ASTR 101 Problem Set 05 Solutions

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Worked Solutions and Rubric Notes

1. Inverse-Square Brightness

Flux scales as 1/d^2, so F_B/F_A = 1/3^2 = 1/9. The farther star appears nine times fainter even though it has the same luminosity.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

2. Radius from Luminosity and Temperature

At the same temperature, L scales as R^2. R/Rsun = sqrt(100) = 10. It is much larger than the Sun at the same temperature, consistent with a giant or bright giant region rather than the main sequence Sun.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

3. Main-Sequence Lifetime Scaling

t/t_sun = 5/600 = 0.00833. Lifetime = 0.00833 x 10 billion years = 83 million years. The high luminosity overwhelms the larger fuel supply.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

4. Cluster Turnoff Interpretation

Cluster B is older. Hot blue stars are massive and short-lived, so if they are still on the main sequence the cluster is young. A Sun-like turnoff means more massive stars have already evolved away, implying older age.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

Textbook Problem Rationale

OpenStax Astronomy 2e, Stars exercises, Review Question 6, extracted index line 22241: sketch an H-R diagram and label stellar populations.
OpenStax Astronomy 2e, Stellar distances exercises, Review Question 1, extracted index line 23305: parallax measurements and distance limits.
OpenStax Astronomy 2e, Stellar evolution exercises, Review Question 11, extracted index line 27175: why star clusters are useful for studying stellar evolution.
OpenStax Astronomy 2e, Stellar death exercises, Review Question 3, extracted index line 28874: evolution of a massive star toward supernova.
OpenStax Astronomy 2e, Black holes exercises, Figuring for Yourself 20, extracted index line 30395: Schwarzschild radius for a solar-mass black hole.

Use these recommendations for additional practice or adaptation. Confirm numbering against the final adopted edition before assigning.