Astronomy midterm question: correcting the National Geographic Society

Astronomy 210 Midterm 1, spring semester 2010
Cuesta College, San Luis Obispo, CA

Consider the following excerpt regarding Copernicus' heliocentric model of planetary motion:

"Copernicus had begun the job of dethroning Ptolemy, but he hadn't quite finished the work. And this is what brings us back to Mars. For all the strengths of the Copernican system, it failed to explain the motion of Mars, including its occasional, peculiar backwards march across the constellations of the zodiac."
--Paul Raeburn, Uncovering the Secrets of the Red Planet: Mars, National Geographic Society (1998), p. 30.

Discuss why this statement is wrong. Support your answer using a diagram showing how Copernicus' model does explain the "occasional, peculiar backwards" motion of Mars.

Solution and grading rubric:

• p:
  Correct. Draws a diagram with the sun at the center (Copernicus' heliocentric model of planetary motion), showing how Earth (moving faster in an inner orbit) "lapping" Mars (moving slower in an outer orbit) explains the retrograde motion of Mars.
  
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Understands how the "lapping" illusion explains retrograde motion, but does not explicitly draw a diagram, or explanation/diagram has minor errors/omissions, e.g. Mars in an orbit inside of Earth's.
  
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Has sun at center, but Mars has epicycles along a deferent to explain prograde/retrograde motion, even with discussion of "lapping."
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Explains retrograde motion using epicycles on deferents, whether the sun or Earth is at the center of Mars' motion.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Describes retrograde motion, but problematic explanation even with Ptolemy's geocentric model.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 30674
p: 18 students
r: 3 students
t: 5 students
v: 9 students
x: 8 students
y: 1 student
z: 0 students

A sample "p" response (from student 1802):
Another sample "p" response (from student 2360):
A sample "r" response (from student 5280), with Mars in an inner orbit:

A sample "t" response (from student 2425), with "lapping" discussed along with epicycles and deferents in a heliocentric model:
A sample "v" response (from student 4742), with epicycles and deferents being the sole cause of pro- and retrograde motion in a geocentric model:
A sample "x" response (from student 1187), appealing to parallax?