Difficulty: Easy
Correct Answer: 24 hours 50 minutes
Explanation:
Introduction / Context:The Moon’s apparent daily motion combines Earth’s rotation and the Moon’s own orbital motion around Earth. As a result, the time between the Moon’s successive meridian transits (the “lunar day”) is longer than a mean solar day. This fact is essential for planning astronomical observations, tide predictions, and instrument checks that depend on the Moon’s position.
Given Data / Assumptions:
Concept / Approach:Because the Moon moves eastward about 13° per day relative to the stars, Earth must rotate slightly more than 360° for the Moon to return to the local meridian. This adds roughly 50 minutes to the 24-hour solar day, making the mean interval about 24 h 50 min. This is analogous to the difference between a solar and a sidereal day, but larger because the Moon’s orbital angular speed (relative to the stars) is much greater than the Sun’s apparent motion.
Step-by-Step Solution:
Moon’s mean motion ≈ 360° / 27.3 d ≈ 13.2° per day eastward.Earth must rotate 360° + 13.2° for the Moon to return to the meridian.Extra 13.2° corresponds to roughly 13.2°/15° per hour ≈ 0.88 h ≈ 53 minutes. The commonly used rounded practical value is about 50 minutes.Verification / Alternative check:Astronomical almanacs list lunar transit intervals around 24 h 50 min on average, with variations due to orbital eccentricity and declination effects.
Why Other Options Are Wrong:
Common Pitfalls:Confusing sidereal day (≈ 23 h 56 m) with the lunar day; forgetting the Moon’s significant eastward drift each day.
Final Answer:24 hours 50 minutes
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