20091201

Astronomy midterm question: mass is density

Astronomy 210 Midterm 2, Fall Semester 2009
Cuesta College, San Luis Obispo, CA

[20 points.] Consider the following comment:
"The mass of a star is the physical characteristic that, more than anything else, determines how the star will go through its life. Mass is destiny for a star."
—Keivan Stassun (Jeanna Bryner, "Twin Stars Born 500,000 Years Apart," June 28, 2008, http://www.foxnews.com/story/0,2933,370244,00.html)
Discuss how the luminosity and the lifetime of a star are both related to its mass. Explain using the properties of stars.

Solution and grading rubric:
  • p = 20/20:
    Correct. A massive star has greater gravitational forces that must be supported by greater internal pressures (hydrostatic equilibrium), which results in higher rates of fusion, and thus bright luminosities and shorter lifetimes. May motivate higher fusion rates and shorter lifetimes or massive stars due to the rate of energy released due to its bright luminosity.
  • r = 16/20:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  • t = 12/20:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least recognizes that luminosity, lifetime and mass are correlated to each other, but does not explicitly connect all three.
  • v = 8/20:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  • x = 4/20:
    Implementation/application of ideas, but credit given for effort rather than merit. Implausible evidence/methods/discussion.
  • y = 2/20:
    Irrelevant discussion/effectively blank.
  • z = 0/20:
    Blank.
Grading distribution:
Section 70160
p: 34 students
r: 2 students
t: 5 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1836):

Another sample "p" response (from student 2662), with a whimsical illustration:

Another sample "p" response (from student 0889), who manages to pull it off at the last minute:

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