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Lecture 12
ASTR 111 – Section 002
Measurements in Astronomy
• In astronomy, we need to make remote and indirect measurements– Think of an example of a remote and indirect
measurement from everyday life
Using Light
• Light has many properties that we can use to learn about what happens far away
• Light interacts with matter in a special way
• Only photons with special wavelengths will interact with atom
• How will this affect what a person will see at point X?
• When is the atom “hotter”?
X
Why is UV light usually blamed for skin cancer? What is special about it compared to other light sources?
Cloudof
GasA prism bends photons more or less depending on their wavelength
Cloudof
GasA prism bends photons more or less depending on their wavelength
What will the spectrum look like here?
Emission line spectrum
Continuous Spectrum• A blackbody emits
photons with many energies (wavelengths) – a continuous spectrum
What will the spectrum look like here?
Absorption Spectrum
Absorption vs. Emission
• What type of spectrum is produced when the light emitted from a hot, dense object passes through a prism?
• What type of spectrum is produced when the light emitted directly from a cloud of gas passes through a prism?
• Describe the source of light and the path the light must take to produce an absorption spectrum
• There are dark lines in the absorption spectrum that represent missing light. What happened to this light that is missing in the absorption line spectrum?
From Lecture Tutorials for Introductory Astronomy, page 61.
Each chemical element produces its own unique set of spectral lines
• Stars like our Sun have low-density, gaseous atmospheres surrounding their hot, dense cores. If you were looking at the spectra of light coming from the Sun (or any star), which of the three types of spectra would be observed?
• If a star existed that was only a hot dense core and did not have a low-density atmosphere surrounding it, what type of spectrum would you expect this particular star to give off?
• Two students are looking at a brightly lit full Moon, illuminated by reflected light from the Sun. Consider the following discussion between two students about what the spectrum of moonlight would look like:– I think moonlight is just reflected sunlight, so we will see the Sun’s
absorption line spectrum.– I disagree, an absorption spectrum has to come from a hot, dense
object. Since thie Moon is not a hot, dense object, it can’t give off an absorption line spectrum.
Do you agree or disagree with either or both of these students? Explain your reasoning.
• Imagine that your are looking at two different spectra of the Sun. Spectrum #1 is obtained using a telescope that is in a high orbit far above Earth’s atmosphere. Spectrum #2 is obtained using a telescope located on the surface of Earth. Label each spectrum below as either Spectrum #1 or Spectrum #2.
Would this make sense?
This dark line was removed
Energy and electromagnetic radiation Planck’s law relates the
energy of a photon to its frequency or wavelength
E = energy of a photonh = Planck’s constantc = speed of light = wavelength of light
The value of the constant h in this equation, called Planck’s constant, has been shown in laboratory experiments to be
h = 6.625 x 10–34 J s
hc
E
• Which electromagnetic wave has a higher energy: one with f=10 cycles per second or f=1 cycles per second?
Three Temperature Scales
Color and Temperature
An opaque object emits electromagnetic radiationaccording to its temperature
http://www.straightdope.com/mailbag/mhotflame.html
Blue: Hot or Not?
Blackbody Definition• Does not reflect incoming radiation, only
absorbs• Emits radiation, depending on temperature• Temperature and emitted radiation
intensity follow a special relationship
Photon enters
If hole is very small, what is probability that it exits?
One way of creating a blackbody
Wien’s law and the Stefan-Boltzmann law are useful tools for analyzing
glowing objects like stars
• A blackbody is a hypothetical object that is a perfect absorber of electromagnetic radiation at all wavelengths
• Stars closely approximate the behavior of blackbodies, as do other hot, dense objects
• Blackbodies do not always appear black!
–The sun is close to being a “perfect” blackbody
–Blackbodies appear black only if their temperature very low
Special Relationship
Wavelength
Inte
nsity
For Intensity, think photons/second on a small area
Question
• Why is photon/second similar to energy/second? How are they related?
Watt? Energy Flux?
Flux
Flux is a measure of how much “stuff” crosses a small patch in a given amount of time. Can have flux of green photons, red photons, etc.
Blackbodies and Astronomy
Blackbody Laws• Stefan-Boltzmann Law – relates
energy output of a blackbody to its temperature
• Wein’s law – relates peak wavelength output by a blackbody to its temperature
Special Relationship
Wavelength
Ene
rgy
Flu
x In
tens
ity For Intensity, think photons/second on a small area
Stefan-Boltzmann Law
• A blackbody radiates electromagnetic waves with a total energy flux F directly proportional to the fourth power of the Kelvin temperature T of the object:
4~ TF
Special Relationship
Wavelength
Stefan-Boltzmann Law tells us that if we add up the energy from all wavelengths, then the total energy Flux
4~ TF
Ene
rgy
Flu
x In
tens
ity
Special Relationship
Wavelengthmax
Wien’s law tells us that max depends on temperature
Max intensity at max
T
1~max
Ene
rgy
Flu
x In
tens
ity
Special Relationship
Wavelength
Sketch this curve for larger and smaller T
Ene
rgy
Flu
x In
tens
ity
Overall amplitude increases with Temperature
At high wavelengths, intensity goes to zero
As wavelength goes to zero, intensity goes to zero
Wavelength of peak decreases as temperature increases
Color and Temperature
What would this object look like at these three temperatures?
Why does it glow white before blue?
• Can this figure help us explain?
• Can this figure help us explain?
Near this temperature, this special combination of intensities is what we call white. Also, the realcurve is a little flatter near the peak
The Sun does not emit radiation with intensities that exactly follow the blackbody curve
So, what color is the sun in space?
• http://casa.colorado.edu/~ajsh/colour/Tspectrum.html
Right side is (should be) alittle “pinker”
Left side is white
If blue light has higher energy, and energy is proportional to temperature, why are my cold spots blue?
AB
C
Ene
rgy
Flu
x
1
2
3
4
5
0
• Which curve represents an ideal blackbody?– Curve A– Curve B– Curve C
• If the object in Figure 1 were increased in temperature, what would happen to curves A, B, and C?
• Curve C is more jagged. The locations where the curve C is small correspond to– Spectral lines of a blackbody– Spectral lines of atmospheric molecules– Instrumentation error– Diffraction lines– Spectral lines of the lens used to the light into
colors
• What is the intensity of curve B at 550 nm?– Impossible to tell; 550 nm is not shown in this
figure– Nearest 0.2– Nearest 0.1– Nearest 0.05– Nearest 0.0
• Venus has no atmosphere. If you measure the spectrum from its surface, – Curves B and C would not change– Curve C would look more like A– Curve C would look more like B– Curve B would look more like A– Curve B would look more like C
• White light is composed of– Equal intensities of all colors of the rainbow– Unequal intensities of all colors of the rainbow– Equal number of photons of all colors of the
rainbow– Unequal number of photons of all colors of the
rainbow– Equal numbers of red, green, and blue
photons
• Does a blackbody have color?– Yes, and they all appear the color of the sun– No, you cannot see a blackbody– Yes, but its depends on its temperature– Maybe, it depends on if it is an ideal
blackbody
• Why is the best reason for putting a telescope in orbit? – Closer to stars– Better view of celestial sphere– The speed of light is higher in space– Less atmospheric interference– Cost