Arizona State University Differences in Colors of Star and Peak Emission Questions


I need support and a starting path for this lab. It is about lab covering temperature of a planet and albedo, distance
from the sun, and surface temperature. A starting point would be amazing and so appreciated. thanks in advance

ATS 201 Module 2 Lab:
Blackbody Radiation and Radiative Equilibrium
50 points total. 1.5 points per question, except the last one is 2 points.
For this lab, you will first use an interactive online simulator of blackbody radiation to
study the relationship between the temperature of an object and the amount and type of
electromagnetic (EM) radiation that it emits. Then, you will use another simulator to
study the effect of planetary albedo, distance from the sun, and surface temperature on
the energy budget of a planet. Our overall goal is to explain the relationship between the
radiative equilibrium temperature of a planet and these different variables.
Directions: Submit your answers as a Word (DOC) file or a PDF file (preferable).
Please number your answers. Include units for all numerical values (that have units).
To make it easier to type, you can express exponents using the ^ symbol. For example,
5.67 x 10^-8 W m^-2 K^-4. Use complete sentences for “Why” and “Explain”-type
For calculations, show your steps, starting with the equation that you use. If you do
not write the equation and you make a calculation mistake, then the grader has no
choice but to heavily penalize you for your mistake. You can write the equation in a
very crude form without the use of equation editors. For example, if you are calculating
the blackbody emission of a star with a temperature of 5778 K:
Stefan-Boltzmann law: E = sigma T^4.
E = 5.67 *10^-8 W m^-2 K^-4 * (5778 K)^4
E = 6.3*10^7 W m^-2.
Please complete the readings, view the narrated lectures, and take the quiz for the
module before you do this assignment, so that you have had practice with some of the
equations. I recommend keeping Lectures 2.3 and 2.4 handy, since you will be referring
to them.
Be sure to include units for all values.
Part a: Blackbody Radiation
Start by opening the Phet blackbody simulator
( web page.
The y-axis indicates the amount of radiation emitted by the object for a given
wavelength. Don’t worry about the specific units here; we are interested in the relative
emission for different wavelengths or for objects at other temperatures. The vertical
rainbow indicates the visible wavelengths.
To increase the temperature, move the slider up and down. The + and – magnifying
glasses zoom in on the x- or y-axis. Notice that the y-axis buttons increase or decrease
the range of the y-axis by an order of magnitude (multiply or divide by 10) for every two
clicks, while the x-axis buttons double or halve the x-axis range for every click.
Comparing EM emission from the sun and the Earth
Use the slider to set the temperature closest to that of the sun (5800 K, the
actual temperature of the sun is more like 5778 K). Estimate the wavelength of
maximum emission from the plot.
What type of EM radiation is this?
How does this compare with the value calculated in the Lecture?
Change the temperature to 250 K, approximating Earth without an atmosphere
(which is actually ~ 255K but we are limited in the increments we can put into
the simulator. What happens to the curve? Why do you think this happens?
Calculate the wavelength of maximum emission for the new temperature.
What type of EM radiation is this?
Note that this wavelength is too high to appear on the default graph (assuming
you haven’t already zoomed in or out at all). Now, zoom OUT (- magnifying
glass) on the x-axis until you are past the wavelength of maximum emission.
How many times do you have to zoom out? [Note: you still will not be able to
see the curve yet; that is the next question.]
Now zoom IN (+ magnifying glass) on the y-axis until you can see the new
curve. How many times do you need to zoom in before the peak of the curve is
near the middle of the plot? (This won’t be exact; you’ll likely need to adjust the
x-axis once or twice to really center everything up).
Calculate the total emission of radiation (power per unit area) of a planet at a
temperature of 255 K (using the equation from the lecture).
10. What is the ratio of this total emission at 255 K to the total emission at 5778 K
(from lecture 2.3)?
11. If every power of ten corresponds to two clicks on the y-axis, about how many
clicks do you estimate it would take to go from the well-displayed 250 K
spectrum to the 5800 K spectrum? [Note that this is actually less than the real
number required by the simulation, since the shapes of the curves are different
(see the Key Figure in Lecture 3.3).]
12. Why, if the sun emits so much more radiation than the Earth, does the Earth’s
emitted radiation approx. balance the Earth’s absorbed solar radiation?
Other stars
The temperature of stars in the universe varies with the type of star and the age of the
star among other things. By looking at the shape of the spectrum of light emitted by a
star, we can tell something about its average surface temperature. This photo (from
Wikipedia page for Wien’s Law), shows start in the constellation Orion.
The star symbol in the upper center of the simulator shows the color of an object at the
specified temperature.
13. Betelgeuse (in the upper left of the photo) has a temperature of 3300 K. Using
the simulator, where in the spectrum is the peak emission?
14. What color is the star on your screen (not asking anything fancy here)?
15. Vega is the brightest star in the constellation Lyra, and will become our next
northern pole star in about 10,000 years. Vega has a temperature of 9,200 K. In
what part of the spectrum is its peak emission?
16. What color is the star on your screen?
17. Why do the colors of the stars not necessarily match their peak emissions?
Further exploration (beyond planets and stars)
18. What is the wavelength at which the most power is emitted for an incandescent
light bulb operating at 3045K?
19. Explain why regular incandescent bulbs waste a lot of energy. Be sure to
include your reasoning.
20. For a given wavelength, does the intensity always decrease as you decrease
the temperature? Support your answer.
Part b: Radiative Equilibrium (or not)
Now switch to this website: Planetary Climates (*see note)
Once you’ve launched the visualization, click on the “Go to” menu and select “Build a
On the bottom of the window, you can adjust the sliders to alter the albedo, greenhouse
effect, distance from the sun, and surface temperature of the planet. To specify a
variable to be a specific value, click on “#” and enter the value into the pop-up box.
We’ll talk more about the greenhouse effect in the next module. For now, just think of it
as a reduction in terrestrial radiation emitted by the planet. While the emission still
increases with temperature, the planet does not emit as much radiation to space as it
would if it were a perfect black body.
The distance from the sun determines the incoming solar radiation. 1 AU (astronomical
unit) corresponds to the Earth-sun distance. That is, Earth is one AU away from the sun.
The “Planetary Data” menu shows the albedo, distance from the sun, and surface
temperature for some planets in the solar system. [Note: there is a typo for the Earth’s
The main window shows an illustration of the distance from the sun and the energy
budget of the planet. If the energy balance for a planet is (close to) in balance, the
numbers will turn green.
21. If the albedo is 0, the “Energy In” value is the Incident (on Incoming) Solar
Radiation (Q, lecture 2.4). Although the simulator only allows a minimum albedo
of 0.01, this is close enough to zero for our purposes. Specify the planet to have
Mars’ distance from the sun, and set the albedo to 0.01. Using the simulator,
what is Q for Mars?
22. According to the simulator, what is the approximate Q for a planet that is Earth’s
distance from the sun? [Note: it does not match the value we use b/c the albedo
is not exactly zero.]
23. What fraction of the Earth’s incident sunlight is Mars’ incident sunlight?
24. Now set Mars’ albedo and distance from sun to its actual values. What is the
“Energy in”?
25. What do we call this value in the lectures?
26. Define radiative equilibrium.
27. Assuming Mars is in radiative equilibrium, calculate its temperature (in K) using
the appropriate equation from this weeks lecture.
28. Mars has almost no greenhouse effect, so we can set it to 0 and use the
simulator to calculate the energy emitted. Adjust the “Surface Temp” slider to
the value you calculated in the previous step. Note that you will need to first
convert the temperature from K to °C. What is the Energy Out? [If you did the
previous calculations correctly, the energy numbers should turn green,
indicating the planet is in radiative equilibrium. Congratulations!]
29. Jupiter is unusual (for our solar system) in that it is not in radiative equilibrium.
Using the given albedo and distance from the sun, what is the absorbed solar
radiation of Jupiter?
30. Assume Jupiter does not have a greenhouse effect. Calculate the emitted
terrestrial radiation assuming a temperature of -148 °C. You can verify your
result using the simulator.
31. What would the temperature of Jupiter need to be for it to be in radiative
32. Is Jupiter warming or cooling?
33. Speculate as to why Jupiter is not in radiative equilibrium. The specific reason
you give does not have to be true as long as the reasoning explains the sign of
the difference between energy in and energy out. For example, aliens have
placed a special device inside Jupiter that …

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