Solar coordinates at solstices: On which date does the Sun have declination δ ≈ 23°27′ S and right ascension ≈ 270°?

Introduction / Context:
Surveyors sometimes need approximate solar coordinates for sun-shot azimuths or timing. The declination and right ascension of the Sun vary predictably throughout the year.

Given Data / Assumptions:

• Right ascension (RA) is measured eastward along the celestial equator from the First Point of Aries.
• Declination (δ) is measured north (+) or south (−) from the celestial equator.
• Solstice and equinox dates are approximate reference points.

Concept / Approach:
At the northern winter solstice the Sun reaches its most southerly declination, about δ = −23°27′ (i.e., 23°27′ S). The RA increases roughly 360° over a year: RA ≈ 0° at about March 21 (vernal equinox), ≈ 90° at June 21, ≈ 180° at late September, and ≈ 270° at late December.

Step-by-Step Solution:
Recognize δ = 23°27′ S → winter solstice in the northern hemisphere.Match RA ≈ 270° → also late December.Therefore the correct date is approximately December 22.

Verification / Alternative check:
Almanacs list declination near −23.4° and RA near 18h (270°) around December 21–22; small shifts occur each year.

Why Other Options Are Wrong:
Equinoxes (March/September) have δ ≈ 0° and RA ≈ 0°/180°.June solstice has δ ≈ +23°27′ (north), RA ≈ 90°.Perihelion (early January) is an orbital distance event, not tied to δ = −23°27′.

Common Pitfalls:
Confusing the sign of declination; remembering that RA advances continuously while declination oscillates between ±23°27′.

Final Answer:
December 22 (northern winter solstice).