There's an optical illusion known by names akin the "lunar terminator paradox". This has much conversation and descriptions online, but none made awareness in my head, so I wrote this program to fig out what was going on. The paradox:
- The moon is illuminated by the sun
- After sunset, the sun is below, so we would anticipate the illuminated part of the moon to item down, towards anywhere the sun is
- This isn't what continually happens!
I was camping in the mountains alongside a companion recently. We were looking up at the sky, fair following the sun has set. The moon was plainly pointing up.
After playing alongside this program, I have clarity: we're looking up at the moon from below. The most pathological case is a complete moon. Let's say the moon is on the horizon: elevation=0. If we're looking at this low moon, and the moon is full, the sun is immediately rearward us. The moon is completely illuminated, and we see 100% of the moon disc lit up.
Now, what happens if the moon is not at the horizon, but higher up at the sky? Effectively, the sun is infinitely far away, so the identical part of the moon is lit up. But we're now looking at the moon from below, and we would see several of the dark flank on the base edge. I.e. the moon appears brilliant at the top, but has a dark piece missing at the bottom: it points up! Even at sunset.
This is the most plainly weird case. A half-moon has no paradoxical behavior, and the additional complete the moon, the additional plainly we can detect the brilliant moon pointing up notwithstanding the sun being down.
I create two plots. At 3/4-full moon at sunset we appearance at the moon as it rises from the horizon all the way up to the zenith:
If the moon is at the horizon (elevation = 0), we see the expected 3/4-lit disc. As the moon rises, we see additional and additional of its bottom, and thus additional and more dark areas display up: It plainly points up at sunset!
We can additionally move the sun around. Let's say the moon is 60deg up; let's move the sun from new-moon to a full-moon:
In the darkest configuration, we can motionless see a lit crescent on the bottom: the illumination is all on the contrary side, but we can see a piece of the illuminated rear side. As the sun swings around, we see additional and additional of the moon. At azimuth = 90deg, we have a half-lit moon. Past that, additional and additional of the moon is visible, continually pointing up.
This was additionally a excellent engaging study of the current province of AI tools. As I was penning this and debugging, I would conversation to Claude and Gemini concerning how this worked and what I have to be seeing. They were the two entirely unable to comprehend this, and would create infinite circular arguments. Clearly they read some incomplete explanations on the net (as I have), and deficiency the reasoning capability necessary to distill it into item resembling "understanding". AGI is not current yet.
