'P' is the key

[Loose_Spell_9313]

Now between the 11 o'clock spike and the 2-3 o'clock spikes, the numbers of stars that appear above drops to 1.If we consider the stars as representations as two celestial bodies in the sky, the sun and the moon, the inference then becomes that at between 11 o'clock and 2-2:30 o'clock, there is only one in the sky- while the rest of the hours feature both.

There are times when the sun and moon are both visible in the sky at the same time but at night the sun is not visible in the sky and the appearance of the moon in the sky is variable.  I think it is a huge stretch to get times of sunrise and sunset from this illustration.

[i]"There are times when the sun and moon are both visible in the sky at the same time.." 
Correct, this would be the 2 stars. 

"but at night the sun is not visible in the sky" 
Correct, this would be the one star.

"the appearance of the moon in the sky is variable." 
You are choosing an example of 1 day/30 days to disprove an argument. The math is not in your favor. [/i]

Edit: Even if the question becomes "what about months where there is no sunrise/sunset in the arctic?" The answer remains that there is nowhere else in the world where the time between sunrise and sunset is 3-4 hours other than the arctic circle.