<p>I think it makes sense to first think of the directions not in terms of equatorial coordinates (right ascension and declination) but in galactic coordinates (galactic latitude and galactic longitude, like on the Wikipedia page you linked. The galactic coordinate system is a version of spherical coordinates centered on Earth and defined so that -  very roughly:</p>
<ul>
<li>A latitude of <span class="math-container">$b=0^{\circ}$</span> corresponds to all points in the Galactic plane</li>
<li>A longitude of <span class="math-container">$l=0^{\circ}$</span> corresponds to the Galactic center</li>
<li>A longitude of <span class="math-container">$l=180^{\circ}$</span> corresponds to the Galactic anticenter</li>
</ul>
<p>Galactic North is then at <span class="math-container">$b=90^{\circ}$</span> and &quot;Galactic South&quot; is at <span class="math-container">$b=-90^{\circ}$</span>, both roughly perpendicular to the plane of the Milky Way. The system looks like this:</p>
<p><a href="https://i.sstatic.net/vO0AD.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/vO0AD.png" alt="Diagram of galactic coordinates, with the Galactic center, anticenter and poles labeled" /></a></p>
<p>If I understand your proposal correctly, &quot;left&quot; and &quot;right&quot; correspond to <span class="math-container">$l=90^{\circ}$</span> and <span class="math-container">$l=270^{\circ}$</span>, respectively, both with <span class="math-container">$b=0^{\circ}$</span>. You can convert this to right ascension and declination using <a href="https://en.wikipedia.org/wiki/Galactic_coordinate_system#Conversion_between_equatorial_and_galactic_coordinates" rel="nofollow noreferrer">the explicit formulas</a> by hand, but I prefer <a href="https://ned.ipac.caltech.edu/coordinate_calculator" rel="nofollow noreferrer">this coordinate transform calculator</a>. This tells me that &quot;Galactic left&quot; and &quot;Galactic right&quot; correspond to <span class="math-container">$$(\alpha=21\mathrm{h}12\mathrm{m}01\mathrm{s},\;\delta=48^{\circ}19'46.39"),\quad(\alpha=9\mathrm{h}12\mathrm{m}01\mathrm{s},\;\delta=-48^{\circ}19'46.75")$$</span>
respectively, in J2000.0 coordinates.</p>

CC BY-SA 4.0
2022-01-14T14:24:23.197Z
Simplest way to do it! Use the "proper frame" and then convert to the frame you need.
zephyr
CC BY-SA 4.0
2022-01-13T13:44:39.757Z
2022-01-13T13:44:39.757Z
HDE 226868
<p>For the purpose of being able to align my model to the galactic plane, I want to know the directions of the galactic center, anti-center, north, south, <em>left &amp; right</em>.</p>
<p><a href="https://en.wikipedia.org/wiki/Galactic_coordinate_system" rel="nofollow noreferrer">This gives me the answer for center, anti-center, north &amp; south</a>... <strong>but not left &amp; right</strong>. I presume astronomy doesn't even have a concept for galactic left &amp; right, so my definition / what I'm interested in is: if galactic north is above your head, and you're facing the galactic center, which way is left?</p>
<p>I need that number but in terms of right ascension hour,minute,second (+ declination) as it's how my code works.</p>
<p>But I haven't figured out the math. I think the Galactic Left's Right Ascension will be an average of the North &amp; Anti-Center. For Declination, I don't know... 90deg - their average declination? But RA of 21h,18m,30s &amp; D of 61h,57m,54s is not giving me the correct answer. (I'll know I got it when Left has the exact same distance between center, anti-center, north &amp; south - which I have code to check).</p>
<hr />
<p>I know this probably sounds like I'm trying to get someone to do my math/astronomy homework, but I promise it's not - I'm not even in school. I'm making my own 3D model of our local interstellar neighborhood and, prior to starting this personal project, I'm new to <a href="https://en.wikipedia.org/wiki/Right_ascension" rel="nofollow noreferrer">Right Ascension</a> &amp; <a href="https://en.wikipedia.org/wiki/Declination" rel="nofollow noreferrer">Declination</a>.</p>
<hr />
<p>To clarify, I'm not asking you for a math lesson on how to do this: if you just have the answer I would like to have it, but if you want to teach it I suppose it would be good to learn!</p>

<coordinate><mathematics><declination><right-ascension><galactic-center>
What's the Right Ascension & Declination of Galactic Left & Galactic Right?
danglingPointer
# What's the Right Ascension & Declination of Galactic Left & Galactic Right?

(Asked by: username_0 on 2022-01-13)

For the purpose of being able to align my model to the galactic plane, I want to know the directions of the galactic center, anti-center, north, south, *left & right*.

[This gives me the answer for center, anti-center, north & south](https://en.wikipedia.org/wiki/Galactic_coordinate_system)... **but not left & right**. I presume astronomy doesn't even have a concept for galactic left & right, so my definition / what I'm interested in is: if galactic north is above your head, and you're facing the galactic center, which way is left?

I need that number but in terms of right ascension hour,minute,second (+ declination) as it's how my code works.

But I haven't figured out the math. I think the Galactic Left's Right Ascension will be an average of the North & Anti-Center. For Declination, I don't know... 90deg - their average declination? But RA of 21h,18m,30s & D of 61h,57m,54s is not giving me the correct answer. (I'll know I got it when Left has the exact same distance between center, anti-center, north & south - which I have code to check).

---

I know this probably sounds like I'm trying to get someone to do my math/astronomy homework, but I promise it's not - I'm not even in school. I'm making my own 3D model of our local interstellar neighborhood and, prior to starting this personal project, I'm new to [Right Ascension](https://en.wikipedia.org/wiki/Right_ascension) & [Declination](https://en.wikipedia.org/wiki/Declination).

---

To clarify, I'm not asking you for a math lesson on how to do this: if you just have the answer I would like to have it, but if you want to teach it I suppose it would be good to learn!

**Tags:** coordinate, mathematics, declination, right-ascension, galactic-center


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## 1 answers

### Answer by username_1 on 2022-01-13. Score: 4

I think it makes sense to first think of the directions not in terms of equatorial coordinates (right ascension and declination) but in galactic coordinates (galactic latitude and galactic longitude, like on the Wikipedia page you linked. The galactic coordinate system is a version of spherical coordinates centered on Earth and defined so that - very roughly:

* A latitude of $b=0^{\circ}$ corresponds to all points in the Galactic plane
* A longitude of $l=0^{\circ}$ corresponds to the Galactic center
* A longitude of $l=180^{\circ}$ corresponds to the Galactic anticenter

Galactic North is then at $b=90^{\circ}$ and "Galactic South" is at $b=-90^{\circ}$, both roughly perpendicular to the plane of the Milky Way. The system looks like this:

[![Diagram of galactic coordinates, with the Galactic center, anticenter and poles labeled](https://i.sstatic.net/vO0AD.png)](https://i.sstatic.net/vO0AD.png)

If I understand your proposal correctly, "left" and "right" correspond to $l=90^{\circ}$ and $l=270^{\circ}$, respectively, both with $b=0^{\circ}$. You can convert this to right ascension and declination using [the explicit formulas](https://en.wikipedia.org/wiki/Galactic_coordinate_system#Conversion_between_equatorial_and_galactic_coordinates) by hand, but I prefer [this coordinate transform calculator](https://ned.ipac.caltech.edu/coordinate_calculator). This tells me that "Galactic left" and "Galactic right" correspond to $$(\alpha=21\mathrm{h}12\mathrm{m}01\mathrm{s},\;\delta=48^{\circ}19'46.39"),\quad(\alpha=9\mathrm{h}12\mathrm{m}01\mathrm{s},\;\delta=-48^{\circ}19'46.75")$$
respectively, in J2000.0 coordinates.

> **Comments:**
> **username_2**: Simplest way to do it! Use the "proper frame" and then convert to the frame you need.  

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