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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?
A prism bends
photons more
or less
depending on
their
wavelength
Cloud
of
Gas
A prism bends
photons more
or less
depending on
their
wavelength
Cloud
of
Gas
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
hc
l
E = energy of a photon
h = Planck’s constant
c = speed of light
l = 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
• 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 radiation
according to its temperature
Blue: Hot or Not?
http://www.straightdope.com/mailbag/mhotflame.html
Blackbody Definition
• Does not reflect incoming radiation, only
absorbs
• Emits radiation, depending on temperature
• Temperature and emitted radiation intensity
follow a special relationship
One way of
creating a
blackbody
Photon enters
If hole is very small,
what is probability that
it exits?
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
Intensity
Special Relationship
For Intensity, think
photons/second on a
small area
Wavelength
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
Energy Flux Intensity
Special Relationship
For Intensity, think
photons/second on a
small area
Wavelength
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:
F ~T
4
Special Relationship
Energy Flux Intensity
Stefan-Boltzmann
Law tells us that if we
add up the energy
from all wavelengths,
then the total energy
Flux
F~T
Wavelength
4
Energy Flux Intensity
Special Relationship
Wien’s law tells us that
lmax depends on
temperature
Max intensity at lmax
lmax Wavelength
lmax
1
~
T
Energy Flux Intensity
Special Relationship
Sketch this curve for larger and
smaller T
Wavelength
Wavelength of peak
decreases as
temperature
increases
At high wavelengths,
intensity goes to zero
Overall amplitude
increases with
Temperature
As wavelength
goes to zero,
intensity goes to
zero
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 real
curve 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?
Left
side is
white
Right side is
(should be) a
little “pinker”
• http://casa.colorado.edu/~ajsh/colour/Tspectrum.html
If blue light has higher energy,
and energy is proportional to
temperature, why are my cold
spots blue?
Energy Flux
5
4
3
2
1
0
A
B
C
• 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