1. Inverse-Square Brightness 12 points
Two identical stars have the same luminosity. Star B is three times farther away than Star A. What is the ratio of observed flux F_B/F_A? Explain in words.
Instructions
Show reasoning, units, diagrams or plots where useful, and source acknowledgments. Numerical answers without explanation receive limited credit. Eligible submissions may be revised after feedback.
Concrete Problems
2. Radius from Luminosity and Temperature 16 points
Star X has the same temperature as the Sun but luminosity 100 times the Sun's luminosity. Use L = 4 pi R^2 sigma T^4 to estimate its radius in solar radii. What region of the H-R diagram might it occupy?
3. Main-Sequence Lifetime Scaling 14 points
Suppose a 5 solar-mass star has luminosity about 600 solar luminosities. Estimate its main-sequence lifetime relative to the Sun using t/t_sun approximately (M/Msun)/(L/Lsun). If the Sun's main-sequence lifetime is about 10 billion years, estimate the lifetime.
4. Cluster Turnoff Interpretation 14 points
Cluster A has a main-sequence turnoff at hot blue stars. Cluster B has a turnoff near Sun-like stars. Which cluster is older? Explain using stellar mass and lifetime.
Recommended OpenStax Practice
- 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.