| Notes
Equatorial
coordinates
By
extending the lines of latitude and longitude outward from
the Earth and onto the inside of the celestial sphere we get
the equatorial coordinate system. The coordinates of stars,
planets, and other celestial objects corresponding to latitude
and longitude are declination (DEC) and right ascension
(RA).
The
declination of an object is its angle in degrees, minutes,
and seconds of arc above or below the celestial equator. The
right ascension is the angle between an object and the location
of the vernal equinox (First Point in Aries) measured eastward
along the celestial equator in hours, minutes, and seconds
of sidereal time. Since the location of the vernal equinox
changes due to the precession of the Earth's axis of rotation,
coordinates must be given with reference to a date or epoch.
Right
ascension is given in time units. One hour corresponds to
1/24 of a circle, or 15° of arc. As the Earth rotates, the
sky moves to the West by about 1 hour of right ascension during
each hour of clock time or exactly one hour of sidereal time.
The Earth makes one full revolution in about 23 hours and
56 minutes of clock time or 24 hours of sidereal time. Sidereal
time corresponds to the right ascension of the zenith, the
point in the sky directly overhead.
For
example, the coordinates of the star Regulus (Leo a) for epoch
J2000 are:
RA: 10h 08m 22.3s
DEC: +11° 58' 02"
When
the local sidereal time is 10h 08m 22.3s, it would be on the
local meridian.
Horizon
coordinates: azimuth and altitude
This
is a local coordinate system to use for locating objects in
the night sky as seen from a point on the Earth's surface.
Azimuth is the angle of a celestial object around the sky
from north. It is measure along the horizon in from North
0° through East 90°, South 180°, West 270° and back to North.
Altitude is the complement of the zenith angle, which is the
angle from the local meridian to the hour circle of object
being observed. An object directly overhead would have an
altitude of 90°. An object with a calculated altitude of 0°
may not appear exactly on the horizon due to the refraction
of light through the atmosphere. Generally, refraction makes
objects near the horizon appear higher than their computed
altitude.
Coordinate
transformation
The
azimuth (AZ) and altitude (ALT) of an object
in the sky can be calculated easily using the date, universal
time (UT), and the latitude (LAT) and longitude
(LON) of the observing site and the right ascension
(RA) and declination (DEC) of the object.
All coordinates are expressed in degrees in the range 0° to
360°, so that trigonometric functions can be used for coordinate
conversion.
Local
Mean Sidereal Time
The
mean sidereal time (MST) is calculated from a polynomial
function of UT since epoch J2000. This formula gives
MST, the sidereal time at the Greenwich meridian
(at longitude 0°) in degrees. To get local mean sidereal time
(LMST), add longitude if East or subtract longitude
if West.
MST = f(UT)
LMST = MST + LON
Hour
Angle
The
hour angle (HA) is the angle between an observer's
meridian projected onto the celestial sphere and the right
ascension of a celestial body. It is used in coordinate conversion.
HA = LMST - RA
Conversion
of HA and DEC into ALT and AZ
Using
the RA, DEC and HA for the object,
and the latitude (LAT) of the observing site, the
following formulas give the ALT and AZ of
the object at the time and longitude that was used to calculate
HA.
sin(ALT) = sin(DEC)·sin(LAT) + cos(DEC)·cos(LAT)·cos(HA)
sin(DEC) - sin(ALT)·sin(LAT)
cos(A) = ----------------------------
cos(ALT)·cos(LAT)
If sin(HA) is negative, then AZ = A, otherwise AZ = 360 - A
This
gives the computed horizon coordinates without correction
for atmospheric refraction.
Copyright
© 2004, Stephen R. Schmitt
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