I have a question regarding the apparent and absolute magnitude of space debris objects or meteors reentering the earth's atmosphere. I already understand the difference between apparent and absolute magnitude. The absolute magnitude is the brightness of the object if the object is at a distance of 100km and at zenith. And the apparent magnitude is how bright the objects appears to the observer.
But how can I determine the apparent magnitude of an objects observed from an observer? The objects has the distance $d$, the zenith distance $Z$ and the height $h$. On the internet I found the following equation:
$$ M = m +5 \log(\cos(Z)) $$ $M$ = absolute magnitude, and $m$ = apparent magnitude. I posted a picture below.
But how is this equation derived? I do not understand the equation. What can I do, if the height $h$ of the objects does not equal 100 km?
The book where i found this is "The Observer's guide to Astronomy" (Volume 2) pages 659 to 660!