<p>I would like to be able to compute the sky surface brightness, which is based on the object's apparent magnitude.
We have formulas, which allow us to compute the sky surface brightness based on the position of the Sun below the horizon.
How about the formula, which could include both the position of the body below the horizon as well as its apparent magnitude?
Then we could compute the twilight sky surface brightness for the lunar twilight or eclipsed twilight.
I mean exactly a situation like this:
The apparent magnitude of the Sun is -26.77Mag. Once the Sun is about 3 degrees below the horizon, then the sky surface brightness at solar azimuth is just about 10 mag/arcsec2. What value of sky surface brightness be if we placed the Moon instead of the Sun in the same position against the horizon or if the Sun had -24Mag only?
Are there some computations available?
Any ideas where could I find it?</p>
<p><strong>UPDATE:</strong></p>
<p>On this website:</p>
<p><a href="https://stjarnhimlen.se/comp/radfaq.html#11" rel="nofollow noreferrer">https://stjarnhimlen.se/comp/radfaq.html#11</a></p>
<p>We can find some tables, which refer to the solar magnitude of -26.7</p>
<p><a href="https://i.sstatic.net/pJkEY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/pJkEY.png" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/7O3og.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/7O3og.png" alt="enter image description here" /></a></p>
<p>and then the twilight brightness is calculated.</p>
<p>I am searching for the formula, which could do it for any other apparent magnitude &amp; random altitude of the object.</p>
<p>Imagine, that I would like to compute the sky surface brightness for the section of sky located about 30 degrees above the horizon when the Sun is i.e. 5 degrees below the horizon.</p>
<p>How could I do it? Is there some formula, which would calculate it?</p>

CC BY-SA 4.0
2024-02-16T07:49:57.847Z
I am not sure I understand your question correctly. When we perform photometry to get the apparent magnitude of the objects, we usually define an aperture with no objects inside, which serves as the background sky. It's usually done for each frame as the background brightness changes even at different positions in the sky. Do you want to generate a template for the background sky?
vivek
CC BY-SA 4.0
2024-02-16T14:04:14.890Z
I would like to generate the template if I know how to do it. I mean that the Sun has an apparent magnitude of -26.77 and when it's  3 degrees below the horizon, the sky surface brightness at solar direction is for example 10mag/arcsec2. What brightness could be if the Sun had not -26.77Mag but for example -24Mag? This is what I am after.
Geographos
CC BY-SA 4.0
2024-02-17T13:18:54.510Z
To first order it should just scale with the brightness of the illuminating object (or at least, the contribution from that object will).
ProfRob
CC BY-SA 4.0
2024-02-19T09:20:33.843Z
I've already found a formula for this, but still don't know how things stand with respect of the whole atmosphere.
Geographos
CC BY-SA 4.0
2024-03-25T16:54:31.493Z
Basically I am looking for the formula
Geographos
CC BY-SA 4.0
2024-03-21T20:27:23.163Z
You should post the formulas you do have and explain the issues you're having getting them to work for this.
Greg Miller
<night-sky><brightness><twilight>
Calculation of twilight sky surface brightness based on object's apparent magnitude
Geographos
# Calculation of twilight sky surface brightness based on object's apparent magnitude

(Asked by: username_0 on 2024-02-15)

I would like to be able to compute the sky surface brightness, which is based on the object's apparent magnitude.
We have formulas, which allow us to compute the sky surface brightness based on the position of the Sun below the horizon.
How about the formula, which could include both the position of the body below the horizon as well as its apparent magnitude?
Then we could compute the twilight sky surface brightness for the lunar twilight or eclipsed twilight.
I mean exactly a situation like this:
The apparent magnitude of the Sun is -26.77Mag. Once the Sun is about 3 degrees below the horizon, then the sky surface brightness at solar azimuth is just about 10 mag/arcsec2. What value of sky surface brightness be if we placed the Moon instead of the Sun in the same position against the horizon or if the Sun had -24Mag only?
Are there some computations available?
Any ideas where could I find it?

**UPDATE:**

On this website:

<https://stjarnhimlen.se/comp/radfaq.html#11>

We can find some tables, which refer to the solar magnitude of -26.7

[![enter image description here](https://i.sstatic.net/pJkEY.png)](https://i.sstatic.net/pJkEY.png)

[![enter image description here](https://i.sstatic.net/7O3og.png)](https://i.sstatic.net/7O3og.png)

and then the twilight brightness is calculated.

I am searching for the formula, which could do it for any other apparent magnitude & random altitude of the object.

Imagine, that I would like to compute the sky surface brightness for the section of sky located about 30 degrees above the horizon when the Sun is i.e. 5 degrees below the horizon.

How could I do it? Is there some formula, which would calculate it?

**Tags:** night-sky, brightness, twilight
> **Comments:**
> **username_1**: I am not sure I understand your question correctly. When we perform photometry to get the apparent magnitude of the objects, we usually define an aperture with no objects inside, which serves as the background sky. It's usually done for each frame as the background brightness changes even at different positions in the sky. Do you want to generate a template for the background sky?  
> **username_0**: I would like to generate the template if I know how to do it. I mean that the Sun has an apparent magnitude of -26.77 and when it's  3 degrees below the horizon, the sky surface brightness at solar direction is for example 10mag/arcsec2. What brightness could be if the Sun had not -26.77Mag but for example -24Mag? This is what I am after.  
> **username_2**: To first order it should just scale with the brightness of the illuminating object (or at least, the contribution from that object will).  
> **username_0**: I've already found a formula for this, but still don't know how things stand with respect of the whole atmosphere.  
> **username_3**: You should post the formulas you do have and explain the issues you're having getting them to work for this.  
> **username_0**: Basically I am looking for the formula  

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## 0 answers

