Lunar Terminator Paradox

dvh

> Now, what happens if the moon is not at the horizon, but higher up at the sky? Moon follows the sun to the west so to move moon "higher" up in the sky you need to rewind time (15deg/hour). In e.g. 4 hours moon barely moves in it's 28 day cycle so the moon will look exactly the same (you can take a picture and compare). It's the earth rotation that make moon "go down" or up. I've read your article 2 times and I still don't understand what is apparent problem, no wonder AI had trouble. Also it's hard to reason about up and down when moon move along ecliptic which is curve. Down at noon points elsewhere as down at sunset.

ionwake

is this a bad moment to mention how weird it is that the moon is perfectly positioned to create eclipses? I think its pretty incomprehensible odds if you ask google. But I could be wrong I know literally nothing about astronomy, it just always surprised me its not common, but it be cool if someone could explain that

Sharlin

The sky is spherical, so straight lines in the sky aren’t straight lines on its 2D projection on the retina. Rather, straight lines are great circles. So if you trace the great circle that connects the sun and the moon, the moon should "point" along that great circle – which can be considerably off of what we think of as a straight line (which is curved in reality).

willrshansen

Was expecting time travelling moon robots. :(

teamonkey

It’s cool and all, but I do worry about this instinctive reaching for AI to build convoluted answers to stuff like this, which is easily demonstrated by, say, two balls and a lamp, not to mention the myriad of astronomical simulators that already exist. The software is being written to teach the user something, but it’s not novel software, or a novel problem, and the creator doesn’t actually care about the process of making the software, or actually thinking about how to solve the question. But they have access to an automatic wheel reinvention machine and so...

j1mr10rd4n

To me, this article conflates lunar elevation and phase. Together with the use of ambiguous terms "up", "down", "above", and "below" makes it difficult to understand the author's intent and what their software is meant to visualise. Lunar elevation (aka "altitude" in celestial coordinates) is sidereal, so the maximum range is determined by the viewer's latitude. The moon's orbital plane is not perfectly aligned with that of the sun-earth so there's another component there, but this only varies +/- 5 degrees of the sun's declination. Lunar phase is synodic, so there's no significant variation in the observed illuminated portion with the moon's elevation over one night. The full moon occurs when the moon is on the opposite side of the earth from the sun, so it rises at sunset, transits the meridian at midnight and sets at sunrise, (+/- a few minutes for seasonal variation). Here's a nice visualisation of the lunar analemna - the figure described by the apparent position of the moon over a month - from Mt. Laguna at 32.8 degrees north. https://www.hpwren.ucsd.edu/news/20250212/ I also found this page with a decent explanation of the apparent effects of orbital cycles. https://www.cyclecalcs.com/learn/synodic-sidereal.html#faq

oofbey

Omg this paradox has bothered me for so long. I’m thrilled to have it finally explained.

shiandow

I understand less than before I read this article. When has anyone ever noticed a full moon becoming less full during the night? Not that the effect doesn't happen, but it is minor. This effect also occurs during first and last quarter, despite what the article claims. And what on earth is the first plot? A moon that rises to its zenith doesn't become half lit. And is the dark coloured part li?, Where is the 3/4 moon?

madaxe_again

The TLDR is that the sun is very, very far away compared to the moon. It’s actually quite fun to look at the moon, adjust your mental model based on where the sun is relative to you and what you see illuminated, and experience the scale of the solar system.

divbzero

This isn’t really a paradox if you just visualize the Moon as a sphere and visualize where the Sun is shining from, and I think that’s what the plots in OP demonstrate. The “paradox” might be in the initial assertion which does not use an accurate mental model: “After sunset, the sun is below, so we would expect the illuminated portion of the moon to point down, towards where the sun is.” This assertion might be true if at sunset the Sun ducks just behind the horizon, around the same distance or closer than the Moon is to the Earth. In reality, the Sun is of course much farther from Earth than the Moon. Factoring the relative distances into the mental model will lead you to the correct conclusion.

MarkusQ

Was this known as the "Lunar Terminator Paradox" or called that anywhere before this article? So far as I can tell this seems to be entirely made up and the only references I can find are to TFA or related. As others have noted, there doesn't even seem to be an actual paradox other than a possible confusion about how a half-lit sphere looks from various perspectives.

tiborsaas

I was also confused by the article, but I've noticed that I'm not the only one. I think I get what confused the author, it's the fact that angle the shadow appear to us depends on the latitude of the viewer on Earth. It's not super intuitive. https://www.youtube.com/watch?v=XHzzRbw0lgI

Veedrac

Simple way to imagine this in your head. Hold two ping pong balls at arms' length, one above and further away than the other. Right now you are the sun. Put a red dot on top of the lower one, and then rotate it just slightly until you can't see it. This is the observer on Earth, who is after sunset. Put a red dot directly in the middle of what you can see on the upper ball. This is the center of where the sun is striking the moon. Keep looking at this dot on the moon. Now, keeping their relative positions fixed, bring the balls towards you and up, until you are looking from the perspective of the observer on Earth. What happens to the dot on the moon? It appears to rise up away from you. That's the paradox.

fizzbuzzbarbazz

You walk into a dark basketball court through a doorway with a single bright light above it. as you approach the free-throw line, you realize someone has left a basketball at center court. part of it is lit by the light of the doorway. even though you are very drunk, you don't assume that spinning around will allow you to se more of the basketball than you currently do. even leaning left and right while looking at the ball doesn't give you much of a different view. the sun is the door. the moon is the ball. you are a person looking at the ball from earth. leaning shifting left a step might give you a perspective that may correlate roughly with moon-at-dusk. shifting right a step might give you a perspective that is roughly moon-at-dawn. leaning forward or backward, left or right, drunkenly, and spinning around might give you different angles (relative to the line drawn from your ass to your head) that the shiny-side of the basketball seems to be pointing. but you're just drunk. the shiny part of the basketball always points towards the light above the door. it is just your local perspective that is changing.

gholap

This article was quite hard to understand, and the author called it "Lunar Terminator Paradox", which does not give too many Google hits. "Lunar Terminator Illusion" is the thing to search for. This 11-year old Vsauce video did the trick for me: https://www.youtube.com/watch?v=Y2gTSjoEExc Check around the 5m3s timestamp if in hurry, and not interested in other stuff he discusses.

dreamcompiler

Author uses the words "top" and "bottom" but these words are ambiguous when it comes to objects in the sky. A better way to describe the geometry is to notice that at sunset when the sun is in the west, if the moon is directly overhead its western half will be illuminated.