# Talk:Horizontal coordinate system

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Azimuth and altitude? I thought it was azimuth and elevation. Denelson83 10:28, 21 Dec 2004 (UTC)

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## False Generalization

"The horizontal coordinate system is fixed to the Earth, not the stars. Therefore, the altitude and azimuth of an object changes with time". True for stars, but false by design for geostationary satellites. Simple fix: "the altitude and azimuth of a star changes..." —Preceding unsigned comment added by 82.210.249.81 (talk) 13:15, 22 June 2010 (UTC)

## Incorrect Image

Isn't the image to the right at the start of the article incorrect? The north pole is pointing in the opposite direction of that indicated by the north in the horizon plane. --Lodorand (talk) 20:51, 5 July 2009 (UTC)

Yes, it is incorrect. Tfr000 (talk) 20:50, 20 April 2012 (UTC)

## Wrong formula

The second conversion formula

$\sin \delta = \sin \phi \cdot \sin a - \cos \phi \cdot \cos a \cdot \cos A$

$\cos \delta \cdot \cos H = \cos \phi \cdot \sin a + \sin \phi \cdot \cos a \cdot \cos A$

$\cos \delta \cdot \sin H = \sin A \cdot \cos a$

seems to be wrong IMHO and according to e.g. http://star-www.st-and.ac.uk/~fv/webnotes/chapter7.htm

it should be

$\sin \delta = \sin \phi \cdot \sin a + \cos \phi \cdot \cos a \cdot \cos A$

$\cos \delta \cdot \cos H = \cos \phi \cdot \sin a - \sin \phi \cdot \cos a \cdot \cos A$

$\cos \delta \cdot \sin H = - \sin A \cdot \cos a$

### Derivation of Formula and Terms

In this description, it talks about the Azimuth from the North, but derives the formula as by Meeus (ISBN 978-0943396354) which takes the 0° reference from the South. So I believe this description is incorrect. The third term is written as:

$\sin A \cdot \cos a = - \cos \delta \cdot \sin H$

but should be, if taken clockwise, with North as 0°

$\sin A \cdot \cos a = \cos \delta \cdot \sin H$

The formula, which I derived to show the result from Meeus, when taking the Azimuth reference point at 0° as South:

$\begin{array}{lrl} \Rightarrow & - \sin A \cos h &= \sin H \cos \delta \\ & \cos A \cos h &= \cos \phi \sin \delta - \sin \phi \cos H \cos \delta \\ \Rightarrow & \tan A &= \frac{\sin H \cos \delta}{\sin \phi \cos H \cos \delta - \cos \phi \sin \delta} \\ \Rightarrow & &= \frac{\sin H \cos \delta}{\sin \phi \cos H \cos \delta - \cos \phi \sin \delta \frac{\cos \delta}{\cos \delta}} \\ \Rightarrow & &= \frac{\sin H}{\sin \phi \cos H - \cos \phi \tan \delta} \end{array}$
 \begin{align} \sin h &= \cos \phi \cos H \cos \delta + \sin \phi \sin \delta \\ \tan A &= \frac{\sin H}{\sin \phi \cos H - \cos \phi \tan \delta} \end{align}

Jason Curl (talk) 21:03, 12 January 2011 (UTC)

I agree, having also run some test numbers with the Azimuth measured eastwards from the North.

For a nice symmetry with the forward conversion the last line could read:

$\cos \delta \cdot \sin H = - \cos a \cdot \sin A$

Copyeditor42 (talk) 20:37, 16 February 2011 (UTC)

## incorrect equations

Both the altitude and azimuth of an object in space are constantly changing as the earth rotates and as it moves in orbit around the sun(constantly changing with time); thus, are time dependent. The Right Ascension (RA) and Declination (DEC) of an object are fixed to the celestial sphere and are not time dependent. Any conversion between the two coordinate systems, must consider time of the day and the time of the year. The equations in the article fail to do this; thus, are not valid. 178.146.173.141 (talk) 17:01, 18 October 2011 (UTC)

The article could certainly use some improvement. In this case the hour angle computed is the Local Hour Angle, not the RA. In order to convert from LHA to RA, the formula is something like: RA=Greenwich Sidereal Time+longitude+LHA. The Greenwich sidereal time is the time dependent part of the formula you are looking for. So the equations as given are valid, but don't take you all of the way through the conversion. Someday, when I have more time, I'll try to update the article to be more coherent, and make a new figure (the current one has a rather egregious error....). Sailsbystars (talk) 19:00, 18 October 2011 (UTC)

## Position of the Sun is off-topic

The section about the position of the Sun has little to do with the Horizontal Coordinate System; in fact no horizontal position is calculated in the whole section. It should be moved to Position_of_the_Sun. Opinions?

I will move it within a few weeks if there are no objections. Tfr000 (talk) 18:57, 23 June 2012 (UTC)

Done. I moved it to Talk:Position_of_the_Sun because that article (among others!) already has a section very similar to this one. Tfr000 (talk) 16:29, 2 July 2012 (UTC)

## Transformation of coordinates

...now points to Celestial coordinate system. There was little point in moving it, as it is already well covered (with nearly exactly the same equations) there. Tfr000 (talk) 15:29, 20 July 2012 (UTC)