Astronomy midterm question: midnight Venus?

Astronomy 210 Midterm 1, fall semester 2009
Cuesta College, San Luis Obispo, CA

Consider the following excerpt regarding viewing Venus near midnight:

"When [Harry, Ron, Hermione] reached the top of the Astronomy Tower at eleven o'clock they found a perfect night for stargazing, cloudless and still... They entered the precise positions of the stars and planets they were observing... Half an hour passed, then an hour... Harry put his eye...to his telescope and refocused it, now examining Venus."
--J. K. Rowling, Harry Potter and the Order of the Phoenix, Scholastic (2003), pp. 718-719.

Discuss whether this is plausible or implausible. Support your answer using a diagram showing the positions of the sun, Venus, and Earth.

Solution and grading rubric:

• p:
  Correct. Discusses the implausibility of this scenario by drawing a diagram with Venus' orbit closer in to the sun than Earth's orbit, making it not possible for midnight observer (assumed to be at/near the equator) to observe Venus anywhere in its inner orbit.
  
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Draws Venus in a geocentric orbit (and along or near the sun-Earth line) and argues implausibility based on this model (which is incorrect, but does reproduce the relative maximum possible angular separation between the sun and Venus).
  
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Argues plausibility based on a problematic heliocentric diagram, with Venus' orbit larger than Earth's orbit. Or argues implausibility based on a correct heliocentric diagram, with Venus' orbit closer in to the sun than Earth's orbit).
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. May discuss evening/morning star nature of Venus, elliptical orbital shapes, prograde/retrograde motion, phases, etc.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 70160
p: 18 students
r: 2 students
t: 6 students
v: 12 students
x: 1 student
y: 2 students
z: 1 student

A sample "p" response (from student 2416):
A sample "t" response (from student 5474), with Venus' heliocentric orbit larger than Earth's:
A sample "y" response (from student 2662), given credit for effort rather than merit: