20111227

Astronomy final exam question: apparent magnitudes replaced with absolute magnitudes?

Astronomy 210 Final Exam, fall semester 2011
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:
Pd...: If the apparent magnitude of every star in our night sky were changed to its absolute magnitude value what would the night sky look like then?
tham153: The sky would be brighter, as most stars are further away than [10 parsecs]...
Discuss whether or not if this answer is correct, and how you know this. Explain using the properties of apparent magnitude, absolute magnitude, and distances to stars.

[*] Source: http://answers.yahoo.com/question/index?qid=20111121163651AAds3i5.

Solution and grading rubric:
  • p = 20/20:
    Correct. Understands difference between apparent magnitude (m) values and absolute magnitude (MV) values, and that stars closer or farther than 10 parsecs away will appear dimmer or brighter, respectively, if apparent magnitudes were replaced with absolute magnitude values. May argue night sky will be brighter assuming this is done to all stars in Milky Way (or universe), or may argue night sky will be dimmer assuming that this is done only to (visible?) stars in night sky.
  • r = 16/20:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  • t = 12/20:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least understands the difference between m and MV values with respect to star distances, and that smaller positive (or more negative) magnitudes are brighter.
  • v = 8/20:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Garbled definitions/relations between d, m, and MV.
  • x = 4/20:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y = 2/20:
    Irrelevant discussion/effectively blank.
  • z = 0/20:
    Blank.
Grading distribution:Section 70158
Exam code: finalsf4R
p: 15 students
r: 2 students
t: 2 students
v: 13 students
x: 0 students
y: 0 students
z: 1 student

Grading distribution:Section 70160
Exam code: finalN3aR
p: 16 students
r: 2 students
t: 3 students
v: 0 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1985):
Another sample "p" response (from student 6288):
A sample "v" response (from student 8436), claiming "SWAG" (a scientific wild-a## guess):

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