# How do you calculate declination?

In terms of latitude and elevation.

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• Anonymous

A star's declination and its latitude are the same thing.

A star's declination, δ, can be found like this:

δ = ArcSin { sin φ sin E + cos φ cos E cos A }

where

φ = the observer's latitude

E = the star's elevation

A = the star's azimuth

• Declination is the measurement of the star's position above or below the celestial equator. As previously stated, cannot be calculated. It can be measured easily enough. Setting circles on a properly set up telescope, even a stick and protractor with weighted string and where in the sky the celestial equator is at that time.

• The position of a star on the celestial sphere is marked with 'Right Ascension' (from 0 to 24 hours) and 'Declination' (from -90 to + 90 degrees).

The position of the star above the horizon is marked with 'Azimuth' (along the horizon from 0 to 360 degrees) and 'Altitude' (height above horizon, from 0 to 90 degrees).

If you need to calculate above from the first system to the second system, or opposite, then you need the 'latitude' of the observer on earth (from -90 South to +90 North) and his 'time'. (Think of the rotating earth in a day time.) These are mathematical formulas with lots of 'cos' and 'sin', but it can.

Edit: you can also wait until the star is highest, which is always in south, and then the declination simply is:

AltitudeStar - 90 + LatitudeObserver

• Coldfieldgirl has described the different systems well. The conversion calculation from Alt/Az to RA/Dec is a tad tricky (understatement!) - but there's a calculator and a rather scary text description in the supplied links.

Warning - I haven't thoroughly examined either for errors!

Would I use them? No way! I just use a decent planetarium program like Stellarium...