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I would like to determine the brightness of the light source at twilight based upon its apparent magnitude. In the question here: What are the average wavelengths and brightnesses of sunlight across the stages of twilight? we can find the query referring to the brightness of sunlight at different stages of twilight. Indeed, they're calculated well and published under this link: https://stjarnhimlen.se/comp/radfaq.html#11 where the apparent magnitude of the Sun overhead is -26,7Mag. Next, we have the other data, as listed in the screenshot below: enter image description here

enter image description here but as you can see, the overhead sun's stellar magnitude of -26.7Mag is crucial for all of them. How they could look in a situation when the solar apparent magnitude could be lower (eclipse-induced circumstances) with about -21Mag for example? What do all of these values look like?

I am looking for some decent formula or calculator, which could compute these values if it's any available.

UPDATE:

I found some hint here

What's the conversion between apparent magnitude and lux?

and the calculator here: https://www.vcalc.com/wiki/vCalc/vMag+-+to+-+lux

but the calculator computes only the full values, no decimal are allowed.

I've tried the formula and put the solar magnitude of -26.77. Finally I got the result of about 108642Lux whereas the website here: https://stjarnhimlen.se/comp/radfaq.html#11

says, that the Sun at zenith should give us about 130000Lux. The difference is quite large, what could be the reason behind it?

UPDATE: https://www.chegg.com/homework-help/questions-and-answers/sun-lights-daytime-sky-average-surface-brightness-y-4-mag-asec2-apparent-brightness-sun-26-q43913905

This task reflects pretty much my question.

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