Astronomy quiz question: stellar distances

Astronomy 210 Quiz 4, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

[4.0 points.] Procyon A is a star that has an apparent magnitude m = +0.3 and an absolute magnitude M_v = +2.64. Approximately how far away is Procyon A from the Earth?
(A) Much farther away than 10 parsecs.
(B) A little farther away than 10 parsecs.
(C) Exactly 10 parsecs away.
(D) Closer than 10 parsecs away.

Section 70160
(A) : 3 students
(B) : 3 students
(C) : 0 students
(D) : 25 students

Correct answer: (D)

When brought to the "fair distance" of 10 parsecs (thus changing its apparent magnitude to absolute visual magnitude), Procyon A now seems to be dimmer, indicating that it must have moved away to the Earth during this process. Thus Procyon A must be closer than this fair distance of 10 parsecs.

"Difficulty level": 81%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50