Cuesta College, San Luis Obispo, CA
[Version 1]
[20 points.] Consider the stars Polaris and Vega. Polaris is hotter, but its luminosity is dimmer; while Vega is cooler, but its luminosity is brighter. Discuss if it is possible for these stars to be the same size; if this is not possible, then determine which star (Polaris or Vega) must be larger. Support your answer using Wien's law and/or the Stefan-Boltzmann law.
Solution and grading rubric:
- p = 20/20:
Correct. Discusses how the Stefan-Boltzmann law (luminosity (brightness) proportional to size * (Temperature)^4) explains that the cooler of the two stars must be much larger in order to have a greater luminosity than the hotter star. Or may plot points on an H-R diagram, and shows that these two stars cannot lie along an equal radius diagonal. - 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 how the Stefan-Boltzmann law is applicable, but argument is garbled (e.g., has stars being the same size as possible). - v = 8/20:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Involves other factors such as distance, fusion rates, dimming by the interstellar medium, etc., typically confusing luminosity with apparent magnitude rather than absolute visual magnitude. - 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.
Section 30674
p: 27 students
r: 2 students
t: 11 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students
A sample "p" response (from student 1415):
Another sample "p" response (from student 5239), referring to an H-R diagram:
Another sample "p" response (from student 6042), using a table of Stefan-Boltzmann law entries:
[Version 2]
[20 points.] Consider the stars Deneb and Polaris. Deneb is hotter and its luminosity is brighter; while Polaris is cooler and its luminosity is dimmer. Decide if it is possible for these stars to be the same size; if this is not possible, then determine which star (Deneb or Polaris) must be larger. Support your answer using Wien's law and/or the Stefan-Boltzmann law.
Solution and grading rubric:
- p = 20/20:
Correct. Discusses how the Stefan-Boltzmann law (luminosity (brightness) proportional to size * (Temperature)^4) explains that the cooler of the two stars must be much larger in order to have a greater luminosity than the hotter star. Or may plot points on an H-R diagram, and shows that these two stars may lie along an equal radius diagonal. - 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 how the Stefan-Boltzmann law is applicable, but argument is garbled (e.g., has stars being the same size as possible). - v = 8/20:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Involves other factors such as distance, fusion rates, dimming by the interstellar medium, etc., typically confusing luminosity with apparent magnitude rather than absolute visual magnitude. - 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.
Section 30676
p: 38 students
r: 1 student
t: 27 students
v: 8 students
x: 2 students
y: 0 students
z: 0 students
A sample "p" response (from student 9033):
A sample "p" response (from student 1007):
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