Extending the equatorial plane
Earth’s axis defines the celestial poles, while the perpendicular equatorial plane intersects the celestial sphere in its equator. This divides northern and southern directions without requiring a physical belt of stars.
The equator is a coordinate construction. Sources projected near it need not share a distance or belong to one material structure.
References: [1]
A basis for equatorial coordinates
Declination is measured north or south from this circle, while RA is measured longitudinally along it. Traditional coordinates use a specified equinox as the RA origin.
The ecliptic intersects rather than coincides with the equator. Their angle reflects the relationship between Earth’s equatorial and orbital planes and helps describe the Sun’s annual direction changes.
References: [1]
The reference plane needs a time convention
Precession and nutation change Earth’s orientation, so precise work specifies date and mean or apparent reference conventions. Equatorial planes under different conventions should not be mixed merely because their names agree.
Modern catalogues also use systems such as ICRS. Converting their values for an observation requires the relevant frame transformations, rather than treating a local horizon, equator of date and catalogue axes as identical.