Final answer:
The paths of the planets lie close to the ecliptic because they orbit the Sun in almost the same flat plane, which aligns with the solar system's general flatness and marks the apparent path of the Sun against the celestial sphere.
Step-by-step explanation:
The paths of the planets across the celestial sphere are very close to the ecliptic because the planets all orbit in almost the same plane. This is the same plane in which Earth orbits the Sun, and as a result, the solar system is relatively flat. The ecliptic itself is based on the apparent motion of the Sun against the celestial sphere and is inclined about 23.5° relative to the celestial equator.
Consequently, the planets, which follow similar paths due to their closely aligned orbital planes, appear to travel within the zodiac, a narrow band centered on the ecliptic encompassing the paths of the Moon and visible planets like Mercury, Venus, Mars, Jupiter, and Saturn.