How do I calculate the hours of daylight on an arbitrary planet for a given day at a given latitude?

I want to be able to graph the change in daylight hours across the year for a given latitude, to get an idea of what kind of cycle in available daylight people at that latitude would live through and adapt to. I'm assuming "daylight hours" is the time between the two periods the top of the star is tangent with the horizon in a solar day (sunrise/sunset), assuming the horizon is flat.

The problem is I have no background in mathematics or astrophysics, and all the answers I've found so far seem to assume I know a bunch of terms and formulas off-hand. I'm asking about an arbitrary planet because I can't even find a clear answer on what information about my planet I even need to consider, thus I've no idea what information I should be giving.

The closest to an answer I found was here: https://forum.cosmoquest.org/showthread.php?106741-How-to-calculate-day-length-on-a-generic-planet

...and it reads: Here's how I'd go at it:

1) For a given orbit day (elapsed planetary days since perihelion, for simplicity) calculate the true anomaly.

2) From the true anomaly, calculate the orbital angular velocity.

3) From the orbital angular velocity and the rotation angular velocity, calculate the mean angular velocity of the sun across the sky.

4) From the latitude, axial tilt and [true anomaly-solstice anomaly], calculate the angular length of sun's path in the sky at the required latitude.

5) From 3) and 4), derive the day length.

Now thru google and wikipedia I've learned enough (I think) to make it past step 2. However, "rotation angular velocity" is not a a specific term I can find any info on. I ASSUME it's the angular velocity for the spin of the planet, but I'm not really sure... and then we have "calculate the mean angular velocity of the sun across the sky", which sounds like something that translates to a fairly long equation that clearly isn't given here, nor anywhere else I've searched. Am I supposed to just average the 2 other angular velocities in this step? That doesn't seem right.

Steps 4 and 5 utterly defeat me. If I knew what equations to plug those values into, I don't think I would need to ask this question at all. "solstice anomaly" is another term that seems to exist nowhere else but in this post. Another problem is that these angular values can be expressed in radians or degrees, and I have no idea how those wildly different values should factor into the equation, which I should use, how it would change the final answer...

In essence, I just wanna know what numbers I need to know about my planet and what formulas to plug them into to get a basic idea of what the damn sun is doing. I'm aware that doing this at multiple latitudes for every day will be hilariously tedious, but as long as I know the process, I can at least get started.

I'll also have to calculate the movement of multiple celestial objects eventually, as the movement of particular planets/stars/constellations tends to have a notable effect on what traits/gods people ascribe to them, so I might as well start off relatively easy...

posted about 4 years ago

The Quivering Frond of Destiny‭

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