ASTR 101 Problem Set 06 Solutions

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Worked Solutions and Rubric Notes

1. Flat Rotation Curve

If v is constant, M(r) is proportional to r. Doubling radius requires roughly doubling enclosed mass. If visible matter fades at large radius, continued mass increase suggests unseen mass such as dark matter.

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

2. Galaxy Classification with Evidence

Likely elliptical. Complications: projection effects, faint shells/tidal features, dust not visible in the image, low surface-brightness disk, or limited wavelength coverage.

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

3. Hubble-Law Distance

d = v/H0 = 7000/70 = 100 Mpc. Imperfections include peculiar velocities, measurement uncertainty, local gravitational motions, and limitations of the linear Hubble law at larger redshift.

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

4. Redshift Interpretation

z = (515.7 - 500.7)/500.7 = 15.0/500.7 = 0.030. Approximate speed = zc = 9000 km/s. This is a low-redshift approximation.

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, galaxies exercises, Review Question 1, extracted index line 32606: distinguishing features of spiral, elliptical, and irregular galaxies.
OpenStax Astronomy 2e, galaxies exercises, Review Question 7, extracted index line 32621: importance of Hubble's law.
OpenStax Astronomy 2e, galaxies exercises, Review Question 8, extracted index line 32622: what it means for the universe to expand.
OpenStax Astronomy 2e, galaxies exercises, Figuring for Yourself 27, extracted index line 32662: Hubble-law recession velocity calculation.
OpenStax Astronomy 2e, galaxies exercises, Figuring for Yourself 30, extracted index line 32669: mass-to-light ratio for a globular cluster.

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