Astronomy quiz question: comparing brightnesses of stars moved to 10 parsecs away

Astronomy 210 Quiz 5, spring semester 2019
Cuesta College, San Luis Obispo, CA

The apparent magnitudes and distances of two stars are listed below.

	m apparent magnitude	d distance (parsecs)
Alsafi	+4.7	5.8 pcs
Eltanin	+2.2	47 pcs

When placed at 10 parsecs away, the star that is brightest is:
(A) Alsafi.
(B) Eltanin.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

The absolute magnitude of a star is the brightness it has when placed 10 parsecs away from Earth. Alsafi has an apparent magnitude of +4.7 at 5.8 parsecs away from Earth, and so when placed at 10 parsecs away it will have an absolute magnitude that is dimmer than +4.7 (a larger positive number). Eltanin has an apparent magnitude of +2.2 at 47 parsecs away from Earth, and so when placed at 10 parsecs away it will have an absolute magnitude that is brighter than +2.2 (a smaller positive number, or a negative number). Thus when both stars are placed 10 parsecs away, Alsafi will be dimmer, while Eltanin will be brighter.

Section 30674
Exam code: quiz05NiR0
(A) : 17 students
(B) : 12 students
(C) : 1 student
(D) : 0 students

Success level: 59% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.75

Section 30676
Exam code: quiz05S4re
(A) : 20 students
(B) : 18 students
(C) : 0 students
(D) : 0 students

Success level: 56% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80