Astronomy final exam question: comparing distances of two stars

Astronomy 210 Final Exam, fall semester 2013
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

linkinhardyy: Two stars, A and B, have apparent magnitudes +1 and +3 and absolute visual magnitudes +3 and +1, respectively. Which is closer to Earth?
balbes: A is closer than B.

Discuss why this answer is correct, and how you know this. Explain using the properties and evolution of stars.

[*] Adapted from http://answers.yahoo.com/question/index?qid=20080825115842AAgL23C.

Solution and grading rubric:

• p = 20/20:
  Correct. Understands (1) difference between apparent magnitude m (brightness as seen from Earth, when placed at their actual distance from Earth) and absolute visual magnitude (M_V (brightness as seen from Earth, when placed 10 parsecs away), and (2) discusses how star A appears to be bright at its location, but is dimmer when placed 10 parsecs away, and how star B appears to be dim, but is brighter when placed 10 parsecs away, thus star A is closer than star B (being located closer than 10 parsecs, and farther from 10 parsecs, respectively).
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Typically discusses how star A is closer than 10 parsecs, but does not explicitly discuss how star B is farther than 10 parsecs.
• 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. Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use relationships between apparent magnitudes, absolute visual magnitudes, and distances.
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on apparent magnitudes, absolute visual magnitudes, and distances.
• y = 2/20:
  Irrelevant discussion/effectively blank.
• z = 0/20:
  Blank.

Grading distribution:
Section 70160
Exam code: finaln4A6
p: 14 students
r: 2 students
t: 3 students
v: 2 students
x: 2 students
y: 0 students
z: 2 students

A sample "p" response (from student 1012):
Another sample "p" response (from student 2691):