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(time on which to base celestial coordinates)

Epoch simply means date and the term is used for specifying the reference date and time on which to base a celestial coordinate system. The current standard epoch is the J2000 epoch (aka J2000.0 epoch or epoch J2000.0), January 1, 2000, 11:58:55.816 UTC. Previous epochs used in astronomy have been B1950.0 and B1900.0 with years 1950 and 1900.

J stands for Julian date and B stands for Besselian date, which are based on a different specifications of the length of a year.

The difference between epoch and equinox:

Epoch gives a time when something was at a particular coordinate.

Equinox specifies the coordinates by specifying a time. Coordinates are based upon the position of visible astronomical bodies (e.g., the Sun), but these move relative to us with time in complicated ways, e.g., cycles. The equinox time specifies at what date/time we're using the positions to specify the coordinates.

(coordinate,equatorial,celestial sphere,time)

Referenced by:
epoch B1950.0
equatorial coordinate system
International Celestial Reference System (ICRS)
epoch J2000.0
J2000.0 equinox
J designator