The Moon over Bogotá
- Round
- Theory
- Points
- 6
- Level
- Bronze
- Taught in
- Section 1.6
Adapted from IOAA 2021 (Bogotá, held online), theory problem 8, part 3. We have restated it in our own words and kept the original data. The solution was last checked on 15 October 2026.
At 20:00 local time on 21 September 2021, the Moon was observed from the National Astronomical Observatory of Colombia in Bogotá (4°35′53″ N, 74°04′37″ W), towards the hills east of the city. Its azimuth, measured from north through east, was 90°42′59″, its altitude 19°01′42″, its ecliptic longitude 12°20′16″ and its ecliptic latitude −4°24′14″. Find the right ascension and declination of the Moon at that moment.
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In degrees,
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The first line of (1.25) gives
so
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The other two lines give
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As a check, the cosine rule for the side PX of the astronomical triangle at Bogotá gives
so
AnswerThe Moon's right ascension was 0h 52.3m, or 13.06°, and its declination +0.82°. The official solution gives 0h 50m 52s and +1°34′. The check in step 4 shows that its declination is a slip, and its right ascension is close to the angle whose tangent is 0.2260, as if the division by 0.9740 in step 3 had been left out.
This problem also appears among the olympiad problems of Section 1.6, Ecliptic and galactic coordinates, which teaches the ideas it uses. Equation and figure numbers refer to the course.