Solar coordinates — when does the Sun have declination +23°27′ and right ascension 90°? Identify the date (northern hemisphere seasons) when the Sun’s coordinates are approximately δ = +23°27′ and α = 90° (i.e., 6 hours of right ascension).

Introduction / Context:
The Sun’s apparent position on the celestial sphere is described by right ascension (α) and declination (δ). At the solstices and equinoxes, these coordinates take characteristic values used in astronomy, geodesy, and navigation. Recognizing these values enables quick identification of seasonal points without consulting tables.

Given Data / Assumptions:

• Declination δ = +23°27′ (approximately +23.44°) — maximum positive declination.
• Right ascension α = 90° = 6 h (since 15° per hour).
• Northern hemisphere seasonal naming.

Concept / Approach:
At the northern summer solstice, the Sun reaches its maximum positive declination, about +23.44°. The ecliptic is divided into 24 hours of right ascension; at the summer solstice the Sun’s RA is about 6 h (90°). By contrast, at the vernal and autumnal equinoxes δ = 0°, with RA ≈ 0 h and 12 h respectively, and at the winter solstice δ ≈ −23.44° with RA ≈ 18 h (270°).

Step-by-Step Solution:

Verification / Alternative check:
Astronomical almanacs list the Sun near α ≈ 6 h, δ ≈ +23.4° around June 21; values vary slightly year to year due to orbital elements.

Why Other Options Are Wrong:

• March 21 / September 21: equinoxes with δ = 0°.
• December 22: minimum declination (negative), not positive.
• “None” is unnecessary because June 21 fits.

Common Pitfalls:
Forgetting that right ascension increases eastward from the vernal equinox; mixing up degrees and hours for RA.

Final Answer:
June 21 (summer solstice)