<p>The human eye has an angular resolution of about <a href="https://plus.maths.org/content/what-can-we-see." rel="nofollow noreferrer">1 arcmin</a>.</p>
<p>This means that the light coming from point like stars would be visible if it significantly exceeds the luminance of the sky over an area of 1 <span class="math-container">$\mathrm{arcmin}$</span> <span class="math-container">$\times$</span> 1 <span class="math-container">$\mathrm{arcmin}$</span>.</p>
<p>Sky luminance is usually measured and reported in <span class="math-container">$\mathrm{mag/arcsec}^2$</span>. It can be converted to <span class="math-container">$\mathrm{mag/arcmin}^2$</span> as follows:</p>
<p><span class="math-container">$m$</span> <span class="math-container">$\mathrm{mag/arcmin}^2 = s$</span> <span class="math-container">$\mathrm{mag/arcsec}^2 - 2.5 \mathrm{log}_{10}(3600) = s - 8.89$</span> [<a href="https://academic.oup.com/mnras/article/493/2/2429/5722125" rel="nofollow noreferrer">Further Read</a>]</p>
<p>Therefore, the limiting magnitude of a sky with luminance <span class="math-container">$s$</span> <span class="math-container">$\mathrm{mag/arcsec}^2$</span> will be significantly more than <span class="math-container">$s-8.89$</span>.</p>
<p>In practice, the subtraction factor is close to <a href="https://en.wikipedia.org/wiki/Bortle_scale" rel="nofollow noreferrer">~14</a>. That is, in practice, the limiting magnitude of a sky with luminance <span class="math-container">$s$</span> <span class="math-container">$\mathrm{mag/arcsec}^2$</span> is about <span class="math-container">$s-14$</span>.</p>
<p>The minimum sky luminance at the horizon, even during a total solar eclipse, <a href="https://iopscience.iop.org/article/10.1088/1742-6596/771/1/012013/" rel="nofollow noreferrer">is not known to exceed</a> 14 <span class="math-container">$\mathrm{mag/arcsec}^2$</span>.</p>
<p>So, the limiting magnitude will almost always remain negative as long as even a sliver of the Sun is visible. Post that, there will be a gradual increase towards the limiting magnitude of the night sky at that location.</p>

CC BY-SA 4.0
2023-04-11T17:06:25.290Z
2024-09-28T10:42:39.820Z
2024-09-28T10:42:39.820Z
Ritesh Singh
<p>I am wondering how we can calculate the magnitude limit of the celestial object, which could be visible at the given sky surface brightness conditions.</p>
<p>We already know that Venus and Jupiter are visible in the daylight. Occasionally also Mars too. I've read, that the magnitude visibility threshold is about -2 Mag for a full day. It changes, and as the Sun goes closer to the horizon it causes the light to diminish in the thick atmosphere. I found information, that the Arcturus star (-0,04Mag) was once visible even 24 minutes before sunset!
If, for example, we consider the civil twilight. Is there a chance of seeing the objects with a magnitude of +3 or even +4?
A good example can be the 12P/Pons-Brooks comet, which will pass the perihelion on late April 2024. Its maximum brightness is estimated to be about +4.1Mag, but its proximity to the Sun probably excludes it from good visual observation.
I am aware, that these assumptions will be completely different for the naked-eye approaches than for observations made through binoculars or telescopes.
I am rather interested in naked-eye observations, but I would be really happy to know the source, which would include some comparisons/tables regarding this.</p>
<p>Does anyone know the article/book or presentation, which would cover my question?</p>

CC BY-SA 4.0
2023-04-03T23:03:10.370Z
This might be of interest: "The Visibility of Stars and Planets During Twilight"
https://opg.optica.org/viewmedia.cfm?r=1&rwjcode=josa&uri=josa-43-3-177&seq=0
Greg Miller
CC BY-SA 4.0
2023-04-04T02:58:46.930Z
different but related (and premise-supporting) [Can an average person see stars from the bottom of a well or through cardboard tubes? Definitive answer required!](https://astronomy.stackexchange.com/q/38504/7982) and [See Venus in daylight](https://astronomy.stackexchange.com/q/51859/7982) and [What is the easiest way to photograph stars during daylight hours?](https://astronomy.stackexchange.com/q/46776/7982) and [Is it possible to do planet observation during the day?](https://astronomy.stackexchange.com/q/40362/7982)
uhoh
CC BY-SA 4.0
2023-04-04T10:22:25.313Z
@GregMiller this script is unfortunately not for free. If you could have the source for PDF download, that could be awesome! In fact thanks to your hint I found something similar: https://www.researchgate.net/publication/258488562_Model_of_the_stellar_visibility_during_twilight and admittedly is a good source too.Thank you for your help
Geographos
CC BY-SA 4.0
2023-04-05T03:27:04.543Z
@Geographos *great find!* Also potentially a bit helpful is Kastner, S. O. (1976) [Calculation of the twilight visibility function of near-sun objects](https://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1976JRASC..70..153K&defaultprint=YES&filetype=.pdf)
uhoh
CC BY-SA 4.0
2023-04-05T09:10:34.977Z
@uhoh thank you very much for this text. It's too technical, but quite a lot of graphs might be helpful. Despite it, even the relevant keywords can be useful for further research. Maybe you know how to get the text proposed above (1st comment) for free in PDF?
Geographos
CC BY-SA 4.0
2023-04-05T09:20:32.773Z
@Geographos I've added a bounty to encourage answers. We'll get an answer to this that's useful to you within probably a day or two I hope. :-)
uhoh
CC BY-SA 4.0
2023-04-05T09:24:27.203Z
Potential answer authors, see my areal brightness math in [this answer to *Will the Artemis Gateway Lunar Space Station be visible from Earth by amateur observers?*](https://space.stackexchange.com/a/61472/12102) See also [How bright is Andromeda's center, in magnitudes per square arcminute or something similar?](https://astronomy.stackexchange.com/q/27307/7982) and [What would go into the design of a simple sky quality meter, used to measure night sky brightness?](https://astronomy.stackexchange.com/q/27305/7982) (currently unanswered)
uhoh
CC BY-SA 4.0
2023-04-05T09:24:49.870Z
and while you're at it Astronomy.com's July 4, 2016 [Surface brightness How easy is it to see a deep-sky object?](https://astronomy.com/magazine/glenn-chaple/2016/07/surface-brightness)
uhoh
CC BY-SA 4.0
2023-04-05T09:33:25.337Z
@uhoh many thanks for this contribution. I wish I could bounty more questions, but I need more "points". I hope, all the answers will be useful to anyone who concerned :)
Geographos
CC BY-SA 4.0
2023-04-10T00:34:29.637Z
Have you looked at Andrew Crumey's "Human Contrast Threshold and Astronomical Visibility", MNRAS 442 (2014) 2600–2619, available at [https://arxiv.org/abs/1405.4209](https://arxiv.org/abs/1405.4209)?
David Bailey
CC BY-SA 4.0
2023-04-11T08:34:05.043Z
No, I haven't, but it looks interesting. Thanks!
Geographos
<apparent-magnitude><night-sky><magnitude><sky-survey><brightness>
Sky surface brightness vs magnitude limit visibility
Geographos
# Sky surface brightness vs magnitude limit visibility

(Asked by: username_0 on 2023-04-03)

I am wondering how we can calculate the magnitude limit of the celestial object, which could be visible at the given sky surface brightness conditions.

We already know that Venus and Jupiter are visible in the daylight. Occasionally also Mars too. I've read, that the magnitude visibility threshold is about -2 Mag for a full day. It changes, and as the Sun goes closer to the horizon it causes the light to diminish in the thick atmosphere. I found information, that the Arcturus star (-0,04Mag) was once visible even 24 minutes before sunset!
If, for example, we consider the civil twilight. Is there a chance of seeing the objects with a magnitude of +3 or even +4?
A good example can be the 12P/Pons-Brooks comet, which will pass the perihelion on late April 2024. Its maximum brightness is estimated to be about +4.1Mag, but its proximity to the Sun probably excludes it from good visual observation.
I am aware, that these assumptions will be completely different for the naked-eye approaches than for observations made through binoculars or telescopes.
I am rather interested in naked-eye observations, but I would be really happy to know the source, which would include some comparisons/tables regarding this.

Does anyone know the article/book or presentation, which would cover my question?

**Tags:** apparent-magnitude, night-sky, magnitude, sky-survey, brightness

> **Comments:**
> **username_1**: This might be of interest: "The Visibility of Stars and Planets During Twilight" https://opg.optica.org/viewmedia.cfm?r=1&rwjcode=josa&uri=josa-43-3-177&seq=0  
> **username_2**: different but related (and premise-supporting) [Can an average person see stars from the bottom of a well or through cardboard tubes? Definitive answer required!](https://astronomy.stackexchange.com/q/38504/7982) and [See Venus in daylight](https://astronomy.stackexchange.com/q/51859/7982) and [What is the easiest way to photograph stars during daylight hours?](https://astronomy.stackexchange.com/q/46776/7982) and [Is it possible to do planet observation during the day?](https://astronomy.stackexchange.com/q/40362/7982)  
> **username_0**: @username_1 this script is unfortunately not for free. If you could have the source for PDF download, that could be awesome! In fact thanks to your hint I found something similar: https://www.researchgate.net/publication/258488562_Model_of_the_stellar_visibility_during_twilight and admittedly is a good source too.Thank you for your help  
> **username_2**: @username_0 *great find!* Also potentially a bit helpful is Kastner, S. O. (1976) [Calculation of the twilight visibility function of near-sun objects](https://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1976JRASC..70..153K&defaultprint=YES&filetype=.pdf)  
> **username_0**: @username_2 thank you very much for this text. It's too technical, but quite a lot of graphs might be helpful. Despite it, even the relevant keywords can be useful for further research. Maybe you know how to get the text proposed above (1st comment) for free in PDF?  
> **username_2**: @username_0 I've added a bounty to encourage answers. We'll get an answer to this that's useful to you within probably a day or two I hope. :-)  
> **username_2**: Potential answer authors, see my areal brightness math in [this answer to *Will the Artemis Gateway Lunar Space Station be visible from Earth by amateur observers?*](https://space.stackexchange.com/a/61472/12102) See also [How bright is Andromeda's center, in magnitudes per square arcminute or something similar?](https://astronomy.stackexchange.com/q/27307/7982) and [What would go into the design of a simple sky quality meter, used to measure night sky brightness?](https://astronomy.stackexchange.com/q/27305/7982) (currently unanswered)  
> **username_2**: and while you're at it Astronomy.com's July 4, 2016 [Surface brightness How easy is it to see a deep-sky object?](https://astronomy.com/magazine/glenn-chaple/2016/07/surface-brightness)  
> **username_0**: @username_2 many thanks for this contribution. I wish I could bounty more questions, but I need more "points". I hope, all the answers will be useful to anyone who concerned :)  
> **username_3**: Have you looked at Andrew Crumey's "Human Contrast Threshold and Astronomical Visibility", MNRAS 442 (2014) 2600–2619, available at [https://arxiv.org/abs/1405.4209](https://arxiv.org/abs/1405.4209)?  
> **username_0**: No, I haven't, but it looks interesting. Thanks!  

---

## 1 answers

### Answer by username_4 on 2023-04-11. Score: 7 | Accepted answer

The human eye has an angular resolution of about [1 arcmin](https://plus.maths.org/content/what-can-we-see.).

This means that the light coming from point like stars would be visible if it significantly exceeds the luminance of the sky over an area of 1 $\mathrm{arcmin}$ $\times$ 1 $\mathrm{arcmin}$.

Sky luminance is usually measured and reported in $\mathrm{mag/arcsec}^2$. It can be converted to $\mathrm{mag/arcmin}^2$ as follows:

$m$ $\mathrm{mag/arcmin}^2 = s$ $\mathrm{mag/arcsec}^2 - 2.5 \mathrm{log}\_{10}(3600) = s - 8.89$ [[Further Read](https://academic.oup.com/mnras/article/493/2/2429/5722125)]

Therefore, the limiting magnitude of a sky with luminance $s$ $\mathrm{mag/arcsec}^2$ will be significantly more than $s-8.89$.

In practice, the subtraction factor is close to [~14](https://en.wikipedia.org/wiki/Bortle_scale). That is, in practice, the limiting magnitude of a sky with luminance $s$ $\mathrm{mag/arcsec}^2$ is about $s-14$.

The minimum sky luminance at the horizon, even during a total solar eclipse, [is not known to exceed](https://iopscience.iop.org/article/10.1088/1742-6596/771/1/012013/) 14 $\mathrm{mag/arcsec}^2$.

So, the limiting magnitude will almost always remain negative as long as even a sliver of the Sun is visible. Post that, there will be a gradual increase towards the limiting magnitude of the night sky at that location.


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