Astronomy quiz question: comparing absolute magnitudes given apparent magnitudes, distances

Astronomy 210 Midterm 2, spring semester 2015
Cuesta College, San Luis Obispo, CA

The apparent magnitudes and distances of three stars are listed below.
from Earth
Regulus +1.4 24 pcs
Ankaa +2.4 24 pcs
Izar +2.4 62 pcs

When placed at 10 parsecs away, the star that appears dimmest is:
(A) Regulus.
(B) Ankaa.
(C) Izar.
(D) (There is a tie. )

Correct answer (highlight to unhide): (B)

Ankaa and Ikar both appear to be equally dimmer (m = +2.4) as seen from their true distances from Earth than Regulus, which appears to be brightest (m = +1.4). Regulus is the same distance from Earth as Ankaa, but when both are placed at 10 parsecs away from Earth, Regulus would appear to be brighter than Ankaa, meaning that Ankaa would have a dimmer absolute magnitude M.

When Ankaa and Izar are both placed 10 parsecs away from Earth, Ankaa would appear dimmer than Izar, as it would move a smaller distance closer to Earth than Izar.

Thus Ankaa would be dimmest at 10 parsecs away from Earth (having the dimmest absolute magnitude M), as it has a dimmer absolute magnitude than Regulus or Izar. (It is not readily apparent whether Regulus or Izar has the brighter absolute magnitude, without explicitly solving for it using the logarithmic relationship between distance, apparent magnitude, and absolute magnitude.)

Section 30674
Exam code: midterm02N4ra
(A) : 6 students
(B) : 18 students
(C) : 6 students
(D) : 8 students

Success level: 51% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80

Section 30676
Exam code: midterm02s0Ju
(A) : 7 students
(B) : 27 students
(C) : 10 students
(D) : 5 students

Success level: 59% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.44

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