Astronomy midterm question: retrograde Mars

Astronomy 10 Midterm 1, spring semester 2008
Cuesta College, San Luis Obispo, CA

An observer in San Luis Obispo, CA notices that Mars is on the meridian at midnight. Discuss whether Mars is undergoing prograde (proper) or retrograde motion with respect to the background stars on that night. Explain your answer using a diagram showing the positions and motions of an observer, Mars, and Earth.

Solution and grading rubric:

• p:
  Correct. Draws heliocentric orbits of Mars (outer) and Earth (inner), with Mars being on the meridian of a midnight observer located on Earth. Since Mars is at opposition, Earth is in the process of "lapping" it, resulting in Mars appearing to move retrograde (east-to-west, "backwards") with respect to the background stars. Diagram and discussion consistent, with some minor details omitted.
  
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Diagram problematic/incomplete (e.g. Mars' orbit inside Earth's, or observer missing), but demonstrates some understanding of relative orbital motion and prograde/retrograde motion with respect to the background stars.
  
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Some attempt at explaining the "lapping" illusion to motivate retrograde discussion. May conclude prograde but diagram is otherwise correct.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distributions:
Section 4160
p: 15 students
r: 4 students
t: 5 students
v: 14 students
x: 1 student
y: 0 students
z: 0 students

Section 5166
p: 18 students
r: 4 students
t: 9 students
v: 35 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 1316):
This "p" response (from student 2431) explicitly shows the changing line-of-sight that Mars makes as it is "lapped" by Earth, resulting in retrograde motion with respect to the background stars:
Another "p" response (from student 2887), with anthropomorphized celestial bodies: