Astronomy midterm question: ranking distances given apparent magnitudes, absolute magnitudes

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

The apparent magnitudes and absolute magnitudes of three stars are listed below.

	m apparent magnitude	M absolute magnitude
Avior	+1.9	–4.5
Benetnash	+1.9	–3.0
Tau Ceti	+3.5	+5.7

Determine which star is farthest away (or indicate a tie, if any). Explain using the relationships between apparent magnitude, absolute magnitude, and distance.

Solution and grading rubric:

• p:
  Correct. Understands difference between apparent magnitude m (brightness as seen from Earth, when placed at their actual distance from Earth) and absolute magnitude M (brightness as seen from Earth, when placed 10 parsecs away), and compares:
  1. how star A (Avior) and star B (Benetash) appear equally bright (same apparent magnitude m), but star A is brighter than star B when both are placed at 10 parsecs away from Earth (brighter absolute magnitude), thus star A had to be moved a greater distance closer to Earth than star B; and
  2. how star C (Tau Ceti) appears dimmer than star A and star B (dimmer apparent magnitude m), and when star C is moved further back to 10 parsecs away from Earth, it will be even dimmer than star A and star B at 10 parsecs (and thus star C is the closest of these three stars).
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Discusses (1), but does not discuss (2).
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of relationships between apparent magnitudes, absolute magnitudes, and distances. May have order of brightnesses reversed, picking star C as having the brightest absolute magnitude.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use relationships between apparent magnitudes, absolute magnitudes, and distances.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion based on garbled definitions of, or not based on proper relationships between apparent magnitudes, absolute magnitudes,
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Section 70160
Exam code: midterm02sP3c
p: 27 students
r: 3 students
t: 9 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1022):