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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?

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  • $\begingroup$ Please explain what you are trying to do, rather than being abstract. $\endgroup$ – ProfRob Apr 19 '20 at 17:58
  • $\begingroup$ You're projecting a sphere onto a plane, just like when mapping the world to a flat map. Choose a projection, and google around for how people map latitude and longitude to a plane. $\endgroup$ – user21 Apr 19 '20 at 18:20
  • $\begingroup$ 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? $\endgroup$ – maisteRR Apr 19 '20 at 19:49
  • $\begingroup$ @maisteRR Oh I will add that back into your question, it makes it much clearer! $\endgroup$ – uhoh Apr 20 '20 at 0:32
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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.

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    $\begingroup$ Thank you very much, I appreciate your help! will this projection give something like this: 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? $\endgroup$ – maisteRR Apr 20 '20 at 7:33
  • $\begingroup$ @maisteRR Yes indeed I think so. I recommend you use in-the-sky.org or Stellarium 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. $\endgroup$ – uhoh Apr 20 '20 at 8:23
  • $\begingroup$ 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... $\endgroup$ – maisteRR Apr 20 '20 at 10:20
  • $\begingroup$ @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 $\endgroup$ – uhoh Apr 20 '20 at 10:25
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    $\begingroup$ @maisteRR I've answered the question as posted. If you'd like to introduce a new problem please post it as a new question. $\endgroup$ – uhoh Apr 20 '20 at 16:47
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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.

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  • $\begingroup$ 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? $\endgroup$ – maisteRR Apr 19 '20 at 19:52

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