Astronomy final exam question: brighter absolute magnitude star?

Astronomy 210 Final Exam, spring semester 2016
Cuesta College, San Luis Obispo, CA

Two stars have the same apparent magnitude m, but one is 5 parsecs away from Earth, while the other is 8 parsecs away from Earth. Determine which star has a brighter absolute magnitude M, and discuss how you know this. Explain using the relationships between apparent magnitude, absolute magnitude, and distance.

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 as seen from Earth, when placed at the "comparison distance" of 10 parsecs away), and discusses:
  1. relocating a star that is closer than 10 parsecs away to the farther "comparison distance" of 10 parsecs will decrease its apparent magnitude to become its absolute magnitude; and
  2. because the star located 5 parsecs away will need to travel a greater distance to be brought to the "comparison distance" than the star located 8 parsecs away, this star will experience a greater increase in brightness; such that
  3. the star that was located 5 parsecs away will have a dimmer absolute magnitude M than the star that was located 8 parsecs away.
• 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. At least discussion demonstrates understanding of relationships between apparent magnitudes, absolute magnitudes, and distances.
• 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 magnitudes, and distances.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion based on garbled definitions of, or not based on proper relationships between apparent magnitudes, absolute magnitudes, and distances.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 30674
Exam code: finalNKPd
p: 7 students
r: 3 students
t: 2 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students
A sample "p" response (from student 1503):