# Positional Astronomy: Coordinate systems: the second equatorial or "RA-dec." system

{Note: If your browser does not distinguish between "a,b" and " α, β " (the Greek letters "alpha, beta") then I am afraid you will not be able to make much sense of the equations on this page.}

Coordinates in the first equatorial system (HA and declination)
still depend on the time of observation.
Now we change the zero-point for our coordinates.
We choose a fixed point on the celestial equator,
called the vernal equinox, or the First Point of Aries.
The symbol for this is the astrological symbol for Aries:

(The function of this point will become clearer later on.)

The declination (δ) of object X is measured in the same way as before.
The Right Ascension or RA (α) of object X
is the angle along the celestial equator measured eastwards
from the vernal equinox to the meridian of X.
Like HA, RA is measured in hours 0-24h, but it goes in the opposite direction.

Comparison of these celestial coordinate systems with the terrestrial system:

 terrestrial alt-az HA-dec. RA-dec. equator horizon celestial equator celestial equator North Pole zenith North Celestial Pole North Celestial Pole South Pole nadir South Celestial Pole South Celestial Pole latitude altitude declination declination co-latitude zenith distance North Polar Distance North Polar Distance parallel of latitude parallel of altitude parallel of declination parallel of declination meridian of longitude vertical circle meridian meridian Greenwich Meridian Principal Vertical celestial meridian vernal equinox longitude azimuth Hour Angle Right Ascension

Exercise:

The four stars at the corners of the “Great Square of Pegasus” are:

 star R.A. declination α And 00h 08m +29°05' β Peg 23h 04m +28° 05' α Peg 23h 05m +15° 12' γ Peg 00h 13m +15° 11'

Calculate the lengths of the two diagonals of the “Square”.