Astronomy midterm question: Ptolemy's "windings to and fro"

Astronomy 210 Midterm 1, Spring Semester 2010
Cuesta College, San Luis Obispo, CA

[20 points.] Consider the following excerpt from the writings of Ptolemy:

"Mortal as I am, I know that I am born for a day. But when I trace at my pleasure the windings to and fro of the heavenly bodies I no longer touch the earth with my feet."
—Ptolemy, Tetrabiblos, 150 A.D.

Explain how Ptolemy's model of planetary motion explained the "windings to and fro" of a planet. Support your answer using a diagram showing the positions of the sun, Earth, and a planet.

Solution and grading rubric:

• p = 20/20:
  Correct. Shows Ptolemy's geocentric model, with Earth at (or near) center, and planet's motion along epicycles on deferents reproduce prograde and retrograde motion.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Has the sun at center of epicycles and deferents instead of Earth.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Shows "spirograph" prograde and retrograde motion of a planet (around either Earth or the sun), but does not show how this is due to epicycles and deferents. Or discusses how a heliocentric model explains retrograde/prograde motion as a "lapping" illusion (which is not Ptolemy's model!), but explanation is sound despite being non-relevant to Ptolemy's comment.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least shows Ptolemy's geocentric model but with no indication of prograde/retrograde motion nor epicycles/deferents.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30676
p: 23 students
r: 6 students
t: 23 students
v: 13 students
x: 13 students
y: 1 student
z: 3 students

A sample "p" response (from student 9033):

A sample "r" response (from student 6433), with the sun at the center of motion:

A sample "t" response (from student 2424):

A sample "v" response (from student 9107), at least showing Earth at the center of motion:

A sample "x" response (from student 6000), alluding to the Sphinx's riddle answered by Oedipus?