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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
Latitude [^o] +/- [^o]
(Apparent) altitude determination click one of 4 radio buttons and follow the column by filling in
distant-object 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
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.=0^o) cross 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]

Remember:

The accuracy of the above azimuth is around 0.3 degrees.
If latitude is around the polar circle then, depending on the altitude of the horizon, the azimuth's can not be calculated and are thus not available [N.A.].
The above azimuths are only correct if the filled-in Astronomical date is close to the real event. So for Sun in March, July, September and December of each year and for the Moon it are the dates that the minor/major events happen (like in 2016/2006 with a cycle of appr. 18.61 years). Happily the declinations don't change fast in 18.61 years, so if one has the year wrong no large error occurs (<0.02 degrees which is well with accuracy of the azimuth itself).

Sites with more ephemeris data

A site that has sun/moon rise/setting time is also available (valid up to 5000 years ago, according to the webmaster). A more general page is this one.
JPL's HORIZONS System
Solar system dynamics
Astronomy formulas: by James Q. Jacobs
Sun calculations: by Jean-Pierre Lacroix
Sunrise sunset calculator

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 azimuth	Weight declination	Measurement accuracy	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 declination
-	^o
solstice sun	+/- 24^o.0
major moon*	+ 28^o.3, -30^o.0
minor moon*	+ 18^o.0, -19^o.7
cross quarter	+/- 17^o.1
equinox	0^o

* 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