ASTR 101 Problem Set 02 Solutions

Do not distribute unless solutions are intended for release.

Worked Solutions and Rubric Notes

1. Parallax Distance with Uncertainty

d = 1/p = 25 pc. Using 1 pc = 3.26 ly gives about 81.5 ly. Fractional uncertainty is approximately dp/p = 0.004/0.040 = 0.10, so the distance uncertainty is about 10%, or about +/-2.5 pc and +/-8 ly.

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

2. Solar-System Scale Model

If 1 AU is 15 m, 30 AU is 450 m. Light travel time is 30 x 8.3 min = 249 min, about 4.15 hours.

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

3. Kepler's Third Law

P^2 = 2.5^3 = 15.625, so P = sqrt(15.625) = 3.95 years. The period is longer than Mars because the orbit is larger than Mars's 1.5 AU orbit, and shorter than Jupiter because Jupiter is much farther out at 5.2 AU.

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

4. Tidal Reasoning

It would be much smaller. Tidal effects scale approximately as 1/r^3, so doubling distance reduces the effect to about 1/8. Students are not required to know the exact scaling if they explain that tides depend on gravitational differences, not just gravitational force at one point.

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, Science and Universe / scale exercises, Review Question 8, extracted index line 2674: angular motion of the Sun relative to fixed stars.
OpenStax Astronomy 2e, Orbits and Gravity exercises, Review Question 1, extracted index line 3826: Kepler's three laws.
OpenStax Astronomy 2e, Orbits and Gravity exercises, Thought Question 22, extracted index line 3867: forces in circular motion.
OpenStax Astronomy 2e, Orbits and Gravity exercises, Thought Question 23, extracted index line 3869: satellite orbital speed during inward spiral.

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