are made by cool (comparatively) low pressure gases. Emission line spectra are made by (comparatively) hot, low pressure gases.

40. Below are the 3 kinds of spectra again. As you can see from the labels on the left, different elements produce different spectral lines.

41. A spectrum of our Sun: The lines give us composition! So we can see what our Sun is made of !

42. Now we can get the Sun's composition. By Mass 76% Hydrogen 22% Helium 0.8% Oxygen 0.4% Carbon 0.2% Neon 0.1% Iron and Nitrogn ~0.08% Silicon and Magnesium ~0.24% Everything else Astronomers call this stuff “metals”

43. We want to know: How hot are stars? How BIG are stars (size)? How massive are stars? What are stars made of? How much energy do stars emit? Where does that energy come from? How far away are stars? Are stars in motion? Yes!

44. Now we can ask, What provides the energy our Sun emits?

45. How to solve the problem. To determine the energy source of the Sun, astronomers tried to calculate the total energy emitted by the Sun in its lifetime. To do this, you simply multiply the amount of energy the Sun radiates each second (L=3.9 x 10 26 W) by its age.

46. In the beginning.... Chemical burning is a way to generate heat. Chemical reactions (burning) could power the Sun for ~3,000 years. This agreed with religious dogma at the time.

47. Another way Back in the 1850s, scientists thought the Sun's energy came from gravity- the Sun was converting gravitational energy to heat. E grav =GMm/R. So as R get smaller, energy can be released. Lord Kelvin estimated the Sun could last 30 million years based on this.

48. The Earth's age By late in the 19 th century, Darwin had determined that the Earth must at least be hundreds of millions of years old. Early in the 20 th century, radiation provided a new power source and the age of atomic physics was born.

49. Einstein We now know that the Sun is 4.6 billion years old and converts hydrogen to helium via nuclear fusion. This releases energy based on Einstein's famous equation: E=mc 2. In each reaction, the Sun converts a little bit of mass into energy.

50. The Sun puts out a million billion tons of TNT worth of energy each second. By converting hydrogen to helium.