# Announcements. There is no homework next week. Tuesday s sections (right after the midterm) will be cancelled.

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1 1 Announcements The Midterm is one week away! Bring: Calculator, scantron (big red form), pencil No notes, cellphones, or books allowed. Homework #4 is due this thursday There is no homework next week. Tuesday s sections (right after the midterm) will be cancelled. Review sessions: -This thursday s lecture will turn into a summary -Friday s and Monday s sections will turn into review sessions (come prepared for them with questions!) Sample questions will be posted tomorrow Keep an eye on the class website, all announcements are posted there. I am working on grading the essay questions on HW#2.

2 2 Lecture #9 Measuring Luminosity Doppler effect Our star, the Sun.

3 3 Quiz #8 (from last lecture) 1. Which object is hotter? left or right? why? Toolkit: Light λ f = c E = h f 2. Which object is brighter? left or right? why? 3.Which object is brighter? left or right? why? Flux = σt 4 Lum = Flux Area λ peak T=2.9mmK c = m/s σ = J m 2 K 4 s

4 4 Quiz #8 1. Which object is hotter? left or right? why? Bluer colors have smaller wavelengths. Wien s law tells us that if the wavelength decreases then the temperature (T) needs to increase to compensate. Toolkit: Light λ f = c E = h f Flux = σt 4 Lum = Flux Area λ peak T=2.9mmK c = m/s σ = J m 2 K 4 s

5 5 Quiz #8 1. Which object is hotter? left or right? why? 2. Which object is brighter? left or right? why? Since the object on the right was hotter, then looking at Stefan-Boltzmann law, we see that if we increase the temperature, then the FLUX also increases. This means more light is coming out of the hotter object, i.e. it is brighter. Toolkit: Light λ f = c E = h f Flux = σt 4 Lum = Flux Area λ peak T=2.9mmK c = m/s σ = J m 2 K 4 s

6 6 Quiz #8 3.Which object is brighter? left or right? why? Toolkit: Light λ f = c E = h f Flux = σt 4 Lum = Flux Area λ peak T=2.9mmK Both objects are the same color, according to Wien s law they have the same temperature. This means that the flux (per unit area) that comes out of these objects is the same. The object on the right has a bigger area than the object on the left, so it is brighter overall. c = m/s σ = J m 2 K 4 s

7 7 Measuring Luminosity Luminosity = Energy / Time Can we ever measure the luminosity of a star directly? (can we ever catch ALL the light it emits?) No, but all the light must go through each sphere that we put around the star.

8 8 Measuring Luminosity Luminosity = Energy / Time Can we ever measure the luminosity of a star directly? (can we ever catch ALL the light it emits?) No, but all the light must go through each sphere that we put around the star. What can we measure? The flux we get on one patch Flux = Luminosity Area = Energy/time Area Once we measure flux, if we know the distance D to the object, then: Luminosity = Flux 4πD 2

9 9 Flux vs. Flux Flux: flow of energy coming out of a patch of a certain area. And that if we account for the entire sphere we can get the TOTAL energy coming out per unit of time (usually a second) Luminosity = Flux 4πD 2 But we had also seen the Stefan-Boltzmann law, which relates flux and temperature. Flux = σt 4 The key point here is to UNDERSTAND what Flux means in each expression! We can only use S-B into the previous expression if D = Radius of the star! Luminosity = σt 4 4πR 2

10 10 The Midterm will include material up to here! The rest of today s lecture will be devoted to new material. Next lecture, we will make a review for the midterm.

11 12 Doppler effect You know this effect for sound. ( nhhheeeeeaaaaaawwwwwwnnnnn! ) If a train is standing still (at rest), its horn sounds the same (very loud!) if you stand in front or behind it.

12 13 Doppler effect You know this effect for sound. ( nhhheeeeeaaaaaawwwwwwnnnnn! ) If a train is standing still (at rest), its horn sounds the same (very loud!) if you stand in front or behind it. If the train is moving, sound waves bunch up in front and spread out behind the train, changing the frequency of sound (pitch).

13 14 Doppler effect The same effect happens to light. The light from an object that is moving TOWARD you : peaks bunch up Wavelengths get shorter, frequency gets faster: light gets bluer. The light from an object that is moving AWAY from you, peaks stretch out Wavelengths get bigger, frequency gets slower: light gets redder. λ f = c redshift blueshift

14 15 Doppler effect The change in wavelength that we measure, either to the red or blue, is proportional to the relative velocity between the light source and us. This is the velocity along our line of sight v relative c = λ λ = λ shift λ rest λ rest v relative : relative velocity between the observer and the source λ rest :wavelength if source is at rest with respect to the observer λ shift :wavelength when the source is moving at v relative c : speed of light (3x10 8 m/s)

15 16 Doppler effect Measuring the doppler shift only tells us about the part of an objects motion that is toward or away from us: Only line of sight velocity Object 1: we see a doppler shift and it will allow us to calculate its velocity. Object 2: we do not see any shift in the lines. There is no line-of-sight component. v Object 3: The velocity of this object can be decomposed into two components. One is the line-of-sight component (a), and the other is perpendicular to the line of sight, and it does not contribute to the shift of spectral lines (b) v v (a) (b)

16 17 Doppler effect Measuring the doppler shift only tells us about the part of an objects motion that is toward or away from us: Only line of sight velocity Let s apply this to astronomical spectra. At rest Redshifted, moving away from us. Redshifted even more, moving away from us faster! Blueshifted, moving toward you. Larger blueshift, moving toward you faster.

17 18 Doppler effect We can also measure the rotation of stars using the doppler effect. One side of the star is moving away from us, while the other side is moving toward us. Which star is rotating faster?

18 19 Doppler effect When an object is rotating, the light gets more spread out Spectral lines get broader and the spectral shape also gets broader for a rotating object.

19 20 Doppler effect Real astronomical example:

20 21 Chapter 14 The Sun

21 22 The Sun: an average star 1. The structure of the Sun Names and characteristics of the layers 2. Hydrostatic equilibrium 3. The Sun s energy source (nucleosynthesis) What could power the Sun? 4. Surface effects - Solar activity a) Magnetic fields b) Solar Winds

22 23 The Sun : Basics Radius: 6.9 x 10 8 m (or 10 9 times Earth) Mass: 2 x kg (300,000 Earths) Luminosity: 3.8 x Watts

23 24 1. Structure of the Sun Core: Here is where the energy is generated by nuclear fusion Temperature ~ 15,000,000 K

24 25 1. Structure of the Sun Radiative Zone: Energy is gradually transported out by photons that are random walking through the densely packed atoms, interacting with atoms at every bounce Energy from the Sun has a thermal radiation spectrum

25 26 1. Structure of the Sun Convection Zone: Energy is transported upwards by rising hot gas Cartoon of the surface

26 27 1. Structure of the Sun Examples of convection: - Lava lamps - miso soup - thermals that lift gliders/birds Convection Zone: Energy is transported upwards by rising hot gas Cartoon of the surface

27 28 1. Structure of the Sun Examples of convection: - Lava lamps - miso soup - thermals that lift gliders/birds Convection Zone: Energy is transported upwards by rising hot gas Why are there bright blobs? Why would they be bright? Why do they look white? Real image of the surface

28 29 1. Structure of the Sun Atmosphere Photosphere: Visible surface of the Sun ~6000 K

29 30 1. Structure of the Sun Atmosphere Photosphere: Visible surface of the Sun ~6000 K Chromosphere: Middle layer of atmosphere ~ K

30 31 1. Structure of the Sun Atmosphere Photosphere: Visible surface of the Sun ~6000 K Chromosphere: Middle layer of atmosphere ~ K Corona: Outermost layer of the atmosphere ~10 6 K

31 32 1. Structure of the Sun Atmosphere Photosphere: Visible surface of the Sun ~6000 K Chromosphere: Middle layer of atmosphere ~ K Corona: Outermost layer of the atmosphere ~10 6 K Solar Wind: Flow of charged particles from the Sun

32 34 2. Holding up the Sun What holds the Sun together? If it is just a ball of gas... GRAVITY! In fact, the weight of the outer layers causes huge pressure on the lower layers. An even better question would be: What keeps the Sun from collapsing? (What is pushing back?)

33 35 2. Holding up the Sun What holds the Sun together? If it is just a ball of gas... GRAVITY! In fact, the weight of the outer layers causes huge pressure on the lower layers.

34 36 2. Holding up the Sun Pressure = Force/area Very intuitive: on which would you rather lean on? The force that causes the pressure can be from gravity, kinetic energy, etc. or?

35 37 2. Holding up the Sun Hydrostatic equilibrium Energy provided by nuclear fusion maintains the pressure. Pressure at the lower layers, near the core, is highest. Pressure is balanced EVERYWHERE by the weight (gravitational force) of the layers above. If this was not the case, the Sun would COLLAPSE! Pressure pushes out, Gravity pushes in

36 38 2. Holding up the Sun Hydrostatic equilibrium (kind of a Solar thermostat) If core temperature then fusion rate and the core contracts and heats up If core temperature then fusion rate and the core expands and cools down

37 39 3. Powering the Sun What powers the sun? Is it a big floating bonfire? (a pile of burning wood? coal?) Is it powered by lithium AA batteries?

38 40 3. Powering the Sun What s the fuel? How about coal? Burning 1kg of coal gives you 3x10 7 Joules of energy Total energy available = Total mass of the Sun (in Kg) x Energy each kg gives = (2 x kg) x (3 x 10 7 J/kg) Total energy available = (2 x 3) x (10 30 x 10 7 ) x (kg x J/kg) How long would the sun burn if it was made out of coal?

39 41 3. Powering the Sun What s the fuel? How about coal? Burning 1kg of coal gives you 3x10 7 Joules of energy Total energy available = Total mass of the Sun (in Kg) x Energy each kg gives = (2 x kg) x (3 x 10 7 J/kg) Total energy available = (2 x 3) x (10 30 x 10 7 ) x (kg x J/kg) How long would the sun burn if it was made out of coal? Let s re-phrase that: If you have \$100 for food, and you spend \$10 each day, how long does the money lasts you? Days money will last = Total amount of money Rate of expenditure

40 42 3. Powering the Sun What s the fuel? How about coal? Burning 1kg of coal gives you 3x10 7 Joules of energy Total energy available = Total mass of the Sun (in Kg) x Energy each kg gives = (2 x kg) x (3 x 10 7 J/kg) Total energy available = (2 x 3) x (10 30 x 10 7 ) x (kg x J/kg) = 6 x10 37 J How long would the sun burn if it was made out of coal? Money the Sun has

41 43 3. Powering the Sun What s the fuel? How about coal? Burning 1kg of coal gives you 3x10 7 Joules of energy Total energy available = Total mass of the Sun (in Kg) x Energy each kg gives = (2 x kg) x (3 x 10 7 J/kg) Total energy available = (2 x 3) x (10 30 x 10 7 ) x (kg x J/kg) = 6 x10 37 J How long would the sun burn if it was made out of coal? Money the Sun has How much energy does the Sun spends each second? Think about the units... what has units of energy over time? J/s =Watts! The luminosity of the sun is the rate it releases energy! LSun=3.8 x Watts 4 x Watts

42 44 3. Powering the Sun What s the fuel? How about coal? Burning 1kg of coal gives you 3x10 7 Joules of energy Total energy available = Total mass of the Sun (in Kg) x Energy each kg gives = (2 x kg) x (3 x 10 7 J/kg) Total energy available = (2 x 3) x (10 30 x 10 7 ) x (kg x J/kg)= 6 x10 37 J How long would the sun burn if it was made out of coal? Time it would last = total energy = 6 x10 37 J = 6 x10 37 J luminosity 4 x W 4 x J/s Money the Sun has = 1.5 x s Time it would last = 1.5 x s x 1min x 1hr x 1day x 1 year = 4800 years 60 s 60 min 24 hr 365 days Can t be! there are whale bones older than that!

43 45 3. Powering the Sun Then what is powering the Sun? Clues from the spectrum? Thermal spectrum with absorption lines: Hot dense source behind cooler gas

44 46 3. Powering the Sun Then what is powering the Sun? Clues from the spectrum? Thermal spectrum with absorption lines: Hot dense source behind cooler gas Absorption lines are fingerprints of elements 70% Hydrogen (H) 27% Helium (He) 3% everything else So, the Sun has a lot of H.

45 47 3. Powering the Sun: Nucleosynthesis The mass of the Sun is 2x kg... that is a LOT of hydrogen! 1) The nucleus is held together by the STRONG force It works like a velcro, really strong (way stronger than the electromagnetic force), but only at very close range. 2) Why is a Helium atom less massive than 4 Hydrogen atoms? 4 H atoms = 4 protons = x kg 1 He atom = 2 protons = x kg (0.7% difference) If you stick together hydrogen atoms to make Helium, the extra mass has to go somewhere. It becomes energy! E=mc 2 Mass and energy are the same thing and can transform back and forth using this equation.

46 48 3. Powering the Sun: Nucleosynthesis Lets see how long can we power the sun by turning H into He. How much energy can we get from 1kg of Hydrogen? 0.7% of the mass gets turned into energy E=mc 2 = x 1 kg x (3 x10 8 m/s) 2 =6.3 x J Energy we get per each kg of H turned into He Total energy available? (Total mass of the sun) x (Energy per each kg) Total energy = (2x10 30 kg) x (6.3 x J/kg) = 1.3 x J

47 49 3. Powering the Sun: Nucleosynthesis Lets see how long can we power the sun by turning H into He. How much energy can we get from 1kg of Hydrogen? 0.7% of the mass gets turned into energy E=mc 2 = x 1 kg x (3 x10 8 m/s) 2 =6.3 x J Energy we get per each kg of H turned into He Total energy available? (Total mass of the sun) x (Energy per each kg) Total energy = (2x10 30 kg) x (6.3 x J/kg) = 1.3 x J How long can this last? Lifespan of the Sun = Total energy available = 1.3 x J Energy released each s. 4 x J/s = 1.0x years That s 100 billion years. The universe is only 13.7 billion years old. That should do it!

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