## Conversion from Celestial Coordinate to Horizon Coordinates

Quantities Needed:

• a = Right Ascension of the celestial object
• d = Declination of the celestial object
• f = Latitude of the observer
• L = Longitude of the observer (positive east, negative west)
• Date: Y = year, M = month of the year, D = day of the month
• Time: UT = Universal Time
UT = Local Standard Time - Local Time Zone
(negative west, positive east of Greenwich)
• JD = Julian Day
 A = int(Y/100) B = 2 - A + int(A/4) JD = int(365.25 (Y + 4716)) + int(30.6001 (M + 1) + D + B - 1524.5
• qo = Siderial Time at Greenwich for the UT
 T = (JD + UT/24 - 2,451,545.0)/36525 qo = 280.46061837 + 360.985647366 29 ( JD -2,451,545.0) + 0.000387933 T2 - T3/38,710,000
• q = Local Siderial Time
q = qo + L
• H = Local hour angle
H = q - a
eg.
• A = Azimuth of the celestial object, measured westward from the south
Note: This is different from the standard definition of the term which is measured eastward from the north
• h = altitude of the celestial object, positive above the horizon
 tan A = sin H / (cos H sin f - tan d cos f ) sin h = sin f sin d + cos f cos d cos H
To Use these relationships:
• Time and Date --> Siderial Time at Greenwich
• Longitude, Siderial Time at Greenwich and Right ascension --> Local Hour Angle, H
• Latitude, Declination, and Local Hour Angle --> Azimuth, A and Altitude, h
So you see that one needs:
• Date
• Time
• Latitude
• Longitude
• Right Ascension
• Declination
If any one of these changes then the Altitude and Azimuth changes.
1. Obviously if you change the celestial object, the a and d change
2. If you move the observatory, Latitude and Longitude change
3. The time is changing continuously

Reference: "Astronomical Algorithms" by Jean Meeus
Willmann-Bell , Richmond VA, 1991
L.Bogan Nov 2000