## 20170329

### Astronomy quiz question: comparing star distances from apparent magnitudes, absolute magnitudes

Astronomy 210 Quiz 5, spring semester 2017
Cuesta College, San Luis Obispo, CA

The apparent magnitudes and absolute magnitudes of three stars are listed below.
 mapparentmagnitude Mabsolutemagnitude G 29-38 +13 +12 Gliese 412B +15 +16 YZ Ceti +12 +14

Which star is nearest to Earth?
(A) G 29-38.
(B) Gliese 412B.
(C) YZ Ceti.
(D) (There is a tie.)

Correct answer (highlight to unhide): (C)

G 29-38 appears to have a brightness of +13 as seen from its actual location from Earth, but when placed at the "fair" distance of 10 parsecs away, it becomes brighter (+12). This means that G 29-38 was brought closer to Earth when moved to 10 parsecs, and thus is located farther than 10 parsecs away from Earth.

Both Gliese 412B and YZ Ceti get dimmer when moved from their actual locations from Earth to be placed at the "fair" distance of 10 parsecs away. This means that both Gliese 412B and YZ Ceti were pushed away from Earth when moved to 10 parsecs, and thus are both located closer than 10 parsecs away from Earth.

Since YZ Ceti gets dimmer by +2 (from +12 to +14) when pushed away from Earth, and Gliese 412B only gets dimmer by +1 (from +15 to +16) when pushed away from Earth, YZ Ceti was pushed back a greater distance away from its original location to 10 parsecs away, while Gliese 412B was only pushed back a small distance from its original location to 10 parsecs away. Thus YZ Ceti is closer to Earth than Gliese 412B (and G 29-38 is farthest away of all these three stars).

Section 30674
Exam code: quiz05ne0W
(A) : 5 students
(B) : 1 student
(C) : 14 students
(D) : 2 students

Success level: 65% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80

Section 30676
Exam code: quiz05s4Ha
(A) : 7 students
(B) : 4 students
(C) : 25 students
(D) : 5 students

Success level: 63% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.46