20131012

Astronomy midterm question: "dark" run illuminated by waning gibbous moon?

Astronomy 210 Midterm 1, fall semester 2013
Cuesta College, San Luis Obispo, CA

The following was posted on Facebook[*]:
Brandy V.: So, this...was my first "dark" run with [my dog] Lilly in tow. She was easy to watch...with the [light from the waning gibbous] moon.
Discuss a specific plausible range of times for this person's first "dark" run with her dog. Support your answer using a diagram showing the positions of the sun, the moon, Earth, and an observer on Earth.

[*] Posted September 4, 2012, facebook.com.

Solution and grading rubric:
  • p:
    Correct. The waning gibbous moon is highest overhead at 3:00 AM, and would have risen six hours before at 9:00 PM, and set six hours later at 9:00 AM. For the skies to be still be dark for Brandy V.'s run would mean any time between 9:00 PM and just before sunrise at 6:00 AM. Complete diagram and reasoning.
  • r:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  • t:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. May have plausible times for waxing gibbous or waning crescent "dark" run.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Diagram and discussion problematic.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Misconceptions or non-relevant concepts: moon phases created by Earth's shadow, diagrams with the moon orbiting the sun, etc.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Section 70158
Exam code: midterm1s73W
p: 44 students
r: 0 students
t: 3 students
v: 1 student
x: 2 students
y: 0 students
z: 0 students

Section 70160
Exam code: midterm1N1t3
p: 20 students
r: 0 students
t: 6 students
v: 0 students
x: 3 students
y: 0 students
z: 0 students

A sample "p" response (from student 0304):
Another sample "p" response (from student 3374):

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