<p>The transformation from projected geometry to heliographic coordinates is straightforward.
As <a href="http://www.petermeadows.com/html/location.html" rel="nofollow noreferrer">Peter Meadows explains</a>, this can be done either mathematically, or graphically using a latitude/longitude grid template.
Since the solar equator is inclined about 7&deg; to the ecliptic, different <a href="http://solar-center.stanford.edu/solar-images/latlong.html" rel="nofollow noreferrer">Stonyhurst disks</a> are used at different times of year.</p>

<p><a href="https://doi.org/10.1051/0004-6361:20054262" rel="nofollow noreferrer">W T Thompson 2006</a> section 2 describes the two main heliographic coordinate systems.
Latitude in both systems is measured from the solar equator.
The central meridian of longitude in Stonyhurst coordinates is fixed facing the Earth.
The Carrington coordinate system rotates rigidly with a sidereal period of 25.38 days, approximating <a href="https://en.wikipedia.org/wiki/Solar_rotation" rel="nofollow noreferrer">solar rotation</a> at a typical sunspot latitude of &plusmn;26&deg;.</p>

<p>The NOAA Space Weather Prediction Center's daily <a href="https://www.swpc.noaa.gov/products/solar-region-summary" rel="nofollow noreferrer">Solar Region Summary</a> provides spherical coordinates in both forms.
Here are excerpts of two reports four days apart:</p>

<pre><code>SRS Number 129 Issued at 0030Z on 09 May 2019
Report compiled from data received at SWO on 08 May
I.  Regions with Sunspots.  Locations Valid at 08/2400Z 
Nmbr Location  Lo  Area  Z   LL   NN Mag Type
2740 N08E14   307  0160 Cao  04   03 Beta
2741 N05E52   269  0160 Hsx  03   01 Alpha

SRS Number 133 Issued at 0030Z on 13 May 2019
Report compiled from data received at SWO on 12 May
I.  Regions with Sunspots.  Locations Valid at 12/2400Z 
Nmbr Location  Lo  Area  Z   LL   NN Mag Type
2740 N08W40   308  0070 Hax  03   02 Alpha
2741 N06W02   270  0210 Hsx  03   02 Alpha
</code></pre>

<p>According to their <a href="ftp://ftp.swpc.noaa.gov/pub/forecasts/SRS/README" rel="nofollow noreferrer">README</a>,
<code>Location</code> is a latitude and longitude relative to the central meridian, and <code>Lo</code> is a Carrington longitude.
A typical sunspot region moves about 13&deg;/day from east to west in Stonyhurst longitude and less than &plusmn;1&deg;/day in Carrington longitude.</p>

<p>GOES X-ray event report columns 29-34 also appear to be Stonyhurst spherical coordinates.
For example, sunspot region 9042 was associated with several X-ray events in June 2000.
If you filter the report by that region number, you can see that its progress from E90 to W90 longitude is roughly linear in time.
In projection, the plot of east-west position vs. time would be sinusoidal, flattening at the limbs.</p>

CC BY-SA 4.0
2019-06-21T13:58:35.290Z
Informative answer; there's more to it than I'd thought!
uhoh
CC BY-SA 4.0
2019-06-25T19:39:37.323Z
Thanks for the very comprehensive answer! Unfortunately I realized that my question left out half of what I was interested in: Are the coordinates _as provided officially_ in spherical positions or in projection? (Happening to have any info on this?)
Helen
CC BY-SA 4.0
2019-06-27T00:35:38.723Z
@Helen: Added discussion of X-ray event reports.
Mike G
CC BY-SA 4.0
2019-06-21T00:03:21.563Z
2019-06-27T00:33:58.403Z
2019-06-27T00:33:58.403Z
Mike G
<p>Sunspot maps are created from a projection of the sun, so the coordinates of sunspots (or active regions in general) are assigned according to it. </p>

<p>Do these coordinates correspond to actual spherical positions, or are they altered as a result of the projection? </p>

<p><strong>Edit:</strong> After seeing the answer, I realized that a part of what I am asking about was not clear in the initial question. So here it is: Are the values of the sunspot coordinates <em>as provided officially</em> in spherical positions or in projection? </p>

<p>A commonly used instance of "official" records is X-ray measurements from the NOAA GOES. The text files are found <a href="https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/" rel="nofollow noreferrer">here</a>. </p>

<p>For example, see file for <a href="https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/goes-xrs-report_2000.txt" rel="nofollow noreferrer">2000</a>. The output is documented <a href="https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/documentation/miscellaneous/software/xraydatareports.pro" rel="nofollow noreferrer">here</a>, under "Output File Specification". </p>

CC BY-SA 4.0
2019-06-20T13:51:55.423Z
Editorial note: It seems that I can't add the tag "sunspot[s]" although it already exists. Could moderators help with this?
Helen
CC BY-SA 4.0
2019-06-20T15:54:49.343Z
It's weird, it doesn't show up in the search but if you try to add it you get `The tag [sunspots] is too similar to [sunspots]. If you think this new tag should be allowed, discuss it on meta.` It does show up in the Tags link but not attached to any questions.
astrosnapper
CC BY-SA 4.0
2019-06-20T17:05:59.323Z
@astrosnapper done! [Strange problem creating sunspots tag & should we have a sunspots tag?](https://astronomy.meta.stackexchange.com/q/520/7982)
uhoh
CC BY-SA 4.0
2019-06-25T22:17:29.273Z
@Helen can you link to the sunspot data you're reading?
Mike G
CC BY-SA 4.0
2019-06-26T19:41:50.657Z
@MikeG good point, I just added it.
Helen
<the-sun><coordinate><positional-astronomy><sunspots>
Is the longitude assigned to sunspots spherical or projected?
Helen
# Is the longitude assigned to sunspots spherical or projected?

(Asked by: username_0 on 2019-06-20)

Sunspot maps are created from a projection of the sun, so the coordinates of sunspots (or active regions in general) are assigned according to it.

Do these coordinates correspond to actual spherical positions, or are they altered as a result of the projection?

**Edit:** After seeing the answer, I realized that a part of what I am asking about was not clear in the initial question. So here it is: Are the values of the sunspot coordinates *as provided officially* in spherical positions or in projection?

A commonly used instance of "official" records is X-ray measurements from the NOAA GOES. The text files are found [here](https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/).

For example, see file for [2000](https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/goes-xrs-report_2000.txt). The output is documented [here](https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/documentation/miscellaneous/software/xraydatareports.pro), under "Output File Specification".

**Tags:** the-sun, coordinate, positional-astronomy, sunspots

> **Comments:**
> **username_0**: Editorial note: It seems that I can't add the tag "sunspot[s]" although it already exists. Could moderators help with this?  
> **username_1**: It's weird, it doesn't show up in the search but if you try to add it you get `The tag [sunspots] is too similar to [sunspots]. If you think this new tag should be allowed, discuss it on meta.` It does show up in the Tags link but not attached to any questions.  
> **username_2**: @username_1 done! [Strange problem creating sunspots tag & should we have a sunspots tag?](https://astronomy.meta.stackexchange.com/q/520/7982)  
> **username_3**: @username_0 can you link to the sunspot data you're reading?  
> **username_0**: @username_3 good point, I just added it.  

---

## 1 answers

### Answer by username_3 on 2019-06-21. Score: 4 | Accepted answer

The transformation from projected geometry to heliographic coordinates is straightforward.
As [Peter Meadows explains](http://www.petermeadows.com/html/location.html), this can be done either mathematically, or graphically using a latitude/longitude grid template.
Since the solar equator is inclined about 7° to the ecliptic, different [Stonyhurst disks](http://solar-center.stanford.edu/solar-images/latlong.html) are used at different times of year.

[W T Thompson 2006](https://doi.org/10.1051/0004-6361:20054262) section 2 describes the two main heliographic coordinate systems.
Latitude in both systems is measured from the solar equator.
The central meridian of longitude in Stonyhurst coordinates is fixed facing the Earth.
The Carrington coordinate system rotates rigidly with a sidereal period of 25.38 days, approximating [solar rotation](https://en.wikipedia.org/wiki/Solar_rotation) at a typical sunspot latitude of ±26°.

The NOAA Space Weather Prediction Center's daily [Solar Region Summary](https://www.swpc.noaa.gov/products/solar-region-summary) provides spherical coordinates in both forms.
Here are excerpts of two reports four days apart:

```
SRS Number 129 Issued at 0030Z on 09 May 2019
Report compiled from data received at SWO on 08 May
I.  Regions with Sunspots.  Locations Valid at 08/2400Z 
Nmbr Location  Lo  Area  Z   LL   NN Mag Type
2740 N08E14   307  0160 Cao  04   03 Beta
2741 N05E52   269  0160 Hsx  03   01 Alpha

SRS Number 133 Issued at 0030Z on 13 May 2019
Report compiled from data received at SWO on 12 May
I.  Regions with Sunspots.  Locations Valid at 12/2400Z 
Nmbr Location  Lo  Area  Z   LL   NN Mag Type
2740 N08W40   308  0070 Hax  03   02 Alpha
2741 N06W02   270  0210 Hsx  03   02 Alpha

```

According to their [README](ftp://ftp.swpc.noaa.gov/pub/forecasts/SRS/README),
`Location` is a latitude and longitude relative to the central meridian, and `Lo` is a Carrington longitude.
A typical sunspot region moves about 13°/day from east to west in Stonyhurst longitude and less than ±1°/day in Carrington longitude.

GOES X-ray event report columns 29-34 also appear to be Stonyhurst spherical coordinates.
For example, sunspot region 9042 was associated with several X-ray events in June 2000.
If you filter the report by that region number, you can see that its progress from E90 to W90 longitude is roughly linear in time.
In projection, the plot of east-west position vs. time would be sinusoidal, flattening at the limbs.

> **Comments:**
> **username_2**: Informative answer; there's more to it than I'd thought!  
> **username_0**: Thanks for the very comprehensive answer! Unfortunately I realized that my question left out half of what I was interested in: Are the coordinates _as provided officially_ in spherical positions or in projection? (Happening to have any info on this?)  
> **username_3**: @username_0: Added discussion of X-ray event reports.  

---

