Astronomy midterm question: apparent magnitude vs. absolute magnitude vs. distance

Astronomy 210 Midterm 2, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board (http://answers.yahoo.com/question/index?qid=20100725173549AAkHpyY ) was asked and answered:
Talia: If a star has an apparent magnitude of +5 and an absolute magnitude of +20, what is its distance?

Stimpy: Very close...[it] would be much less than [10 parsecs away].
Discuss whether or not if this answer is correct, and how you know this. Explain using the properties of apparent magnitude, absolute visual magnitude, and distance.

Solution and grading rubric:
  • p = 20/20:
    Correct. Apparent magnitude is how bright the star appears at its actual distance of 80 parsecs away; absolute visual magnitude (its intrinsic brightness) is how the bright the star would be if located at the "fair distance" of 10 parsecs. Since this star is very dim (+20) when located at 10 parsecs away, but appears a little brighter (+5) at its actual distance from Earth, this star must be located closer than 10 parsecs.
  • 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.
  • 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 M_V, argues for statement being incorrect.
  • 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:
Grading distribution:
Section 70158
p: 21 students
r: 1 student
t: 3 students
v: 15 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7734):

Another sample "p" response (from student 1986):

Yet another sample "p" response (from student 1134):

A sample "x" response (from student 2021):

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