<p>Here is a tentative answer based on your comment that you want to make a star chart. I'm not an expert in this but I used answers to <a href="https://physics.stackexchange.com/q/26786/83380">RA/dec to Alt/Az program or method</a> which link to <a href="http://www.stargazing.net/kepler/altaz.html" rel="nofollow noreferrer">http://www.stargazing.net/kepler/altaz.html</a></p>

<p>You have the star's position on the celestial sphere, convert it to decimal degrees:</p>

<pre><code>     item              original             conversion                  decimal degrees
Declination:      -33°  31′   46″    -33 - 31/60. -  46/3600.         =   -33.529444  
Right Ascension   00h  08m  03.5s   (  0 +  8/60. + 3.5/3600.) x 15   =     2.014583
</code></pre>

<p>You have the time <span class="math-container">$UTC$</span> and longitude <span class="math-container">$LON$</span>, convert it to <span class="math-container">$LST$</span> (local sidereal time). From the question <a href="https://astronomy.stackexchange.com/q/24859/7982">Local Sidereal Time</a> and <a href="https://astronomy.stackexchange.com/a/24863/7982">@DavidHammen's answer</a>:</p>

<p><span class="math-container">$$LST = 100.46 + 0.985647 d + LON + 15 UT $$</span></p>

<p>where </p>

<ul>
<li><span class="math-container">$LST$</span> is local sidereal time in degrees</li>
<li><span class="math-container">$d$</span> is the number of days from J2000, including the fraction of a day</li>
<li><span class="math-container">$UT$</span> is the universal time in decimal hours</li>
<li><code>long</code> is your longitude in decimal degrees, East positive.</li>
</ul>

<p>You have <span class="math-container">$RA$</span> and <span class="math-container">$LST$</span>, get <span class="math-container">$HA$</span> (Hour Angle)</p>

<p><span class="math-container">$$HA = LST - RA$$</span></p>

<p>You have <span class="math-container">$DEC$</span> and <span class="math-container">$HA$</span>, get altitude and azimuth</p>

<p><span class="math-container">$$ALT = \arcsin\left( \sin(DEC) \sin(LAT) + \cos(DEC) \cos(LAT) \ cos(HA) \right)$$</span></p>

<p><span class="math-container">$$AZ = \arccos \left( \frac{\sin(DEC) - \sin(ALT) \sin(LAT)}{\cos(ALT) cos(LAT)} \right)$$</span></p>

<p>From there you have to decide how you want to plot altitude and azimuth on your map.</p>

<p>If you want to plot it on a circle of radius <span class="math-container">$R$</span> then use</p>

<p><span class="math-container">$$X = R (1 - ALT/90) \cos(AZ)$$</span></p>

<p><span class="math-container">$$Y = R (1 - ALT/90) \sin(AZ)$$</span></p>

<p>assuming <span class="math-container">$ALT$</span> is in degrees. In this map "top" or <span class="math-container">$X, Y = 0, R$</span> will be north and <span class="math-container">$X, Y = R, 0$</span> will be East. You will have to decide if that's the best way to plot it or if you want to mirror East-West.</p>

CC BY-SA 4.0
2020-04-20T07:33:27.843Z
Thank you very much, I appreciate your help! 
will this projection give something like this: https://imgur.com/a/x5WLFz7? And one more question, at what point do those stars that I can't see from a particular location on a particular day be screened?
maisteRR
CC BY-SA 4.0
2020-04-20T08:23:20.493Z
@maisteRR Yes indeed I think so. I recommend you use [in-the-sky.org](https://in-the-sky.org/) or [Stellarium](https://en.wikipedia.org/wiki/Stellarium_(software)) your favorite planetarium simulator or website to simulate the altitude and azimuth of a few stars and then check them against these. For screening, $ALT < 0$ will be below the horizon. For drawing lines of $RA$ and $DEC$ like on that image, just plug points from a grid into these same equations.
uhoh
CC BY-SA 4.0
2020-04-20T10:20:08.670Z
Thank you !!! I checked, everything is working fine, I can take any star from the calalogue, do the calculations and this data is the same as the data from these sites. But I have trouble with projection. For example, I calculate X(-768.3199) and Y(133.28), R = 20. Where does the start of the coordinate system and how to bring this data back to normal? Subtract or add 360 if not in range? Help this out please...
maisteRR
CC BY-SA 4.0
2020-04-20T10:25:09.917Z
@maisteRR oh I forgot to divide by 90. I've changed those to $X = R (1 - ALT/90) \cos(AZ)$ and $Y = R (1 - ALT/90) \sin(AZ)$. That way the whole thing will be +/- R in size. X and Y are positions on your page and $R$ is how big you want it on your page. I don't know the details of how you are printing. If you are just plotting then scale it any way you like. There's just not enough information in your short question to know how you are using this
uhoh
CC BY-SA 4.0
2020-04-20T11:16:03.660Z
I think these formulas for X and Y produce an azimuthal equidistant projection. The imgur link looks like a stereographic projection.
Mike G
CC BY-SA 4.0
2020-04-20T14:38:20.540Z
Thank you all for your answers, yes, i need a projection that looks like a photo imgur. And one more feature I have not quite typical coordinate system. Here, I prepared a screenshot: https://imgur.com/a/bC12wD2
Tell me, please, how to get to such a coordinate and projection system as in the previous imgur photo?
maisteRR
CC BY-SA 4.0
2020-04-20T16:47:31.803Z
@maisteRR I've answered the question as posted. If you'd like to introduce a new problem please post it as a new question.
uhoh
CC BY-SA 4.0
2020-04-20T02:08:22.760Z
2020-04-20T10:23:05.803Z
2020-04-20T10:23:05.803Z
uhoh
<p>You calculate the stars local Altitude and Azimuth based on viewing time and position. If you only need the information for one star, at one time, from one viewing location supply that information and wait for someone to give you the answer or download a Planetarium program like Stellarium and get a ton of knowledge for a few ounces of work. </p>

CC BY-SA 4.0
2020-04-19T19:52:35.963Z
Thanks for the reply, i need to use this data to project stars in the form of star maps at a certain place and at some point. What should I do about converting this data to make a projection?
maisteRR
CC BY-SA 4.0
2020-04-19T19:36:07.773Z
2020-04-19T19:36:07.773Z
L d Bonnie
<p>I know very little in astronomy, but I want to use the data in a Bright Star Catalogue to create star map projections for a specific time and place. </p>

<p>For example one line is</p>

<pre><code>{ "Dec": "-33° 31′ 46″", "HR": "13", "K": "4850", "RA": "00h 08m 03.5s", "V": "5.68" },
</code></pre>

<p>How would I convert this to an <span class="math-container">$x, y$</span> point on a printed star chart that could be used for viewing the sky at a specific time and place?</p>

CC BY-SA 4.0
2020-04-19T17:58:24.603Z
Please explain what you are trying to do, rather than being abstract.
ProfRob
CC BY-SA 4.0
2020-04-19T19:49:45.580Z
I want to use the data in this archive to create star map projections at a specific time and place. Forgive my incompetence in this matter, but what steps do I need to take?
maisteRR
CC BY-SA 4.0
2020-04-20T00:32:52.760Z
@maisteRR Oh I will add that back into your question, it makes it much clearer!
uhoh
<coordinate><night-sky>
How to make a star chart from entries in a Bright Star Catalogue?
maisteRR
# How to make a star chart from entries in a Bright Star Catalogue?

(Asked by: username_0 on 2020-04-19)

I know very little in astronomy, but I want to use the data in a Bright Star Catalogue to create star map projections for a specific time and place. 
For example one line is
{ "Dec": "-33° 31′ 46″", "HR": "13", "K": "4850", "RA": "00h 08m 03.5s", "V": "5.68" },

How would I convert this to an $x, y$ point on a printed star chart that could be used for viewing the sky at a specific time and place?

**Tags:** coordinate, night-sky
> **Comments:**
> **username_1**: Please explain what you are trying to do, rather than being abstract.  
> **username_0**: I want to use the data in this archive to create star map projections at a specific time and place. Forgive my incompetence in this matter, but what steps do I need to take?  
> **username_2**: @maisteRR Oh I will add that back into your question, it makes it much clearer!  

---

## 2 answers

### Answer by username_2 on 2020-04-20. Score: 1

Here is a tentative answer based on your comment that you want to make a star chart. I'm not an expert in this but I used answers to RA/dec to Alt/Az program or method which link to http://www.stargazing.net/kepler/altaz.html
You have the star's position on the celestial sphere, convert it to decimal degrees:
     item              original             conversion                  decimal degrees
Declination:      -33°  31′   46″    -33 - 31/60. -  46/3600.         =   -33.529444  
Right Ascension   00h  08m  03.5s   (  0 +  8/60. + 3.5/3600.) x 15   =     2.014583

You have the time $UTC$ and longitude $LON$, convert it to $LST$ (local sidereal time). From the question Local Sidereal Time and @DavidHammen's answer:
$$LST = 100.46 + 0.985647 d + LON + 15 UT $$
where 

$LST$ is local sidereal time in degrees
$d$ is the number of days from J2000, including the fraction of a day
$UT$ is the universal time in decimal hours
long is your longitude in decimal degrees, East positive.

You have $RA$ and $LST$, get $HA$ (Hour Angle)
$$HA = LST - RA$$
You have $DEC$ and $HA$, get altitude and azimuth
$$ALT = \arcsin\left( \sin(DEC) \sin(LAT) + \cos(DEC) \cos(LAT) \ cos(HA) \right)$$
$$AZ = \arccos \left( \frac{\sin(DEC) - \sin(ALT) \sin(LAT)}{\cos(ALT) cos(LAT)} \right)$$
From there you have to decide how you want to plot altitude and azimuth on your map.
If you want to plot it on a circle of radius $R$ then use
$$X = R (1 - ALT/90) \cos(AZ)$$
$$Y = R (1 - ALT/90) \sin(AZ)$$
assuming $ALT$ is in degrees. In this map "top" or $X, Y = 0, R$ will be north and $X, Y = R, 0$ will be East. You will have to decide if that's the best way to plot it or if you want to mirror East-West.

> **Comments:**
> **username_0**: Thank you very much, I appreciate your help!  will this projection give something like this: https://imgur.com/a/x5WLFz7? And one more question, at what point do those stars that I can't see from a particular location on a particular day be screened?  
> **username_2**: @maisteRR Yes indeed I think so. I recommend you use [in-the-sky.org](https://in-the-sky.org/) or [Stellarium](https://en.wikipedia.org/wiki/Stellarium_(software)) your favorite planetarium simulator or website to simulate the altitude and azimuth of a few stars and then check them against these. For screening, $ALT < 0$ will be below the horizon. For drawing lines of $RA$ and $DEC$ like on that image, just plug points from a grid into these same equations.  
> **username_0**: Thank you !!! I checked, everything is working fine, I can take any star from the calalogue, do the calculations and this data is the same as the data from these sites. But I have trouble with projection. For example, I calculate X(-768.3199) and Y(133.28), R = 20. Where does the start of the coordinate system and how to bring this data back to normal? Subtract or add 360 if not in range? Help this out please...  
> **username_2**: @maisteRR oh I forgot to divide by 90. I've changed those to $X = R (1 - ALT/90) \cos(AZ)$ and $Y = R (1 - ALT/90) \sin(AZ)$. That way the whole thing will be +/- R in size. X and Y are positions on your page and $R$ is how big you want it on your page. I don't know the details of how you are printing. If you are just plotting then scale it any way you like. There's just not enough information in your short question to know how you are using this  
> **username_3**: I think these formulas for X and Y produce an azimuthal equidistant projection. The imgur link looks like a stereographic projection.  
> **username_0**: Thank you all for your answers, yes, i need a projection that looks like a photo imgur. And one more feature I have not quite typical coordinate system. Here, I prepared a screenshot: https://imgur.com/a/bC12wD2 Tell me, please, how to get to such a coordinate and projection system as in the previous imgur photo?  
> **username_2**: @maisteRR I've answered the question as posted. If you'd like to introduce a new problem please post it as a new question.  

---

### Answer by username_4 on 2020-04-19. Score: 0

You calculate the stars local Altitude and Azimuth based on viewing time and position. If you only need the information for one star, at one time, from one viewing location supply that information and wait for someone to give you the answer or download a Planetarium program like Stellarium and get a ton of knowledge for a few ounces of work.

> **Comments:**
> **username_0**: Thanks for the reply, i need to use this data to project stars in the form of star maps at a certain place and at some point. What should I do about converting this data to make a projection?  

---

