Astronomy midterm question: stars with absolute magnitude brighter than apparent magnitude

Astronomy 210 Midterm 2, fall semester 2016
Cuesta College, San Luis Obispo, CA

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

un: Is the absolute magnitude of some stars brighter than their apparent magnitude?
Pa: That is the case for stars that are a long way away.

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

[*] answers.yahoo.com/question/index?qid=20121011172202AAobQUe.

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), and discusses either of two arguments:
  1. a star farther than 10 parsecs ("a long way away") with a certain apparent magnitude will get brighter when brought closer up to 10 parsecs away from Earth, and thus its absolute magnitude will be brighter than its apparent magnitude; or
  2. a star at 10 parsecs away with a certain absolute magnitude will get dimmer when placed further away than 10 parsecs away from Earth, and thus its apparent magnitude will be dimmer than its absolute magnitude.
• 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 70158
Exam code: midterm02sU6A
p: 34 students
r: 0 students
t: 1 student
v: 1 student
x: 0 students
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02NbnW
p: 14 students
r: 1 student
t: 5 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 9135):
A sample "p" response (from student 3168):