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Calculating the declination and set/rise azimuth

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Calculate the declination

On this web site we always talk about geocentric declination (if topocentric declination is meant it will be explicitly mentioned).
For some useful conversion see below
General parameters
Air pressure [mbar] (at eye- orsea-height reference)
Temperature [oC] (using same height reference as Air pressure)
Time of day night time  sun set/rise  day time
Astronomical date  (positive for CE and negative for BCE)
Latitude [o] +/- [o]
(Apparent) altitude determination
click one of 4 radio buttons and follow the column by filling in

Distance to distant-object [km]
vast plain horizon given apparent altitude
[o] +/- [o]
given altitude
[o] +/- [o]
Eye height [m]
Distant-object height [m]
(both must use same reference height)
Azimuth [o] +/- [o]
Celestial object
moon  sun other
altitude, declination, days after summer solstice and rise/set angle
apparent altitude [o]
altitude  [o+/- [o]
declination [o] +/- [o]
Days before/after summer solstice [day] +/- [day] (appr. or [proleptic] Greg. calendar)
Angle of rise/set: [o] (only valid for apparent altitudes larger than a 3 degrees. North [1996], page 563)

Calculate the set/rise azimuth

One has to fill in first the above light creme coloured rows
Celestial object event
The Sun
solstice (max. decl.) equinox (decl.=0ocross quarter (0.69*max. decl.)
The Moon
major standstill limit  minor standstill limit
Which part of celestial object on horizon
just fully above horizon,  centre at horizon or  just fully below horizon:
azimuths of the solar or lunar positions
summer/northern sun/moon rise [o]
summer/northern sun/moon set [o]
winter/southern sun/moon rise [o]
winter/southern sun/moon set [o]


Sites with more ephemeris data

Error analysis

Looking at the above calculations one can deduct an idea about the possible errors in the calculations using the above default values:
Parameter Weight
Influence on 
azimuth []
Influence on
declination []
Air pressure [mbar] 0.002 0.002 25 0.05 0.05
Temperature [C] 0.005 0.005 5 0.03 0.03
Time of day [h] 0 0 1 0 0
Age (precession) [y] 0.0002 0 500 0.1 0
Latitude [] 0.9 1 0.01 0.01 0.01
Azimuth [] 0 0.5 0.5 0 0.25
Height [m] 0.07 0.06 2 0.14 0.12
Distance [km] 0.35 0.3 0.1 0.04 0.03
Astronomical refraction [] 1.3 1 0.18 0.23 0.18
Total error []

0.30 0.43
So the error in calculated azimuth and declination is around 0.4.
The dependancy of declination on azimuth, altitude and latitude is also calculated.

When latitude is around the polar circle, the error in the azimuth becomes bigger. 

Some important topocentric declination values around 3000 BCE

Moment Topocentric
- o
solstice sun +/- 24o.0
major moon* + 28o.3, -30o.0
minor moon* + 18o.0, -19o.7
cross quarter +/- 17o.1
equinox 0o
* Compensated for parallax.

Useful conversions

  [oF]      [feet]   [mile]     [in Hg]      [mm Hg]   
of the above :
[oC]  [m]  [km]  [mbar]  [mbar]

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Last major content related changes: Aug. 12, 2000