<p>This is really a math question, but it's for use in astronomy, so:</p>

<p>Because reasons, I'm writing my own sky-viewing code.  I've found a few references for converting right ascension and declination to local azimuth and altitude; so far, so good, now I need to plot that coordinate in 2D.</p>

<p>It's trivial to turn az/alt into an azimuthal equidistant projection; just map azimuth to $\theta$ and altitude to $r$ where +90° is zero and -90° is 2.  However, what I really want is an azimuthal equidistant projection where the center is at a point of my choosing — for example, NW toward the horizon — ideally specified using two angles, $\theta$ and $\phi$.  With no modifications, az/alt is using a focal point directly overhead — how do I rotate that to my point?  (Continuing the example, I'd be rotating by $\theta$ 45°, $\phi$ 90°.)  I believe this is a spherical trigonometry question, but I'm having trouble grokking the references I've found well enough to do what I want.  Any guidance?</p>

CC BY-SA 4.0
2018-08-27T07:28:25.533Z
Converting ra/dec to alt/az also requires the location in lat/long and the local sidereal time. Zenith is always dec = lat and ra = LST.
Mick
<coordinate><mathematics>
Rotating azimuth/altitude to a focal point?
Chris N
# Rotating azimuth/altitude to a focal point?

(Asked by: username_0 on 2018-08-27)

This is really a math question, but it's for use in astronomy, so:

Because reasons, I'm writing my own sky-viewing code. I've found a few references for converting right ascension and declination to local azimuth and altitude; so far, so good, now I need to plot that coordinate in 2D.

It's trivial to turn az/alt into an azimuthal equidistant projection; just map azimuth to $\theta$ and altitude to $r$ where +90° is zero and -90° is 2. However, what I really want is an azimuthal equidistant projection where the center is at a point of my choosing — for example, NW toward the horizon — ideally specified using two angles, $\theta$ and $\phi$. With no modifications, az/alt is using a focal point directly overhead — how do I rotate that to my point? (Continuing the example, I'd be rotating by $\theta$ 45°, $\phi$ 90°.) I believe this is a spherical trigonometry question, but I'm having trouble grokking the references I've found well enough to do what I want. Any guidance?

**Tags:** coordinate, mathematics

> **Comments:**
> **username_1**: Converting ra/dec to alt/az also requires the location in lat/long and the local sidereal time. Zenith is always dec = lat and ra = LST.  

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