Astronomy midterm question: apparent magnitude dimmer than absolute magnitude?

Astronomy 210 Midterm 2, fall semester 2017
Cuesta College, San Luis Obispo, CA

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

Qu: If the distance to a star is 20 parsecs, and its absolute magnitude is +5.5, what is its apparent magnitude?
day: The apparent magnitude would be dimmer than +5.5.

Discuss whether this answer is correct or incorrect, and how you know this. Explain using the relationships between apparent magnitude, absolute magnitude, and distance.

[*] answers.yahoo.com/question/index?qid=20100615201717AAZwXu7.

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 "fair comparison distance" of 10 parsecs away). Discusses how this star with an absolute magnitude value of +5.5 (measured at 10 parsecs) will get dimmer when placed farther away to 20 parsecs, and thus its apparent magnitude will be dimmer than its absolute magnitude of +5.5. Then makes conclusion on correctness of response.
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. As (p), but does not explicitly determine incorrectness of response.
• 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 70158
Exam code: midterm02Sm5n
p: 27 students
r: 7 students
t: 10 students
v: 1 student
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1027):