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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

questions.

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.

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Part a: Blackbody Radiation

Start by opening the Phet blackbody simulator

(https://phet.colorado.edu/sims/html/blackbody-spectrum/latest/blackbodyspectrum_en.html) 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

1.

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.

2.

What type of EM radiation is this?

3.

How does this compare with the value calculated in the Lecture?

4.

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?

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5.

Calculate the wavelength of maximum emission for the new temperature.

6.

What type of EM radiation is this?

7.

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.]

8.

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).

9.

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?

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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)?

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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)

(https://kcvs.ca/details.html?key=planetaryClimates)

Once you’ve launched the visualization, click on the “Go to” menu and select “Build a

Planet”.

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

albedo.]

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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.

Mars

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!]

Jupiter

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.

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31. What would the temperature of Jupiter need to be for it to be in radiative

equilibrium?

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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