Astronomy midterm question: seeing the past

Astronomy 210 Midterm 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

[20 points.] Sir Martin Rees, Astronomer Royal of Great Britain remarked that, "we in astronomy have an advantage in studying the universe, in that we can actually see the past." Explain what makes this possible.

Solution and grading rubric:

• p = 20/20:
  Correct. Explains how the finite speed of light causes distant objects to appear as they did in the past.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Describes how lookback time affects the appearance of distant objects, but does not explain how this is caused by the finite speed of light, and/or explains that this is caused by the expansion of the universe.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Discusses how the motions of objects that be backtracked to determine their motion at some time in the past.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. General discussion of how evidence is used to infer information about the past.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30676
p: 39 students
r: 9 students
t: 2 students
v: 7 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 5659):

Another sample "p" response (from student 1192, who admits to somehow blanking out on this exam):

Another sample "p" response (from student 6969), leading off with some expository statements, but finishing on task:

Another sample "p" response (from student 6615), graphically illustrating the effects of the finite speed of light:

A sample "r" response (from student 0047):

Astronomy midterm question: deep in the thick of things

Astronomy 210 Midterm 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

[20 points.] Consider the following observation by Henry Freudenreich:

"The central reason astronomers have been slow to understand the Milky Way is simply because we are deep in the thick of things: The other stars, the gas and especially all the dust in the disk prevent us from seeing the full extent of the galaxy's structure."
--Henry Freudenreich, Am. Sci. vol. 87 no. 5 p. 418 (1999)

Explain how it is still possible to map the spiral arm structure of the Milky Way.

Solution and grading rubric:

• p = 20/20:
  Correct. Massive stars, due to their extremely short lifetimes, are born and die only in the spiral arms; and are bright enough to be seen through some of the obscuring gas and dust. Similarly for HII (emission) nebulae. Radio waves emitted from cold hydrogen gas are not obscured by gas and dust. Observing the locations of all three result in a spiral arm map of the Milky Way.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Describes direct or indirect evidence other Milky Way properties, such as its thin disk structure, size/mass, and/or location of the center of the Milky Way.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. May use other spiral galaxies to infer that the Milky Way must also have spiral arms, or some other observational evidence that does not directly reveal the structure of the Milky Way.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30676
p: 11 students
r: 4 students
t: 18 students
v: 15 students
x: 9 students
y: 0 students
z: 0 students

A sample "p" response (from student 0008):

Another sample "p" response (from student 0321):

A sample "p" response (from student 9891, who is scared of the implications of this response):

A sample "x" response (from student 2626), going out on a limb:

Astronomy midterm question: cooler, smaller star?

Astronomy 210 Midterm 2, spring semester 2009
Cuesta College, San Luis Obispo, CA

Consider the following statement: "If two stars have the same brightness, the star with the lower temperature will be smaller." Discuss whether this statement is true or not, and support your answer using Wien's law and/or the Stefan-Boltzmann law.

Solution and grading rubric:

• p:
  Correct. Discusses how the Stefan-Boltzmann law (luminosity (brightness) proportional to size×Temp⁴) explains that two stars can have the same brightness if the smaller star is hotter, and the larger star is cooler.
  
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least recognizes that the Stefan-Boltzmann law is applicable, but argument is garbled.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Agrees or disagrees with statement with no discussion.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 30676
p: 38 students
r: 6 students
t: 5 students
v: 7 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 2881):

Another sample "p" response (from student 4489), utilizing a "box" method to compare the blackbody properties of two stars:

Another sample "p" response (from student 5659), using an "obvious" explanation:

A sample "p" response (from student 6615) using a variation of the box method:

A sample "p" response (from student 5065) that uses a H-R diagram:

A sample "p" response (from student 0321) that claims that this was subject was not discussed in class, and yet manages to deduce the correct answer:

A sample "r" response (from student 4498) that garbles the box analysis somewhat:

Physics midterm problem: cable-supported beam

Physics 205A Midterm 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 8.34

[20 points.] A uniform beam of weight 560 N is held horizontal by a pivot and a cable attached as shown at right. The cable is attached halfway between the center of gravity (CG) of the beam, and the pivot point. Determine the x- and y- components of the force exerted by the pivot point on the end of the beam. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Sets up Newton's first law for forces along the x- and y- directions, as well as for torques about an axis that does not include the physical pivot attached to the wall. Solves these three equations for three unknowns T, F_x, and F_y. May directly solve for F_x = 408 N and F_y = 560 N by placing the axis where the cable attaches to the beam. (The tension in the cable is 1,190 N.)
  
• r = 16/20:
  Nearly correct, but includes minor math errors. At least F_x or F_y is correct from applying Newton's first law. May only have correct value for T, with some methodical (but problematic) approach to finding F_x and/or F_y. Or has complete and correct set of Newton's first law equations, but algebra is problematic.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least some serious attempt at applying Newton's first law, and care in resolving components, measuring lever arms, and calculating torques.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Mainly resolving magnitude of weight into 20-70-90 degree triangle components.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Sections 30880, 30881
p: 0 students
r: 9 students
t: 19 students
v: 9 students
x: 2 students
y: 0 students
z: 1 student

A sample "r" response (from student 1830), solving successfully only for T and for F_x:

Another sample "r" response (from student 2679), applying Newton's laws to all three degrees of freedom, but bogged down in the ensuing algebra:

Astronomy midterm question: expansion, not explosion

Astronomy 210 Midterm 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

[20 points.] Discuss why the expansion of the universe is not like an explosion, using observations and evidence related to the Hubble law in your explanation.

Solution and grading rubric:

• p = 20/20:
  Correct. Hubble's law is that the recession velocity of galaxies is proportional to distance, evidence is that there is a greater redshift of absorption lines for distant galaxies compared to nearby galaxies. (Also there is no unique center to this expansion of space.) This is in opposition to an explosion, where the velocity of particles is inversely proportional to the distance from the center of the explosion.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Describes how an explosion is not like the actual expansion of the universe, but Hubble's law discussion is problematic or incomplete.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on other aspects of explosions, with little or no substantive discussion of Hubble's law.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30674
p: 9 students
r: 5 students
t: 10 students
v: 9 students
x: 0 students
y: 0 students
z: 0 students

A similar version of this question was asked as a multiple-choice question in Spring 2009.

A sample "p" response (from student 1959), positing that the galaxies in the universe have all drank the "Haterade":

Another sample "p" response (from student 2902), appealing to the "everyone smelt it, so everyone dealt it" theory:

A sample "p" response (from student 2947) explaining in pictures what word cannot do justice:

Another sample "p" response (from student 5398) using a "no-center" argument:

Astronomy midterm question: type Ia supernova sun?

Astronomy 210 Midterm 2, spring semester 2009
Cuesta College, San Luis Obispo, CA

Decide whether the sun will ever become a type Ia supernova[*]. If so, then specifically discuss how this process will occur. If not, then specifically discuss why this process cannot occur. Explain using the properties and evolution of stars.

[*] Jim Meddick, Monty, NEA Distributors (24 October 2003).

Solution and grading rubric:

• p:
  Correct. A type Ia supernova is when a white dwarf has taken hydrogen from a binary companion star quickly enough to undergo runaway explosive fusion, destroying itself in the process. The sun is a medium-mass main sequence star that will eventually become a white dwarf, but with no binary companion star to take hydrogen from, it will never become a type Ia supernova.
  
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. At least recognizes that an external source of hydrogen/energy is required for the white dwarf endstage of a medium-mass star like the sun to undergo a type Ia supernova.
  
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Explains how the sun will eventually become a white dwarf, or makes the case for/against a type II supernova explosion.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 30674
p: 8 students
r: 6 students
t: 10 students
v: 7 students
x: 1 student
y: 1 student
z: 0 students

A sample "p" response (from student 0528): A sample "r" response (from student 1228): A sample "t" response (from student 7552):

Overheard: "extra" extra-credit?

Astronomy 210L, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

(Overheard in introductory astronomy lab immediately preceding an extra-credit quiz with slightly more possible points than previously announced.)

Student: "Are these extra-extra-credit points?"

(Beat.)

Instructor: "Let's call them unexpected, unannounced points."

Astronomy midterm question: live fast, die young

Astronomy 210 Midterm 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

[20 points.] Massive stars have much more hydrogen in their cores than do less massive stars. Why, then, do they run out of hydrogen in their cores faster than the cores of stars of low mass? Explain using the properties and evolution of stars.

(Adapted from a test bank question from Karl F. Kuhn, Theo Koupelis, In Quest of the Universe.)

Solution and grading rubric:

• p = 20/20:
  Correct. Higher temperatures and pressures in the cores of massive main sequence stars cause them to fuse hydrogen into helium much faster than in the cores of low mass stars (the pressure-temperature thermostat). (Also, low mass stars are cool enough for convection to occur throughout, such that hydrogen from all parts of the star (and not just in the core) can undergo fusion, extending the lifetime for these stars much longer than for massive stars.)
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Some attempt at explaning how the pressure-temperature thermostat sets a faster fusion rate for massive stars.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least recognizes that the rate of fusion for massive stars is greater than for low mass star, but does not explain how the pressure-temperature thermostat sets a faster fusion rate for massive stars.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30674
p: 14 students
r: 4 students
t: 14 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

An artistic sample "p" response (from student 0528) with a graphical representation of hydrostatic equilibrium:

Another sample "p" response (from student 2048) displaying the convection cells inside of massive and low-mass main sequence stars:

And one last sample "p" response (from student 2902) discussing the "higher thermostat setting" for massive stars: