Techniques
of Observational AstronomyAST3722C
Techniques
of Observational AstronomyAstronomical coordinate systems are virtually all spherical coordinate systems; defined by a great circle and its poles. A latitude coordinate measures the angle above or below the circle, a longitude coordinate measures the angle along the circle from some arbitrarily defined point. An example which is useful is the terrestrial latitude and longitude system
The defining great circle for terrestrial coordinate system is the Earth's equator. The poles are the north pole and the south pole. The latitude coordinate is terrestrial latitude, measured north and south from the equator. The longitude coordinate is terrestrial longitude, measured from the reference point defined by the crossing of the prime (Greenwich) meridian and the equator. The International Astronomical Union has defined longitude as positive towards the east, negative towards the west (this is planetocentric longitude). Note: some users and software define positive longitude towards the west. An interesting result of this can be found in the map at the Heavens Above web site showing the distribution of user's coordinates. In central Asia there is a faint reversed pattern shaped like the United States presumably resulting from west longitudes entered as positive values.
The horizon
system is a "local" system centered at the individual observer. The
great circle is the observer's horizon. The poles of that circle are the zenith
(directly overhead) and the nadir.
The reference point on the horizon is the north point, defined by
a great circle (the meridian)
from the zenith through the north celestial pole to the horizon. Extending the
meridian in the oposite direction establishes the south point. The
east and west points are defined by the intersections of the celestial equator
with the horizon.
The latitude coordinate is the altitude (or elevation), measured
from the horizon along a great circle running through the zenith. The longitude
coordinate is azimuth measured either from the north point increasing
towards the east (geographic definition) or from the south point increasing
towards the west (astronomical definition). Because of this ambiguity in definition,
it is important to determine which form is in use. The geographic definition
is most common, even in use by astronomers.
The Equatorial system is defined by the celestial equator, the projection of the Earth's equator onto to celestial sphere. The poles ore the north celestial pole and the south celestial pole. The reference point is the vernal equinox which is the point where the ecliptic (the apparent path of the sun) crosses the celestial equator with the sun moving towards the summer solstice. The latitude coordinate is declination measured from the celestial equator. The longitude coordinate is right ascension (RA) - measured from the vernal equinox increasing in the direction of the sun's motion; ( 0 <= RA < 24 hours ).
The Equatorial system can be a local system centered on the observer, in which
case the longitude coordinate becomes
hour angle (HA) - measured from the observer's meridian increasing towards the
west ( -12 <= HA <= 12 hours ).
The introduction of hour angle and right ascension brings us to a transition between coordinates and timekeeping. An observer has a meridian running overhead from north to south. Objects rise in the east, transit the meridian, and set in the west. An object on the celestial equator (declination = 0) takes 12 hours to cross the sky from east to west. Hour angle (HA) is defined as the length of time since an object transited (crossed) the meridian. Thus an object setting due west is at an hour angle of 6 hours while an object rising due east is at an hour angle of -6 hours. Right ascension (RA) increases to the east from the vernal equinox. If the right ascension of objects transiting the meridian is 12 hours, then an object rising at the same time due east has a right ascension of 18 hours and an object setting due west has a right ascension of 6 hours. It can be seen that the right ascension of objects crossing the meridian increases continuously. Local Sidereal Time (LST) can be defined as the right ascension currently on the meridian. The relationship between RA, HA, and LST is ( LST - RA = HA )
Illustrations of diurnal and annual motion
I have put together some animations and composite images that illustrate the daily motions of the sun and stars, and the changes in the sky due to the annual motion of the Earth around the sun.
last revised September 2, 2003 12:20 PM