Astronomy final exam question: same apparent magnitude stars, different distances

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:
Lauren: If two stars have the same apparent magnitude [but different absolute magnitudes], what can you say about their distance[s]?
arslan: ...[T]he star with the [dimmer] absolute magnitude...is closer...
Decide whether or not if this answer is correct, and how you know this. Explain using the properties of apparent magnitude, absolute visual magnitude, and distance.

*Source: http://answers.yahoo.com/question/index?qid=20100407202836AAKwX3h.

Solution and grading rubric:
  • p = 20/20:
    Correct. Argues that answer is correct, whether from relocating stars from their actual locations (and same apparent magnitudes) to 10 parsecs away (showing their absolute magnitudes), or that the star farther away must be dimmer in order to seem as bright as a nearer star that is brighter.
  • 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. At least understands the difference between apparent (m) and absolute (MV) magnitudes, and that smaller positive (or more negative) magnitudes are brighter.
  • v = 8/20:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Garbled definitions/relations between d, m, and MV.
  • x = 4/20:
    Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on apparent magnitudes, absolute magnitudes, and distances.
  • y = 2/20:
    Irrelevant discussion/effectively blank.
  • z = 0/20:
Grading distribution:
Section 30676
Exam code: final5t4R
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 2259):
Another sample "p" response (from student 5415):
A sample "r" response (from student 8856):

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