<p>I want to express the transformation between horizontal (azimuth <span class="math-container">$A$</span>,elevation/altitude <span class="math-container">$\varepsilon$</span>) coordinates and equatorial (hourangle <span class="math-container">$H$</span>/right ascension <span class="math-container">$\alpha$</span>, declination <span class="math-container">$\delta$</span>) as a mathematical, algebraic relation. I've been checking around the internet and everywhere the relationship shown below (from the textbook Interferometry and Synthesis in Radioastronomy) is given. <a href="http://math_research.uct.ac.za/%7Esiphelo/admin/interferometry/3_Positional_Astronomy/3_3_Horizontal_Coordinates.html" rel="nofollow noreferrer">Here is another version of the explanation</a>.</p>
<p>However, since (for horizontal <span class="math-container">$A,\varepsilon$</span> to equatorial <span class="math-container">$H,\delta$</span>) we should know the latitude <span class="math-container">$L$</span> and the coordinates <span class="math-container">$A,\varepsilon$</span> we want to transform, the system ends up overdetermined and there is no solution. Check for <span class="math-container">$A=39.7$</span>°, <span class="math-container">$\varepsilon=21.6$</span>°, and <span class="math-container">$L=-33.27$</span>.</p>
<p>However, this is the relationship I encounter when I want to know the formulae. Thankfully I can do what I want to do by utilising AstroPy and other tools. How is this system of equations meant to be used?</p>
<p><a href="https://i.sstatic.net/0FrIF.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/0FrIF.png" alt="enter image description here" /></a>
<a href="https://i.sstatic.net/CF8tk.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/CF8tk.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2023-07-03T12:13:34.597Z
It's not overdetermined, you need $\cos A, \sin A$ in order to determine the correct quadrant.  It is actually more convenient to rewrite them in terms of $\tan A$ so that you can use the atan2 function provided in most programming languages. See: https://www.celestialprogramming.com/convert_ra_dec_to_alt_az.html
Greg Miller
CC BY-SA 4.0
2023-07-03T18:05:06.587Z
Try and find Astronomical Algorithms, by Jean Meeus. It explains very well how to convert from one system of coordinates to another.
Pierre Paquette
<radio-astronomy><coordinate-systems>
How to transform between horizontal and equatorial coordinates?
condosz
# How to transform between horizontal and equatorial coordinates?

(Asked by: username_0 on 2023-07-03)

I want to express the transformation between horizontal (azimuth $A$,elevation/altitude $\varepsilon$) coordinates and equatorial (hourangle $H$/right ascension $\alpha$, declination $\delta$) as a mathematical, algebraic relation. I've been checking around the internet and everywhere the relationship shown below (from the textbook Interferometry and Synthesis in Radioastronomy) is given. [Here is another version of the explanation](http://math_research.uct.ac.za/%7Esiphelo/admin/interferometry/3_Positional_Astronomy/3_3_Horizontal_Coordinates.html).

However, since (for horizontal $A,\varepsilon$ to equatorial $H,\delta$) we should know the latitude $L$ and the coordinates $A,\varepsilon$ we want to transform, the system ends up overdetermined and there is no solution. Check for $A=39.7$°, $\varepsilon=21.6$°, and $L=-33.27$.

However, this is the relationship I encounter when I want to know the formulae. Thankfully I can do what I want to do by utilising AstroPy and other tools. How is this system of equations meant to be used?

[![enter image description here](https://i.sstatic.net/0FrIF.png)](https://i.sstatic.net/0FrIF.png)
[![enter image description here](https://i.sstatic.net/CF8tk.png)](https://i.sstatic.net/CF8tk.png)

**Tags:** radio-astronomy, coordinate-systems

> **Comments:**
> **username_1**: It's not overdetermined, you need $\cos A, \sin A$ in order to determine the correct quadrant.  It is actually more convenient to rewrite them in terms of $\tan A$ so that you can use the atan2 function provided in most programming languages. See: https://www.celestialprogramming.com/convert_ra_dec_to_alt_az.html  
> **username_2**: Try and find Astronomical Algorithms, by Jean Meeus. It explains very well how to convert from one system of coordinates to another.  

---

## 0 answers

