Astronomy final exam question: apparent and absolute magnitudes of a star

Astronomy 210 Final Exam, fall semester 2012
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board(*) was asked and answered:

Johan: A star has an apparent magnitude of +5. If the star could be moved to a distance of 10 parsecs, what would be the [e]ffect on the star's absolute magnitude?
tham153: Absolute and apparent magnitudes [will have the same value], although insufficient data provided to say [whether this value would be the same as, brighter, or dimmer than +5].

Decide whether this statement is correct or incorrect, and how you know this. Explain using the properties of apparent magnitude, absolute visual magnitude, and distance.

*Adapted from: http://answers.yahoo.com/question/index?qid=20120324215820AAcrx2o.

Solution and grading rubric:

• p = 20/20:
  Correct. Argues that answer is correct, as there is not enough information to say whether the absolute magnitude (which would be equal to the apparent magnitude at 10 parsecs) would be the same as, brighter, or dimmer than +5, corresponding to the star originally being located at, farther away, or nearer than 10 parsecs. Must at least give a concrete example of a star not located at 10 parsecs, and its expected absolute magnitude.
• 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 that absolute magnitudes are the intrinsic brightness of a star, but that the apparent magnitude of a star depends on its distance from Earth.
• 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 distance, apparent magnitude, and absolute magnitude.
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on apparent magnitudes, absolute magnitudes, and distances.
• y = 2/20:
  Irrelevant discussion/effectively blank.
• z = 0/20:
  Blank.

Grading distribution:
Section 70160
Exam code: finalNon0
p: 17 students
r: 6 students
t: 2 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1105):