Astronomy midterm question: Mercury higher than Venus at sunrise?

Astronomy 210 Midterm 1, fall semester 2012
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

anon: If Mercury and Venus are both morning stars, can Mercury be higher in sky than Venus at dawn?
"?": Yes, Mercury can have a higher altitude [in the sky] than Venus. It depends on exactly where Earth, Mercury and Venus are in their orbits in relationship to each other and your location on Earth.

Discuss why this answer is correct for an observer in San Luis Obispo, CA, and how you know this. Support your answer using a diagram showing the positions of the sun, Mercury, Venus, Earth, and an observer on Earth.

[*] answers.yahoo.com/question/index?qid=20120922122209AAFhP8t.

Solution and grading rubric:

• p:
  Correct. Diagram with observer at sunrise Earth (outer heliocentric orbit) and Mercury and Venus (inner heliocentric orbits); shows and discusses how Mercury at or near western elongation would be higher in the sky above the horizon at sunrise if Venus is just after inferior conjunction, or just before superior conjuction.
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. May show that Venus in a heliocentric orbit inside of Mercury's, and/or how Mercury would be higher than Venus for an observer at sunset instead of sunrise.
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Shows Mercury higher than the sun in the morning sky after sunrise, with Venus below the sun, such that Mercury would be higher than Venus in the morning sky after sunrise, even though both planets would no longer be visible in the sky with the sun above the horizon.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Diagram and discussion problematic. Shows planets orbiting Earth, or in heliocentric orbits outside of Earth's, but still shows how Mercury could be higher in the sky (morning or evening) than Venus.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Misconceptions or non-relevant concepts.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 70158
Exam code: midterm01sLa6
p: 7 students
r: 10 students
t: 9 students
v: 7 students
x: 6 students
y: 0 students
z: 0 students

A sample "p" response (from student 0640):