Homework is due in class at 12:30PM every thursday, starting Sept. 4. Write your name and section (i.e. Wed @ 2) on each homework and please staple your sheets together. The homework questions can be discussed with your classmates, and also in TALC, but must be written up individually. Late homework will not be accepted. Your lowest homework grade will be dropped in determining your final grade.
HOMEWORK
ASSIGNMENTS
1. Read Chapter 1 quickly, especially section 1.3 and figures
1.9-1.13. Read all of Chapter 2 carefully (3 hours).
Problems From CH.2: Problems 2.4, 2.5, 2.6, 2.7, 2.8, 2.12.
Hint for 2.12: Derive an expression for log_10 P in terms of log_10 a and log_10
M from Kepler's 3rd Law. You should get a linear equation, with a slope and intercept.
2. Read Chapter 3: Problems 3.2, 3.6, 3.7, 3.8, 3.9, 3.12
Hint for 3.12: You will arrive at an equation that can't be solved analytically,
but instead must be solved numerically (by a computer or calculator).
You may use trial and error. It helps to define a new variable, x = hc/(lambda k T).
Solving the equation will take some creativity!
3. Read Chapter 4: Problems 4.2, 4.3, 4.6, 4.11 part a) only, 4.17 (use the binomial expansion:
(1 + eps)^b ~ 1 + b eps ,
for eps << 1 . You should verify this approximation with some tests on your calculator.
4. Read Chapter 5: Problems 5.1, 5.5, 5.8, 5.9, 5.16
5. Read Chapter 6: Problems 6.2, 6.6, 6.13, 6.15
Extra Credit: Google "Space Interferometry Mission" and explain in a few sentences how SIM (sometimes called "SIM-Lite") will achieve an angular resolution of 4x10-6 arcsec (4 millionths of an arcsec). Hint: Does the phase delay have to be a full 1/2 lambda to detect the changed angle, or some other delay? (Note: In the statement of this extra credit problem on the blackboard, I erroreously stated that the textbook gave SIM's resolution as 0.004 arcsec. The extra credit problem above is now correct: it is still interesting to figure out how a resolution of 0.000004 arcsec is achieved by SIM.)
6. Read Chapter 7: Problems 7.1, 7.4, 7.6, 7.10, 7.11, 7.12, 7.14
For problems 7.10 and 7.11, you only need one to two sentences containg a clear explanation.
7. Read Chapter 8, pgs 202-219: Problems 8.3, 8.4, 8.5, 8.9
8. Read the rest of Chapter 8!
Problems: 8.10, 8.13, three problems, as follows:
Problem 3. Examine the spectra of stars of all spectral types: O, B, A, F, G, K, M (use Figures 8.4 and 8.5,
or spectra you find on the web.)
Explain in a paragraph of 6-8 sentences why the absorption line, Balmer beta, has the strength (darkness) that it does
as a function of spectral type, from O to M. Write your paragraph as if explaining it
to a physics major who hasn't taken Astro 7A.
Problem 4. Ionized calcium has two strong transitions, at 393 and 396 nm, and they appear in the spectra in Figures 8.4 and 8.5.
Those two lines are just barely resolved in those spectra.
a) Locate those two lines in the spectra in the figures. In which spectral types do you see those lines,
and in which are they absent?
b) Explain in a paragraph why these absorption lines due to ionized calcium appear in some stellar spectra,
but not in others. One paragraph of 5-7 sentences is all you'll need.
Problem 5.
The surface of the sun is 5800K.
Explain in words (no calculation needed) whether you expect the hydrogen line, Paschen alpha,
to appear as an absoption line in the spectrum of the Sun. A few sentences
are all that is needed.
Graphics and slides from Lecture:
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Stellar Spectra
Note: Please write the
name of your GSI and your section number at the top of every problem set.
9. Chapter 9: Read pgs 231-258, 267-272 (34 pages). Most important are pages 240-247.
Six Problems: 9.1, 9.4, 9.6, 9.9, 9.12,
Last Problem #6: Iron atoms in the Sun's atmosphere at 5800K are moving with a Maxwell Boltzmann distribution, some toward us and some away, causing a Doppler shift when the light is absorbed. What is the width of an absorption spectral line (in nm) due to this thermal Doppler Broadening of spectral lines of iron? An answer within a factor of 2 is good enough.
Answer: The iron atoms in the Sun's atmosphere at T = 5800 K are moving with the Maxwell-Boltzmann speed distribution, as stated in the problem. As an atom absorbs light, it may be moving toward or away from us at Earth. The one dimensional Maxwell-Boltzmann distribution was given in class, and we showed that the standard deviation of the component of velocities along one dimension (the x-axis, say) is given by:
sigma = sqrt( kT/m)
Here, sigma is the standard deviation of the radial velocity of the iron atoms. In this equation, T is the temperature (5800K), m is the mass of the atom (Fe), and k is the usual Boltzmann constant. It is OK for students to use: sigma = sqrt(2kT/m) (for the most probable speed). We need the mass of the iron atom. You can look it up, or multiply its atomic "weight", 56, by the mass of a proton: m = 56 * 1.67e-27 = 9.4e-26 kg Applying this equation, we have:
sigma = sqrt(kT/m) = sqrt(1.38e-23 * 5800. / 9.4e-26) = 922 m/s .
Any answer within 50% of this is fine. This "sigma" is the typical velocity toward or away from us. Applying the Doppler formula, we have the wavelength shift that causes the spectral line to have a width: delta lambda = v/c wavelength = 922/3e8 x wavelength The students may choose any wavelength, such as lambda = 527 nm. That gives:
delta lambda = 922/3e8 527 nm = 0.0016 nm = 0.016 Angstroms
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Hints for Problems:
9.1 (For why it's dark, consider Wien's Law and the wavelength senstivity of your retina.),
9.4 (Hint: change variables and use integral tables)
9.12 (Hint: Use the fact that you look back into the star down to tau ~2/3. Only a few sentences are needed for this problem.)
10. Chapter 10: Read pgs 284-300 and 307-312 (22 pages).
Six Problems: 10.1, 10.4 part a) only, 10.7, 10.12, 10.14, 10.21
Homework #11. Chapter 11: Read pgs 349-362 and 381-393 (25 pages).
Two Problems:
Problem #1. Starting with the pp-reaction in the Sun, describe the steps by which energy gets to a Thanksgiving dinner. Start from the core of the Sun and describe in one sentence the type of energy and way it is transported to the next step, from the Sun's center to the center of the turkey in an oven (either gas or electric). For each step, note the type of energy and the transport mechanism to the next step. Explain the path in a numbered sequence, i.e.
1.The pp-reaction converts H to He, producing gamma rays that travel at the speed of light. It also produces fast-moving particles.
2. The gamma rays then deliver their energy to .... by ....
3. etc.
Problem #2
a)Explain two ways that astronomers detect the Solar Sunspot cycle
b)Explain two ways that the spot cycles on other stars can be detected.
Homework #12. Read all of Chapter 23: It's 20 pages of fun, easy reading.
Five Problems:
Problem #1: 23.6
Problem #2: Figure 23.1 shows the measured velocities for 51 Pegasi.
From the noise level in the data, what is the maximum mass that a planet
could have orbiting at 1 AU that would be missed due to that noise.
Assume the mass of 51 Peg is 1 Solar mass.
Problem #3:
b. Draw a sketch of the transit of the planet across the face of the star. Be sure to include the orbital inclination in your calculation. Assume we are viewing it from very, very far away.
c. What is the duration of the transit of the planet across the star, in hours? Be sure to include in your calculation the chord length of the planet's path across the disk of the star.
d. What is the fractional depth of the transit light curve, i.e. what fraction of the star's light is blocked when the planet crosses the star, at the time of mid-transit?
e. Sketch the brightness of the star as a function of time during roughly 10 hours, beginning somewhat before ingress and ending after egress of the transit. Be sure to label your time axis and your vertical axis (the bottom of the vertical scale should be appropriately established, not zero.)
Problem #4: Within a protoplanetary disk at any radius, r, the temperature of the dust and gas is set by equilibrium between the incoming starlight that heats the particles and the blackbody radiation from the dust that cools them. At what radius, r_ice, within the disk (in AU) will water be frozen into ice ? Assume that water freezes at 0C. That radius is called the "ice-line" or "snow line" within the protoplantary disk. Assume the young star has a luminosity equal to that of the Sun.
Problem #5: 23.8 in the chapter.
