Astronomy midterm question: comparing different apparent magnitude, distance stars

Astronomy 210 Midterm 2, spring semester 2012
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board(*) was asked and answered:

Tilly: Which star [has a brighter absolute magnitude]? Please help! :)?
Star A, apparent magnitude [+9.0], ...distance of 10 pc.
Star B, apparent magnitude [+6.5], ...distance of 1,000 pc.
Charles From Collection Agency: Star A.

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=20081002050219AAMlBzk.

Solution and grading rubric:

• p = 20/20:
  Correct. Understands difference between apparent magnitude (m) values and absolute magnitude (M_V) values, and that Star A, 10 parsecs away will have M_V = m = +9. Star B, which at 1,000 parsecs is much further away already has a brighter apparent magnitude, and thus would have a much brighter absolute magnitude if were relocated to only 10 parsecs away.
  
• 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 m and M_V values with respect to star distances, 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 M_V.
  
• 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
Exam code: midterm02n4Rg
p: 23 students
r: 2 students
t: 1 student
v: 7 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7070):
Another sample "p" response (from student 0329), attempting to apply the Stefan-Boltzmann law, but instead illustrating the apparent magnitudes and absolute magnitudes:
An excerpt from yet another sample "p" response (from student 0359), illustrating what would happen if Star B were to be moved to 10 parsecs away from Earth: