Thanks to @ohoh for helped translate ra and dec into alt and az. Now that I have this data(altitude and azimuth), how can I plot it in something like this, with the coordinate system going like this?


1 Answer 1


The example sky map appears to be a stereographic projection; circles of right ascension and declination are projected as circular arcs, and their intersections are projected as right angles. The example has a 195° field of view, and the eastern and western horizons are mislabeled.

Let the celestial sphere be centered at the origin with radius 1, zenith at (0, 0, 1), northern horizon at (0, 1, 0), and eastern horizon at (1, 0, 0). Assuming azimuth 0° is north: $$\begin{align} x &= \sin \mathrm{Az} \cos \mathrm{Alt} \\ y &= \cos \mathrm{Az} \cos \mathrm{Alt} \\ z &= \sin \mathrm{Alt} \end{align}$$

To project from the nadir (0, 0, -1) onto the plane z = 0: $$ (x', y') = \left( \frac{x}{z + 1}, \frac{y}{z + 1} \right) $$

To fit this between (0, 0) and (2R, 2R) on a canvas with northern horizon at (R, 0) and eastern horizon at (0, R), scale by -R and translate by (RR): $$ (X, Y) = (R(1 - x'), R(1 - y')) $$

For a sky map centered overhead, if north is up, east should be on the left.

  • 1
    $\begingroup$ This is so cool! I'm gonna give it a try.. $\endgroup$
    – uhoh
    Commented Apr 21, 2020 at 6:10
  • $\begingroup$ Thanks you and uhoh for helping me out with this project. I owe you big time! $\endgroup$
    – maisteRR
    Commented Apr 21, 2020 at 9:13
  • $\begingroup$ Can I ask you last question? how can i calculate the coordinates for the grid as in the screenshot? $\endgroup$
    – maisteRR
    Commented Apr 21, 2020 at 20:41
  • $\begingroup$ @maisteRR Those appear to be at intervals of 10° in declination and 1h (15°) in right ascension. Process your synthetic grid points the same way as the star data. $\endgroup$
    – Mike G
    Commented Apr 22, 2020 at 3:43
  • $\begingroup$ @MikeG, thanks, but I'm a little confused. This mean, that I must get alt and az for value "previous dec val + 10" and "previous RA + 15" every time when I getting coords the star? I know, most likely I'm wrong and should do it in another way. Can you give one more hint? $\endgroup$
    – maisteRR
    Commented Apr 22, 2020 at 23:06

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