The Celestial Coordinates, Right Ascension and Declination

The celestial coordinate system is a projection of earth's coordinate system into the celestial sphere. Being just like Earth's system it contains an "equator", lines of "latitude" and "longitude", and even poles. (Though we don't use the same words for it.) One suggestion one might have would be to just extend the Earth's latitude, longitude, and equator out into the night sky, but the Earth is constantly spinning. For the Celestial coordinates, we have to pick some fixed reference to go by.

The equivalent of Earth's equator in celestial coordinates is the ecliptic. The ecliptic is an imaginary line which traces out the path of the Sun across the sky.

The equivalent of latitude for the night sky is declination (Dec). Dec measures the angle that a given object is above or below the ecliptic. Dec is measured in degrees, and is usually expressed in degrees, arc-minutes, and arc-seconds. Like the minutes and seconds that measure time, there are 60 arc seconds in one arc minute and 60 arc minutes in one degree. Objects below the ecliptic (further south in the sky) are given a negative value and objects above the ecliptic are given a positive value.

If there are coordinates of latitude, there must be coordinates of longitude. Right ascension, or RA, is the celestial equivalent of longitude. RA measures angular distance along the ecliptic, and is measured in units of hours. These are evenly spaced around the sphere, one every 15 degrees. This makes sense because the Earth rotates roughly once every 24 hours. RA is often expressed in hours, minutes and seconds, where in this case one minute is 1/60 of an hour of angle, and one second is 1/60 of a minute of angle.

In spherical coordinates, right ascension (angular distance around the
celestial equator) can be directly substituted for theta (angular distance
around the x-y plane), but declination (angular distance above or below
the celestial equator) cannot be directly substituted for phi (angular
distance away from the z-axis). Phi can be clearly seen to be

Phi= 90 degrees - Dec

If declination is 90 degrees, this is equivalent to pointing
straight up from the north pole (Phi=0). If declination is
0 degrees, an object is directly above the equator (Phi=90).
If declination is -90 degrees, the object is directly above the south
pole (Phi=180).

If distance is known, spherical coordinates can be used to convert
from RA, Dec, and parallax to X, Y, and Z. The equations for converting from
spherical to cartesian coordinates are:

x = r cos(q) sin(f)
y = r sin(q) sin(f)
z = r cos(f)