Download HOMEWORK #1

HOMEWORK #6 (due start of class October 6)
My Messier object is ____________
(copyright D. McCarthy)
LEARNING GOALS:
1. Continue practicing Polya’s 4-step plan in “How to Solve It.”
2. Practice concepts relating to stellar magnitudes, parallax, luminosity, and brightness.
3. Test your understanding of blackbody spectra and thermal emission.
TO RECEIVE FULL CREDIT:
1. Write your Messier name at the top of your homework.
2. If you submit multiple pages, staple them together.
3. To receive any credit on these problems, you must show how you derived your answer by writing
all the logical steps that led you to it.
4. All sentence responses must be typewritten and in complete sentences. You may handwrite any
arithmetic. Use good English grammar.
5. If you work more than three hours on this assignment, you should stop, record your work
here, and contact Dr. McCarthy.
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1. Optional:
Want to be a better problem solver? Here are some interesting articles.
“Forget What You Know About Good Study Habits” (NYT, B. Carey, Sep. 6, 2010)
http://www.nytimes.com/2010/09/07/health/views/07mind.html?pagewanted=all&_r=0
“Tips on Test Taking” (R. Felder, J. Stice, Chem. Eng. Education, 2014, 48(1), 57-58)
http://www4.ncsu.edu/unity/lockers/users/f/felder/public/Columns/TestTaking.pdf
Choose two problems in Sections #2 & 3 in addition to the problem in Section 4.
2. The “Solar Constant”
#1. The Sun’s luminosity (LSun) is 3.8 x1026 Watts. How much of that energy reaches a 1-meter2 area on
the Earth’s surface? [HINT: Use the inverse-square law of light.]
3. Fundamental Astronomy: Brightness, Luminosity, Magnitudes, Parallax
Read the following paragraph to understand the concept of “absolute magnitude.”
http://astronomy.swin.edu.au/cosmos/A/Absolute+Magnitude
Previously you read that astronomers measure an object’s brightness (B) in “apparent magnitude (m).” In
class we showed that the difference in apparent magnitude between stars #1,2 is related to the logarithm of
their brightness ratio as written below.
m1 – m2 = 2.5 log(B2/B1)
From the inverse-square law of light we also know that a star’s brightness depends on its luminosity and
distance:
apparent brightness = luminosity
4(distance)2
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Just as brightness is related to apparent magnitude, luminosity is related to a term called “absolute
magnitude.” Astronomers refer to a star’s “absolute magnitude (M)” as the apparent magnitude it would
have at an arbitrary standardized distance of 10 parsecs (i.e., 32.6 light-years).
#2. Combine the two equations above to show that the difference between a star’s apparent and absolute
magnitude is given by
m-M = 5 log(d) -5, where “d” is the star’s distance.
#3. The Sun’s absolute visual magnitude is M=4.8. What would the Sun’s apparent magnitude be at the
distance of the Andromeda galaxy, 2.5 million light-years? The Hubble Space Telescope (HST) can detect
stars as faint as 29 in a 10-hour long exposure – its so-called “limiting magnitude.” Could HST detect
“solar-type” stars (i.e., the Sun) inside the Andromeda galaxy?
#4. In Homework #4, we saw that astronomers can measure parallax angles as small as p = 25 as. If HST
can detect stars as faint as m=29, what is the absolute magnitude of the faintest star that could be
detected? If such a star were a “main-sequence” star in the H-R Diagram (below), what is its approximate
temperature?
4. Blackbody Spectra
Read the following articles to understand the concept of blackbody radiation.
https://docs.kde.org/stable/en/kdeedu/kstars/ai-blackbody.html
http://voyager.egglescliffe.org.uk/physics/astronomy/blackbody/bbody.html
Optional reading:
A more thorough summary:
http://galileo.phys.virginia.edu/classes/252/black_body_radiation.html
An interactive blackbody radiation simulator:
http://astro.unl.edu/naap/blackbody/animations/blackbody.html
#5. Figures 1abc below show the blackbody spectra of light emitted by three stars of different
temperatures. According to the “Stefan-Boltzmann Law,” the total energy emitted by a 1-meter2 patch of a
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star’s surface is proportional to temperature to the fourth power, (i.e., T4). Also, Wien’s Law states that
the wavelength (max) of the maximum brightness is inversely-proportional to the star’s temperature.
a). Use Wien’s Law (below) to calculate the temperature of the hottest star.
max = 3 x 106 /T,
where T is the star’s temperature in degrees Kelvin and wavelength is measured in nanometers.
b). As seen by your eye, which object would appear the bluest and which object the reddest? Explain your
reasoning.
c). Based on these graphs, which star emits the most total energy? Explain your reasoning. Relative to star
#3 what are the ratios of the three stars’ total energies?
Figure 1a. The spectrum of star #1 (our Sun!) showing the amount of
light emitted at different wavelengths.
Figure 1b. The spectrum of star #2 showing
the amount of light emitted at
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different wavelengths.
Figure 1c. The spectrum of star #3 showing the amount of light emitted at different
wavelengths.
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