Yesterday morning afforded a lovely coincidence of a crescent moon, Venus, and my southbound drive under a dawning sky. There is something about a crescent with Venus close by on the concave side that looks just right. (Islamic flag designers the world over agree.) It seemed that there would be one more waning crescent in this cycle, and there it was this morning, much thinner than yesterday and no longer in intimate proximity with Venus.
I wondered how long it would stay visible. Twenty minutes before sunrise, it no longer stood out in the sky. I had to use the line between Venus and the coming sun to find it. Ten minutes before sunrise, it faded from view, sometimes seeming to be part of my perceptions, sometimes not. The moon is up there now, as big as the sun, but completely invisible to me.
Roughly calculating, the moon occupies the night sky about half of the time, and when it does it is the brightest object up there regardless of its phase. The moon is also present in the daytime sky half of the time. Though nothing can compare with the sun, a gibbous moon stands out well; I have particular memories from childhood for some reason of the moon over the mountains to the east at mid-afternoon. Crescent moons can take some searching to find, though, and when they’re close enough to the sun they are impossible to see.
If all phases of the moon occured equally at all times of the day, the moon would still dominate the night sky and pale compared to the sun in the day, but the phases are not equally distributed. Orientation of sun, moon, and earth results that full moons only happen at night, and new moons, that we couldn’t have seen anyway, only transit the sky during the day. Gibbous moons spend most of their time in the night sky, and crescents spend most of theirs up during the day, only attracting our attention and admiration around the twilight hours. (See top paragraph above.) I should do a calculation of the relative abundance of lunar photons at the different hours of day and night. Just thinking out loud, if the intensity of lunar light is a sinusoidal function, then noon would experience the trough half of the sinusoid, and midnight would have the crest half, giving a ratio of (π-2)/(π+2), which is about 0.22. For any hour the relative intensity is π+2cosθ, so the total for night is π²+4, and for day it is π²-4. So, 30% of moonlight falls at day and 70% at night.
I have in mind to go out around noon next month, and see when the last day is that I can find the waning crescent, and then how long until I can find the waxing crescent. My guess is six days of mid-day lunar invisibility.
[These words were also posted at Junior Ganymede.]