ASTR 101 Problem Set 01 Solutions

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Worked Solutions and Rubric Notes

1. Angular Speed of the Sky

90 minutes is 1.5 hours, so the sky rotates about 22.5 degrees. The altitude would increase from roughly 35 degrees to roughly 57.5 degrees if the path were vertical. This is approximate because real altitude change depends on declination, observer latitude, and where the object is relative to the meridian.

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

2. Coordinate Systems for an Observing Plan

RA and Dec are celestial-sphere coordinates and can be shared across observers. Whether the object is above the horizon and its altitude/azimuth depend on local sidereal time, latitude, date, and time. Alt-az coordinates are useful because they tell the observer where to point in the local sky at a specific moment.

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

3. Moon Phase Geometry

At first quarter the Sun-Earth-Moon angle is about 90 degrees. First quarter is highest near sunset because it is about 90 degrees east of the Sun. It is not an eclipse because eclipses require alignment near the line of nodes; first quarter is not full Moon and does not pass through Earth's shadow.

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

4. Observing Log Critique

A strong note includes date, clock time and time zone, observing location, sky direction/altitude estimate, weather/seeing/transparency, instrument if any, object identification method, and uncertainty or comparison object. Example: '2026-10-03, 21:15 PDT, campus observatory lawn; Jupiter estimated 18 degrees above ESE horizon, clear sky with thin haze, naked eye, identified using Stellarium chart; brightness compared with nearby Saturn; altitude uncertainty +/-5 degrees.'

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, Observing the Sky exercises, Review Question 1, extracted index line 5155: latitude/longitude compared with declination/right ascension.
OpenStax Astronomy 2e, Observing the Sky exercises, Review Question 3, extracted index line 5158: Moon phases, rise/set timing, and phase visibility.
OpenStax Astronomy 2e, Observing the Sky exercises, Thought Question 24, extracted index line 5199: seasons and the misconception that distance causes seasons.
OpenStax Astronomy 2e, Observing the Sky exercises, Thought Question 25, extracted index line 5203: sky appearance from different places on Earth.

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