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ESS 9 Fall 2009
Week 2 Discussion
Oct. 8-9, 2009
1
Blackbody Radiation
Due Date:
Oct 15-16
Name__________________________ Id#____________________
Section ______________
Summary. The electromagnetic radiation coming from an object in space is a mixture of reflected radiation
(that was originally produced by the Sun) and emitted (radiated) radiation produced by the body itself. The
spectrum of emitted radiation has a characteristic shape-- its amplitude and peak wavelength depend on the
temperature of the body. The reflected and emitted radiation can tell us much about a body (like an asteroid),
such as its temperature, size and composition.
Exercise 1: Blackbody radiation.
Recall that all objects in the universe-- from a lump of ice to a star-- emit electromagnetic (EM)
radiation. The EM waves emitted by an object are not at a single frequency, however, but are spread over a
range of frequencies, as we will see today. This so-called blackbody radiation (so-called because it applies to
opaque bodies that do not reflect light) has a specific temperature-dependant shape when plotted on a graph.
This shape is called the Planck curve after Max Planck who discovered the equations that describe this curve.
Note that a blackbody is a theoretical object that absorbs 100% of the radiation that hits it, i.e., it does not
reflect any radiation, but emits radiation according to its temperature.
To examine the spectrum of radiation from a body, first, load the simulator.
The fraction of incident sunlight reflected by a body is called the albedo. Set the albedo to zero, so
we see only the emitted spectrum.
Set distance = 1 AU
Set diameter = 1 m.
Change the temperature and see how the peak power (Watts, vertical axis), total power (readout), and
peak wavelength (microns, horizontal axis) change with temperature, and how the emitted wavelengths
compare with visible light (illustrated by the rainbow-like strip). Don't be confused when the autoscaling
feature causes the units on the horizontal axis to suddenly change by a factor of 5 or 10; the rainbow strip still
shows you where the visible wavelengths are located.
Start by seeing the large effects that occur when you change the temperature by powers of ten, and
then go to small increments and drop from high temperatures (say 8000 or 9000 K) by the smallest increment
possible, the number in the middle (i.e., change from 9000 to 8900 to 8800 K, etc.).
As the temperature is increased,
total power increases/decreases,
and peak wavelength increases/decreases.
ESS 9 Fall 2009
Week 2 Discussion
Oct. 8-9, 2009
2
Use the simulator to determine the following:
Object
Temperature
Ice at freezing point 270 K
outer SS moon
100 K
Human
310 K
hot oven
620 K
Star
6000 K
Peak
Total Power
Wavelength
Roughly how hot must something be
before it starts glowing red-hot? (watch
the 'Perceived Color' readout)
_____________ (remember to give
the units here and in each of the blanks
you fill out in this experiment).
The human body emits more power than
ice by a factor of ___________.
The 'hot oven' has twice the temperature
of the human. By what factor does the peak wavelength
change? ____________ By what factor does the total power change? _______________ ___.
These factors can be expected from the relationships that relate temperature to wavelength and to power:
Wien’s law: wavelength (m) *temperature (K) = 0.0029
or, in different units:
wavelength (m) *temperature (K) = 2900
Stefan-Boltzman law: Power = σ T4 (power is proportional to T4)
Exercise 2: Using the radiation spectrum to determine the surface temperatures of planets. Use
the simulator to estimate the temperature that produces these peak wavelengths:
Peak
Object
Temperature
Voyager 2 showed that Neptune had a peak wavelength
Wavelength
and temperature essentially identical to that of Uranus.
Uranus 57 m
Why was this unexpected?
Jupiter
29 m.
________________________________
Venus
10 m
____________________________
Does the value you filled in above for Venus’ temperature correspond to the surface temperature of Venus?
yes/no. (hint: where is the radiation that you observe coming from?)
According to the Stefan-Boltzman law, if you double the temperature of an object, how much more power
will it radiate?
Alpha Orionis, aka Betelgeuse, is the second brightest star in the winter
constellation Orion the Hunter, and the 9th brightest star in the sky. It forms Orion’s
right shoulder and is clearly reddish in appearance.
Is Betelgeuse hotter or cooler than the Sun? ____________________________
We know that Betelgeuse is 640 light years from the Earth, and therefore we can
calculate its intrinsic brightness (“luminosity”). It puts out 135,000 times more
power than the Sun! Given its spectral color and this fantastic luminosity, discuss
with your neighbor what might you conclude about Betelgeuse?
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