Astronomy midterm question: comparing same-color stars

Astronomy 10 Midterm 3, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q8.5

[15 points.] Consider the following statement: "If two stars have the same color, the brighter star will be bigger." Discuss whether this statement is true or not, and support your answer using Wien's law and/or the Stefan-Boltzmann law.

Solution and grading rubric:

• p = 15/15:
  Correct. Wien's law says that same color (i.e., same peak wavelength) means same temperature. The Stefan-Boltzmann law says that for the same temperature, a brighter luminosity corresponds to a larger size. Thus the statement is true. (May only implicitly utilize one of the two laws in discussion.)
  
• r = 12/15:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Understands that the two stars must have the same temperature, but typically misapplies the Stefan-Boltzmann law.
  
• t = 9/15:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least attempts some systematic application of Wien's law and/or the Stefan-Boltzmann law.
  
• v = 6/15:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. May involve discussion of apparent versus absolute magnitude.
  
• x = 3/15:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 1.5/15:
  Irrelevant discussion/effectively blank.
  
• z = 0/15:
  Blank.
  

Grading distributions:
Section 0135
p: 15 students
r: 3 students
t: 8 students
v: 9 students
x: 0 students
y: 0 students
z: 0 students

A sample of a "p" response (from student 9389) is shown below:

Another sample of a "p" response (from student 3158):

A "p" response that uses a comparative sample of four stars, as was done in class (from student 7649):