When does the Sun’s declination change sign from north to south? Identify the celestial event (and zodiac reference) at which the Sun’s declination passes from positive (north) to negative (south).

Introduction / Context:
The Sun’s declination varies seasonally between about +23.5° and −23.5°. The instants when declination passes through zero are the equinoxes, which also mark transitions between northern and southern declinations (and vice versa).

Given Data / Assumptions:

• Positive declination = north of the celestial equator; negative declination = south.
• Vernal (March) equinox near the first point of Aries; autumnal (September) equinox near the first point of Libra.

Concept / Approach:
At the autumnal equinox (about September 22–23), the Sun crosses the celestial equator from north to south, so declination changes sign from positive to negative. This point corresponds to the first point of Libra in the zodiacal naming convention.

Step-by-Step Solution:
Identify the crossing from +δ to −δ → autumnal equinox.Match zodiac reference → first point of Libra.Therefore, both descriptions point to the same event.

Verification / Alternative check:
Solar ephemerides show δ = 0° and decreasing immediately after the September equinox. In March, δ crosses from negative to positive (vernal equinox, first point of Aries).

Why Other Options Are Wrong:

• First point of Aries / vernal equinox describe the opposite transition (south to north).
• Autumnal equinox and first point of Libra are the correct pair.

Common Pitfalls:
Confusing zodiacal points Aries and Libra; remembering that Aries = March (northward), Libra = September (southward).

Final Answer:
Both the first point of Libra and the autumnal equinox