<p>I would recommend looking at the &quot;SOFA Astrometry Tools&quot; cookbook in (programming) language of your choice under the <a href="http://www.iausofa.org/cookbooks.html" rel="nofollow noreferrer">&quot;Cookbooks&quot;</a> section of the SOFA site as this explains the different systems and gives a worked example (Section 6).</p>
<p>Positions in star catalogs (all modern ones anyway) are all given in ICRS, the International Celestial Reference System which remains fixed for ever (there will never a 'J2050'). However, because stars move, what is also needed and given in the catalog is an <em>epoch</em>, an instant in time, for when the coordinates are valid. This was often also 2000.0 but with the Gaia catalogs, which are the usual source of catalogs now, these have been 2015.0 (DR1), 2015.5 (DR2) or 2016.0 (EDR3/DR3). The difference between this epoch and when you want the position for has to be combined with the proper motion and parallax information to convert the <em>catalog</em> position to give the correct <em>astrometric</em> position. This can then be converted to a CIRS as seen by a geocentric observer and then further converted to a topocentric and/or observed place as seen by an actual observer on the surface of the Earth (and looking through a refracting atmosphere...)</p>
<p>Looking at the worked example in the Cookbook, we can see starting from our original catalog position for the example star (which has proper motion and parallax):</p>
<pre><code>ICRS, epoch J2000.0: 14 34 16.8118300 -12 31 10.396500
</code></pre>
<p>In the example, we are wanting positions for 2013 April 2, 23h 15m 43s.55 UTC so there is roughly 13.25 years of proper motion to apply. The ICRS-&gt;CIRS can be done in 2 ways, via the astrometric place:</p>
<pre><code>catalog -&gt; astrometric: 14 34 16.4960283 -12 31 02.523786 (using iauAtcc13)
   astrometric -&gt; CIRS: 14 34 20.2370587 -12 34 36.381654 (using iauAtci13, zeroing out p.m.)
</code></pre>
<p>or directly in 1 step:</p>
<pre><code>       catalog -&gt; CIRS: 14 34 20.2370587 -12 34 36.381654 (using iauAtci13 w/proper motion)
</code></pre>
<p>As can ben seen, the 2 ways given identical results. Converting back again from CIRS, we have:</p>
<pre><code>   CIRS -&gt; astrometric: 14 34 16.4960283 -12 31 02.523786 (using iauAticqn)
</code></pre>
<p>which again is identical to the previous astrometric place given previously.</p>
<p>Because there are basically infinite combinations of original positions and proper motions that would result in a star having the same astrometric position on the celestial sphere, when you convert backwards from a CIRS position seen from Earth to the ICRS astrometric position, the star could be any at distance away, you have no motion information and no way of knowing what prior motions could have been present that moved it to that position.</p>

CC BY-SA 4.0
2023-08-31T01:04:16.523Z
2023-08-31T01:04:16.523Z
astrosnapper
<p>I'm new to astronomy and sofa lib. as you know sofa library give us some function to transform star coordinate between varies reference systems. I want to use <em><strong>iauAtci13()</strong></em> function to transform some star coordinate from ICRS(J2000) to CIRS;  as you know this function get star proper motion and parallax as input parameter. on the other side there is <strong>iauAtic13()</strong> function that transform star coordinate from CIRS to ICRS. But this function don't get star proper motion and parallax as input parameter.  This is a bit confusing for me. Could someone explain me about this. I will appreciated for any kind of help.</p>

<observational-astronomy>
ICRS to CIRS in sofa library
Mohammad Sadegh
# ICRS to CIRS in sofa library

(Asked by: username_0 on 2023-08-28)

I'm new to astronomy and sofa lib. as you know sofa library give us some function to transform star coordinate between varies reference systems. I want to use ***iauAtci13()*** function to transform some star coordinate from ICRS(J2000) to CIRS; as you know this function get star proper motion and parallax as input parameter. on the other side there is **iauAtic13()** function that transform star coordinate from CIRS to ICRS. But this function don't get star proper motion and parallax as input parameter. This is a bit confusing for me. Could someone explain me about this. I will appreciated for any kind of help.

**Tags:** observational-astronomy


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## 1 answers

### Answer by username_1 on 2023-08-31. Score: 4 | Accepted answer

I would recommend looking at the "SOFA Astrometry Tools" cookbook in (programming) language of your choice under the ["Cookbooks"](http://www.iausofa.org/cookbooks.html) section of the SOFA site as this explains the different systems and gives a worked example (Section 6).

Positions in star catalogs (all modern ones anyway) are all given in ICRS, the International Celestial Reference System which remains fixed for ever (there will never a 'J2050'). However, because stars move, what is also needed and given in the catalog is an *epoch*, an instant in time, for when the coordinates are valid. This was often also 2000.0 but with the Gaia catalogs, which are the usual source of catalogs now, these have been 2015.0 (DR1), 2015.5 (DR2) or 2016.0 (EDR3/DR3). The difference between this epoch and when you want the position for has to be combined with the proper motion and parallax information to convert the *catalog* position to give the correct *astrometric* position. This can then be converted to a CIRS as seen by a geocentric observer and then further converted to a topocentric and/or observed place as seen by an actual observer on the surface of the Earth (and looking through a refracting atmosphere...)

Looking at the worked example in the Cookbook, we can see starting from our original catalog position for the example star (which has proper motion and parallax):

```
ICRS, epoch J2000.0: 14 34 16.8118300 -12 31 10.396500

```

In the example, we are wanting positions for 2013 April 2, 23h 15m 43s.55 UTC so there is roughly 13.25 years of proper motion to apply. The ICRS->CIRS can be done in 2 ways, via the astrometric place:

```
catalog -> astrometric: 14 34 16.4960283 -12 31 02.523786 (using iauAtcc13)
   astrometric -> CIRS: 14 34 20.2370587 -12 34 36.381654 (using iauAtci13, zeroing out p.m.)

```

or directly in 1 step:

```
       catalog -> CIRS: 14 34 20.2370587 -12 34 36.381654 (using iauAtci13 w/proper motion)

```

As can ben seen, the 2 ways given identical results. Converting back again from CIRS, we have:

```
   CIRS -> astrometric: 14 34 16.4960283 -12 31 02.523786 (using iauAticqn)

```

which again is identical to the previous astrometric place given previously.

Because there are basically infinite combinations of original positions and proper motions that would result in a star having the same astrometric position on the celestial sphere, when you convert backwards from a CIRS position seen from Earth to the ICRS astrometric position, the star could be any at distance away, you have no motion information and no way of knowing what prior motions could have been present that moved it to that position.


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