Astronomy final exam question: implausible/plausible absolute magnitude calculations

Astronomy 210 Final Exam, spring semester 2014
Cuesta College, San Luis Obispo, CA

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

Cic: I'm trying to calculate the absolute magnitudes of stars. Star A has an apparent magnitude of –0.05 and a distance of 11.1 parsecs. Star B has an apparent magnitude of +0.34 and a distance of 3.4 parsecs. My absolute magnitude calculations for star A is +46 and for star B is +2.2.

Discuss why the absolute magnitude calculation for star A is wrong, and for star B is plausible, and how you know this. Explain using the relationships between apparent magnitude, absolute magnitude, and distance.

[*] answers.yahoo.com/question/index?qid=20130319232617AAvWqb9.

Solution and grading rubric:

• p:
  Correct. Understands difference between apparent magnitude m (brightness as seen from Earth, when placed at their actual distance from Earth) and absolute magnitude (M (brightness when placed 10 parsecs away), and discusses (1) for star A, the brightness it has at its actual location (m) farther than 10 parsecs is somehow brighter than the brightness it would have at 10 parsecs away (M), thus making these values suspect; and (2) for star B the brightness it has at its actual location (m) closer than 10 parsecs is brighter than the brightness it would have at 10 parsecs away (M), thus making these values plausible.
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. One of the two points (1)-(2) correct, other is problematic/incomplete.
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Both points (1)-(2) problematic/incomplete, or one point correct while other is missing.
• v:
  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:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on relationships between apparent magnitudes, absolute visual magnitudes, and distances.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 30674
Exam code: finaln0oN
p: 8 students
r: 1 student
t: 5 students
v: 8 students
x: 0 students
y: 0 students
z: s students

Section 30676
Exam code: finals0N6
p: 16 students
r: 2 students
t: 5 students
v: 5 students
x: 3 students
y: 0 students
z: 3 students

A sample "p" response (from student 1133):