<p>Well, your problem is that you have a sphere. To compensate for the polar declination skew, you just calculate $$\sin^{-1}(\mathtt{rand})$$
Where $\mathtt{rand}$ is a number in an evenly divided -1 to 1 range. Alternatively, you can use another trigonometric function based on what you have available, but you get the idea.</p>

<p>RA can obviously be divided evenly.</p>

CC BY-SA 3.0
2016-06-26T01:07:20.227Z
beautiful math  :)
Fattie
CC BY-SA 3.0
2016-06-29T09:54:57.447Z
@hohmannfan  You mean I need to make random Decs, then change them to sin-1(dec)? or sin-1(dec) is a weighing coefficient which correlates with area?
questionhang
CC BY-SA 3.0
2016-06-29T10:52:15.647Z
@questionhang You need to make random numbers evenly in the -1 to 1 area, and pipe them through the sin-1 formula. The output can be used together with random RA's to get random coordinates on a sphere, without any skew.
SE - stop firing the good guys
CC BY-SA 3.0
2016-07-01T16:23:23.333Z
@@hohmannfan I do not understand my question now. What is a random distribution on a 2-D sphere?
questionhang
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2016-06-25T17:39:22.713Z
2016-06-25T19:17:41.807Z
2016-06-25T19:17:41.807Z
SE - stop firing the good guys
<p>How to make random positions in Equatorial coordinate system?</p>

<p>If I divide Dec between -90 and 90 evenly, the space distribution is not random.</p>

<coordinate>
a random distribution of RA&Dec
questionhang
# a random distribution of RA&Dec

(Asked by: username_0 on 2016-06-25)

How to make random positions in Equatorial coordinate system?

If I divide Dec between -90 and 90 evenly, the space distribution is not random.

**Tags:** coordinate


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## 1 answers

### Answer by username_1 on 2016-06-25. Score: 6 | Accepted answer

Well, your problem is that you have a sphere. To compensate for the polar declination skew, you just calculate $$\sin^{-1}(\mathtt{rand})$$
Where $\mathtt{rand}$ is a number in an evenly divided -1 to 1 range. Alternatively, you can use another trigonometric function based on what you have available, but you get the idea.

RA can obviously be divided evenly.

> **Comments:**
> **username_2**: beautiful math  :)  
> **username_0**: @hohmannfan  You mean I need to make random Decs, then change them to sin-1(dec)? or sin-1(dec) is a weighing coefficient which correlates with area?  
> **username_1**: @username_0 You need to make random numbers evenly in the -1 to 1 area, and pipe them through the sin-1 formula. The output can be used together with random RA's to get random coordinates on a sphere, without any skew.  
> **username_0**: @@hohmannfan I do not understand my question now. What is a random distribution on a 2-D sphere?  

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