Coordinate Reference Frames
Please review the following terms from Astro 180/300:
Celestial Sphere,
Celestial Poles,
Celestial Equator,
Latitude,
Longitude,
Meridian,
Altitude,
Azimuth,
Zenith,
Astronomical Horizon,
Equatorial Coordinate System,
Vernal Equinox,
Ecliptic
The location of the stars as a function of time is important to astronomers,
since 1) target sources are not always above the horizon, and 2) sources
are optimally observed when they are most nearly overhead or in transit
across the meridian.
Local Sidereal Time
Local sidereal time (LST) is the most useful form of sidereal
time since it gives the right ascension of a
transiting celestial object at a given location.
Since the sidereal day is ~4 minutes shorter than the solar
day, LST advances relative to local time throughout the year.
To a first approximation, LST is 00 hr at NOON on Vernal Equinox
(~Mar 21), and advances 24 hours through the year, i.e., about
2 hours a month or an hour every 2 weeks. Of course, local
solar time is also function of longitude and time zone, etc., so this
is just an approximation.
To compute LST to better accuracy, consult the
current Astronomical Almanac.
Look up the "Greenwich Sidereal Time"
GST at midnight (0 h) in
the third column corresponding to the current date
universal time. Let T be the current local 24-hour time,
and add 
hours to convert from local time to
Greenwich mean time. For Flagstaff,
this will be 7 hours. Multiply 
by 1.0027379093 (the number of
sidereal days in a solar day).
Then subtract the west longitude
(or add the east longitude) L of your
location converted to hours (hours = degrees/360*24).
Now add or subtract 24 hours as needed. Symbolically,
In order to calculate the precise location of astronomical targets,
astronomers most often use 2 geocentric coordinate reference frames:
Equatorial and Elevation-Azimuth Coordinate Systems
Equatorial coordinates consist of
of right ascension (the angle between an object's longitude and the
First Point in Aries measured eastward along the
celestial equator) and
declination (the angle above or below the celestial equator, from
to -90°). Local Sidereal Time conveniently
agrees with the right ascension (RA) longitudinal circle
that is transiting the local
meridian, and the difference in time between the RA coordinate of
a source and the time of LST gives the hour angle, i.e.,
the angle away from the meridian at which the source is located
as a function of time.
Another geocentric coordinate system is the "Elevation(Altitude)-Azimuth
system. Elevation is the angle above the horizon of a celestial
object and goes from 0o at the horizon to 90o
directly overhead (the Zenith direction). Azimuth is a
compass-direction
angle measured in degrees east of due north.
Elevation Azimuth Coordinates System
If the RA coordinate is
couched in terms of hour angle, then the conversions from elevation
(altitude)-azimuth coordinates to equatorial coordinates hour angle
H and declination 
for an observer at latitude L are
The conversions from equatorial coordinates
hour angle H and declination 
to elevation (altitude)-azimuth coordinates for an
observer at latitude L are
Galactic Coordinates Sometimes, coordinates are given
in a galactic reference frame, rather than a geocentric one.
Given galactic coordinates (b, l),
the equatorial coordinates (declination) and 
(right ascension) can be computed from the formulas
The reverse transformations are:
The first system was defined in 1932 using optical observations of the
Milky Way Galaxy. The new system was defined in 1958
in terms of 21 cm observations of HI (Sullivan 1984, p. 140).
