Astronomy quiz question: distance of ε Centauri from apparent and absolute magnitudes

Astronomy 210 Quiz 5, fall semester 2015
Cuesta College, San Luis Obispo, CA

ε Centauri is star with an apparent magnitude of m = +2.30, and an absolute magnitude M of –3.9. ε Centauri is located __________ 10 parsecs from Earth.
(A) farther than 10 parsecs.
(B) exactly 10 parsecs.
(C) closer than 10 parsecs.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

ε Centauri appears to be +2.30 as seen from its true distance from Earth, but when placed at the "fair" distance of 10 parsecs away, its becomes much brighter (–3.9). Thus it was brought much closer to Earth when moved to 10 parsecs, and was located much farther than 10 parsecs away from Earth.

Section 70158
Exam code: quiz05s3T1
(A) : 16 students
(B) : 1 student
(C) : 13 students
(D) : 0 students

Success level: 68% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.39

Section 70160
Exam code: quiz05ne7A
(A) : 19 students
(B) : 1 student
(C) : 5 students
(D) : 0 students

Success level: 78% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.57