Astronomy midterm question: comparing distances from apparent and absolute magnitudes (1)

Astronomy 210 Midterm 2, spring semester 2019
Cuesta College, San Luis Obispo, CA

The following claim was made by a student on an astronomy exam[*]:

1022: For example, a star could have an apparent magnitude of –3 and an absolute magnitude of +8. This star would be closer to Earth than a star with an apparent magnitude of +8 and an absolute magnitude of +3.

Discuss why this claim is correct, and how you know this. Explain using the relationships between apparent magnitude, absolute magnitude, and distance.

[*] waiferx.blogspot.com/2013/05/astronomy-midterm-question-relative.html.

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. the m = −3, M = +8 star must be closer than 10 parsecs away, as moving it from its actual location to 10 parsecs makes it dimmer; and
  2. the m = +8, M = +3 star must be farther than 10 parsecs away, as moving it from its actual location to 10 parsecs makes it brighter; such that
  3. the m = −3, M = +8 star must be located closer to Earth than the m = +8, M = +3 star.
• 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: midterm02nwF7
p: 19 students
r: 1 student
t: 7 students
v: 4 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 2815):