When is the Sun’s declination north of the equator? Over the course of a year, during which interval(s) does the Sun's declination remain north (positive) with respect to the celestial equator?

Introduction / Context:
The Sun’s declination varies annually due to Earth’s axial tilt. Surveyors and navigators use declination to estimate solar altitude, day length, and seasonal changes relevant to field observations.

Given Data / Assumptions:

• Approximate equinoxes: around March 21 and September 21.
• Approximate solstices: around June 21 (northern summer) and December 21 (northern winter).
• Positive declination means the Sun is north of the celestial equator.

Concept / Approach:
From the March equinox until the September equinox, the Sun has positive declination. Thus the Sun’s declination is north from roughly March 21 → September 21, which includes both sub-intervals listed in options (a) and (b), encompassing the June solstice.

Step-by-Step Solution:
Identify equinoctial crossings: δ = 0° at ~March 21 and ~September 21.Between these dates, δ > 0 (northern declinations).Hence both (a) and (b) are correct collectively.

Verification / Alternative check:
Solar ephemerides show δ rising from 0° up to about +23.4° at June solstice, then decreasing back to 0° by September equinox.

Why Other Options Are Wrong:
(c) and (d) represent the period when δ is south (negative), i.e., from September to March.

Common Pitfalls:
Confusing astronomical seasons between hemispheres; declination sign relates to celestial equator, not local seasons.

Final Answer:
Both (a) and (b)