Note: If anyone finds errors in my calculations or disagrees with something I’ve done, email me at firstname.lastname@example.org, I will fix any errors. Even if you completely disagree with me, feel free to email. I will include any polite emails disagreeing with me at the bottom of this page.
A lot of what we see in relation to the sun is affected by perspective. In short, perspective makes everything look smaller as it gets farther away. When something gets too far away, we can no longer distinguish objects that are next to each other, they merge together. This happens uniformly. Things shrink vertically and horizontally at the same time. How big something appears is called “angular size”. This is something we can calculate based on the size of the object and how far away it is.
Something in the sky at the same altitude will appear higher when its close, and lower when it’s far. How high something appears above your eye level is called “angular elevation”. This is something we can calculate based on it’s elevation and how far away it is.
Sun’s angular elevation
We can calculate how high above the horizon the sun will appear. There’s plenty of good info and pretty pictures so it gets it’s own page.
Sunrise and sunset lateral angle
In progress, in the meantime, watch this video from Wolfie6020.
Angular size of the moon
In progress, have a look and send feedback.