Apparent solar path on the celestial sphere — identify the great circle The Sun appears to trace which great-circle path on the celestial sphere (Earth at the center) during the year?

Introduction / Context:
The ecliptic is fundamental in astronomy and navigation. It is the apparent annual path of the Sun against the background stars and is tilted with respect to the celestial equator by about 23.44° (the obliquity of the ecliptic).

Given Data / Assumptions:

• Geocentric celestial sphere model.
• Mean obliquity ~23.4°.

Concept / Approach:

The ecliptic plane is Earth’s orbital plane around the Sun. Its projection on the celestial sphere is a great circle: the ecliptic. The celestial equator is a different great circle defined by Earth’s rotation axis; the two intersect at the equinoxes.

Step-by-Step Solution:

Verification / Alternative check:

Star maps show the Sun’s changing ecliptic longitude through the zodiac along this great circle.

Why Other Options Are Wrong:

• (b) is the projection of Earth’s equator, not the Sun’s path.
• (a) is not a celestial great circle; (e) is a local vertical circle through east–west points.

Common Pitfalls:

• Confusing daily diurnal motion (due to Earth’s rotation) with annual motion along the ecliptic.

Final Answer:

Ecliptic.