Astronomy final exam question: "Dog Star" versus "Pup Star"

Astronomy 210 Final Exam, spring semester 2012
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board(*) was asked and answered:
Ambrose: Sirius has two [white-hot] stars [the same distance from Earth]: the "Dog Star" and the "Pup Star." [The] Pup Star [is] 6,800 times fainter than the Dog Star. [C]an someone explain [to] me [the] temperatures, luminosit[ies] and sizes of both stars?
tham153: ...Obviously the [Pup Star] is far smaller...
Decide whether or not if this answer is correct, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

*Source: http://answers.yahoo.com/question/index?qid=20110313090825AAUqKdp.

Solution and grading rubric:
  • p = 20/20:
    Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to show that the two stars must have the same temperature (having the same white-hot color), and thus the less luminous star must be smaller.
  • r = 16/20:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. At least successfully uses Wien's law to determine that the stars must have the same temperature.
  • t = 12/20:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors.
  • v = 8/20:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzman law.
  • x = 4/20:
    Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzman law.
  • y = 2/20:
    Irrelevant discussion/effectively blank.
  • z = 0/20:
Grading distribution:
Section 30674
Exam code: finalN34r
p: 11 students
r: 5 students
t: 13 students
v: 2 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1000):
A sample "p" response (from student 6180):
A sample "y" response (from student 0010):

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