Astronomy midterm question: apparent magnitude, absolute magnitude, and distance

Astronomy 210 Midterm 2, fall semester 2008
Cuesta College, San Luis Obispo, CA

Consider a star with an apparent magnitude that is brighter than its absolute magnitude. Discuss whether this star is farther than 10 parsecs, exactly at 10 parsecs, or closer than 10 parsecs from the Earth. Explain your reasoning.

Solution and grading rubric:

• p:
  Correct. Differentiates between apparent ("as is") magnitude, and absolute ("true") magnitude, and explains reasoning as to why a star that seems brighter than it actually is must be closer than the standard 10 parsec distance in the absolute magnitude definition.
  
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. May involve other factors such as the Stefan-Boltzmann law, lookback time caused by the finite speed of light, etc.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 70158
p: 47 students
r: 6 students
t: 6 students
v: 11 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response, with a graphical representation of the relationship between apparent magnitude, absolute magnitude, and distance (from student 0725):
Another "p" response, with a slightly different graphical representation (from student 4492):
A "p" response based on common-sense principles, from a student who claims to have no recollection that this topic was ever covered in class (from student 6789):
A "p" response based on the relating this phenomenon to the movie Jurassic Park (from student 9933):