Short answers, pulled from the story.
The equatorial coordinate system is used to specify the positions of celestial objects in a way that is consistent for observers anywhere on Earth. It defines each object's location using right ascension and declination, two coordinates anchored to the celestial equator and the March equinox.
Declination measures how far an object is north or south of the celestial equator in degrees, ranging from -90 to +90. Right ascension measures how far east an object lies along the celestial equator from the March equinox, expressed in sidereal hours rather than degrees, with 24 hours spanning the full circle.
The equatorial coordinate system is aligned with Earth's equator and poles but remains fixed against the background stars while Earth rotates beneath it. This is by design: a non-rotating frame means that a distant star's coordinates stay constant over time, making the system universally usable.
An epoch is a specific reference date whose equinox is used to define the primary direction of the coordinate system. The most commonly used standard epoch is J2000.0. Specifying an epoch is necessary because Earth's axial precession and nutation cause the equinox to drift over time.
One complete cycle of precession, the slow westward turning of Earth's rotational axis around the poles of the ecliptic, takes about 26,000 years. This motion gradually shifts the primary direction of the equatorial coordinate system and is why every published star position must cite its epoch.
Right ascension is a fixed coordinate measured eastward from the March equinox and does not change as Earth rotates. Hour angle is measured westward from the observer's local meridian and increases continuously with Earth's rotation; a star on the meridian at its highest point has an hour angle of zero hours.