Lecture 8: What we can learn via light

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1 Lecture 8: What we can learn via light As with all course material (including homework, exams), these lecture notes are not be reproduced, redistributed, or sold in any form.

2 Lecture 8: What we can learn via light As with all course material (including homework, exams), these lecture notes are not be reproduced, redistributed, or sold in any form.

3 From Last Lecture What light tells us The color of light emitted by an object can tell us its temperature. [hotter objects are bluer; colder objects are redder -or- hotter objects emit more of their light at shorter wavelengths] Light can tell us about the composition of objects. [different atoms/molecules emit (or absorb) light at specific wavelengths]

4 (and absorption-line)

5 a spectrum of a random galaxy [not all galaxies have spectra like this.] Hydrogen Oxygen

6 What light tells us The color of light emitted by an object can tell us its temperature. [hotter objects are bluer; colder objects are redder -or- hotter objects emit more of their light at shorter wavelengths] Light can tell us about the composition of objects. [different atoms/molecules emit (or absorb) light at specific wavelengths] Light can tell us about the velocity of an emitting object. [via the doppler shift]

7 The Doppler Effect Stationary source of waves

8 The Doppler Effect Moving source of waves Person over here hears a lower pitch [i.e. longer wavelength] Person over here hears a higher pitch [i.e. shorter wavelength]

9 Doppler Effect: Summary If the source of waves is moving toward you, you ll see waves of shorter wavelength. for light waves, this is called a blueshift If the source of waves is moving away from you, you ll see waves of longer wavelength. for light waves, this is called a redshift By measuring the amount of blueshift or redshift, we can determine the object s velocity toward or away from us. Note: the speed of the waves is not affected!

10 Doppler shift of light The Doppler effect depends only on the object s motion along a direction toward or away from the observer

11 Doppler shift of light The Doppler effect depends only on the object s motion along a direction toward or away from the observer If star isn t moving relative to the observer, then the observed spectrum will not be Doppler-shifted

12 Doppler shift of light The Doppler effect depends only on the object s motion along a direction toward or away from the observer Star moving this way: Observer sees redshifted spectrum

13 Doppler shift of light The Doppler effect depends only on the object s motion along a direction toward or away from the observer Star moving this way: Observer receives light that is not Doppler-shifted

14 Doppler shift of light Important note: Doppler effect depends only on the object s motion along a direction toward or away from the observer Star moving this way: The Doppler shift only depends on the component of the star s motion toward or away from the observer

15 Doppler shift of light Important note: Doppler effect depends only on the object s motion along a direction toward or away from the observer Star moving this way: The Doppler shift only depends on the component of the star s motion toward or away from the observer

16 Star at rest relative to observer: No shift Wavelength (nm)

17 Star at rest relative to observer: No shift Star moving away from observer: Spectrum is redshifted Wavelength (nm)

18 Star at rest relative to observer: No shift Star moving away from observer: Spectrum is redshifted Star moving toward observer: Spectrum is blueshifted Wavelength (nm)

19 Doppler shift of light λ λ 0 = v c Note: this equation is valid when the star s velocity is very small compared to the speed of light!

20 Doppler shift of light λ λ 0 = v c Note: this equation is valid when the star s velocity is very small compared to the speed of light! λ0 = the rest wavelength of the photon λobs = the observed wavelength, measured by the observer Δλ = λobs - λ0 = the shift in wavelength v = the velocity of the source relative to the observer c = speed of light If v is negative, the source is moving toward us. If v is positive, the source is moving away from us.

21 λ = v c λ 0 Energy Wavelength

22 λ Star at rest = v c λ 0 Energy Wavelength nm

23 λ Star at rest = v c λ 0 Star moving away Energy Wavelength nm nm

24 λ Star at rest = v c λ 0 Star moving away Energy How fast is this star moving away from us? Wavelength nm nm

25 λ Star at rest = v c λ 0 λ0 = nm Star moving away Energy How fast is this star moving away from us? Wavelength nm nm

26 λ Star at rest = v c λ 0 Energy Star moving away λ0 = nm λobs = nm How fast is this star moving away from us? Wavelength nm nm

27 λ Star at rest = v c λ 0 Energy Star moving away λ0 = nm λobs = nm Δλ = λobs - λ0 = 0.8 nm How fast is this star moving away from us? Wavelength nm nm

28 λ Star at rest = v c λ 0 Energy Star moving away How fast is this star moving away from us? λ0 = nm λobs = nm Δλ = λobs - λ0 = 0.8 nm Δλ/λ0 = 0.8/800 = Wavelength nm nm

29 λ Star at rest = v c λ 0 Energy Star moving away How fast is this star moving away from us? λ0 = nm λobs = nm Δλ = λobs - λ0 = 0.8 nm Δλ/λ0 = 0.8/800 = c = m/sec Wavelength nm nm

30 λ Star at rest = v c λ 0 Energy Star moving away How fast is this star moving away from us? λ0 = nm λobs = nm Δλ = λobs - λ0 = 0.8 nm Δλ/λ0 = 0.8/800 = c = m/sec v = c Wavelength nm nm

31 λ Star at rest = v c λ 0 Energy Star moving away How fast is this star moving away from us? λ0 = nm λobs = nm Δλ = λobs - λ0 = 0.8 nm Δλ/λ0 = 0.8/800 = c = m/sec v = c So, v = m/sec Wavelength nm nm

32 λ Star at rest = v c λ 0 Energy Star moving away How fast is this star moving away from us? λ0 = nm λobs = nm Δλ = λobs - λ0 = 0.8 nm Δλ/λ0 = 0.8/800 = c = m/sec v = c So, v = m/sec Wavelength nm nm or 300 km/sec

33 What light tells us The color of light emitted by an object can tell us its temperature. [hotter objects are bluer; colder objects are redder -or- hotter objects emit more of their light at shorter wavelengths] Light can tell us about the velocity of an emitting object. [via the doppler shift] Light can tell us about the composition of objects. [different atoms/molecules emit (or absorb) light at specific wavelengths] Light can tell us about the distance to a given object. [a given object appears fainter the farther it is from the observer]

34 Apparent Brightness A star s apparent brightness b will depend on intrinsic luminosity L and distance to the star R, as: Units are power per area L = Luminosity (same as power) = energy per second - usually measured in Watts = J/s Brightness = Power per area - usually measured in Watts/m 2

35 Apparent Brightness: why this formula? Surface area of a sphere = 4 π R 2 Apparent brightness b Intrinsic luminosity L Distance to the star R

36 Example using brightness formula If two stars have the same luminosity but one appears 100 times dimmer to the eye, how much farther away is the dim star?

37 Example using brightness formula L =4 R 2 b If two stars have the same luminosity but one appears 100 times dimmer to the eye, how much farther away is the dim star? A: 10 TIMES b 2 = b 1 L =4 R 2 1 b 1 R 2 1 b 1 = R 2 2 b 2 = R 2 2 R 2 1 = R b L =4 R 2 2 b 2 R 1 = R

38 Example using brightness formula You are 1m away from a candle and 5m away from a 100 Watt light bulb, but both the candle and the bulb look to be the same brightness to you. How many watts of luminosity (or power) is the candle producing?

39 What light tells us The color of light emitted by an object can tell us its temperature. [hotter objects are bluer; colder objects are redder -or- hotter objects emit more of their light at shorter wavelengths] Light can tell us about the velocity of an emitting object. [via the doppler shift] Light can tell us about the composition of objects. [different atoms/molecules emit (or absorb) light at specific wavelengths] Light can tell us about the distance to a given object. [a given object appears fainter the farther it is from the observer] Light can tell us about the past!

40 Light (in a vacuum) travels at a fixed and finite speed: speed of light = c = 3 x 10 5 km/s speed = distance / time -or- time = distance / speed The light that we are seeing/observing here on Earth was emitted at some time in the past, where time = distance / c.

41 The farther way an object is from Earth, the farther back in time we are seeing that object. Sun ~8 minutes Jupiter ~35-50 minutes nearest galaxy like the Milky Way ~2.5 Million years

42 Telescopes as Time Machines... distant galaxies Milky Way solar system Distant galaxies provide a view of the Universe when it was much younger.

43 Telescopes as Time Machines... distant galaxies Milky Way solar system Distant galaxies provide a view of the Universe when it was much younger. minutes - hours

44 Telescopes as Time Machines... distant galaxies Milky Way solar system Distant galaxies provide a few yr yr view of the Universe when it was much younger. minutes - hours

45 Telescopes as Time Machines... distant galaxies Milky Way 10 6 yr yr solar system Distant galaxies provide a few yr yr view of the Universe when it was much younger. minutes - hours

46 What light tells us The color of light emitted by an object can tell us its temperature. [hotter objects are bluer; colder objects are redder -or- hotter objects emit more of their light at shorter wavelengths] Light can tell us about the velocity of an emitting object. [via the doppler shift] Light can tell us about the composition of objects. [different atoms/molecules emit (or absorb) light at specific wavelengths] Light can tell us about the distance to a given object. [a given object appears fainter the farther it is from the observer] Light can tell us about the past!

47 What light tells us The color of light emitted by an object can tell us its temperature. [hotter objects are bluer; colder objects are redder -or- hotter objects emit more of their light at shorter wavelengths] Light can tell us about the velocity of an emitting object. [via the doppler shift] Light can tell us about the composition of objects. [different atoms/molecules emit (or absorb) light at specific wavelengths] Light can tell us about the distance to a given object. [a given object appears fainter the farther it is from the observer] Light can tell us about the past!

48 What light tells us The color of light emitted by an object can tell us its temperature. [hotter objects are bluer; colder objects are redder -or- hotter objects emit more of their light at shorter wavelengths] Light can tell us about the velocity of an emitting object. [via the doppler shift] Light can tell us about the composition of objects. [different atoms/molecules emit (or absorb) light at specific wavelengths] Light can tell us about the distance to a given object. or given a distance, [a given object appears fainter the farther it is from the observer] we can measure the luminosity of a Light can tell us about the past! source!

49 Apparent Brightness, Luminosity, and Distance Once we know the distance to a star, we can directly measure its luminosity.

50 The Luminosity of the Sun luminosity is the total energy radiated by an object per unit time (i.e. has units of Watts or Joules/sec) [1 Joule = calories; food calories are kilocalories]

51 The Luminosity of the Sun luminosity is the total energy radiated by an object per unit time (i.e. has units of Watts or Joules/sec) [1 Joule = calories; food calories are kilocalories] Lsun ~ 4 x W that s a lot of energy per second!! For reference, a typical (compact fluorescent) lightbulb has an output of W.

52 The Earth gets only 2 billionth s of the Sun's energy Sun 150,000,000 km Sizes of Earth & Sun are much exaggerated here! Earth

53 So how does the Sun produce all of this energy? What is the relevant physics?

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