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.
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
it was my vague understanding that what is weird is the apparent size matching. since the moon is slowly moving away, eventually we'll no longer have total solar eclipses, just annular and partial.
If there were greater significance to it, I’d have thought the the visual sizes of the Sun and Moon would have been perfectly matched, rather than to within a few percent, give-or-take.
Also since the Sun-Earth distance varies and so does the Earth-Moon distance, the coverage of the Sun varies. We sometimes get annular eclipses where the Sun is not totally covered.
The moon is 400 times smaller than the sun, but the sun is 400 times farther away, so they appear to be the same size. The solar eclipse we see, with the moon obscuring the sun but just allowing light around the edges the way it does, may be a very uncommon phenomena.
It’s more like, if the moon were much farther away then total solar eclipses wouldn’t happen at all. But the opposite is not true. If it were closer than total solar eclipses would be more common.
It is an interesting coincidence. But the statistician in me feels like calculating the probability is a bit spurious. For one, not all combinations of distance and size are equally likely, and running physical simulations to try and get decent Monte Carlo estimates of the odds feels a bit suspect - I imagine a decent chunk of what you’d be measuring is the influence of parameters whose values are empirically unknowable.
But, even more than that, it comes from the same place that requires me, when a cashier sees the total is exactly $50 and asks, “What are the chances of that?” to actively suppress the urge to say, “About the same as for $59.37.”
Im not trying to be mean but nothing you said made any sense, possibly because I wasnt clear.
I do appreciate your time and your feedback and Im not great at patience but Im going to try because I am dim in many subjects.
I meant an exact solar eclipse where the Sun and the moon seem to match perfectly.
As such the math odds are low.
Finally, if I ever went to a shop and I was charged a round number like $50, or in my case even $3 I would immediately assume I am being scammed, as that is rare given the context.
( which incidentally happened to me once in Barcelona due to a local spanish barman trying to charge me a tourist tax ).
But I am grumpy and it is late, please forgive coarseness of my reply.
I think it's easier to understand if you consider the opposite case: how could the moon never be on the Sun-Earth ray? It would have to orbit Earth around the Sun-Earth ray. But the Sun-Earth ray changes direction as Earth orbits the sun, so the Moon's orbit would have to change with it. People in the northern hemisphere would not be able to see the moon at the same time as people in the southern hemisphere for significant portions of the Lunar cycle, and we would always see a half-moon.
That the Earth-Moon orbital axis is not incidental with the Sun-Earth orbital ray means we'd always, eventually, have solar and lunar eclipses.
Perhaps if Earth were in a tidally locked orbit with the Sun, the Moon could be in a tidally locked orbit with the Sun while also orbiting the Earth. But then half the planet would be frozen and the other half would be completely baked and we wouldn't be having this conversation.
It is never a bad moment to mention this. For planets with a single moon, the probability of such an occurrence has been estimated at 4% [1]. I like to think that this is what extraterrestrials would find most fascinating about our world.
It’s also transient. In a few million years, the Moon will have drifted far enough away that it cannot fully eclipse the sun. Long ago, the Moon was so close you wouldn’t have been able to clearly see the Sun’s corona during a total eclipse.
It's simply a huge, beautiful coincidence. If the galaxy was teeming with life capable of interstellar travel, our planet would be famous for its perfect eclipses.
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).
Well sure. Yeah. Do you find this explanation clear and satisfying though? Can you use it to answer a question like "at sunset, during a half-moon, can you see an upward-facing moon"? Maybe you're much smarter than me, but I had to write the simulator to figure out the answer. Claude and gemini never wrote the simulator, so they consistently answer that question incorrectly :)
No, you will not see an "upward facing" moon. At sunset, the west side of a half the moon will be illuminated. I think you are getting your self tangled with terms like "upward" and "downward" and "facing"
Makes perfect sense to me. When starting the shortest path for a flight from San Francisco to Tokyo, you don't point the plane toward Japan, you point it towards Alaska.
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...
I think you're overstating your case. I never said this was novel. I didn't vibe code any of this. Two balls and a lamp were not sufficient to make this clear to me, but writing the simulator was.
The LLMs have read all of the internet, and are thus quite good at answering questions like this, and I have zero problems asking them about it. In THIS case, the answers available on the internet kinda suck, which made the LLM suck as well.
Perhaps I was too harsh, sorry. I’ve seen a huge amount of vibe coded solutions to more trivial questions than this and assumed it was more of the same.
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 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?
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.
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.
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.
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.
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.
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
it was my vague understanding that what is weird is the apparent size matching. since the moon is slowly moving away, eventually we'll no longer have total solar eclipses, just annular and partial.
The relative sizes are approximate, not perfect, but close enough that our monkey brains interpret it as more than a coincidence.
Idk, one could come up with a hypothesis that eclipses provide the first tangible validation of a system of mathematics.
If there were greater significance to it, I’d have thought the the visual sizes of the Sun and Moon would have been perfectly matched, rather than to within a few percent, give-or-take.
Also since the Sun-Earth distance varies and so does the Earth-Moon distance, the coverage of the Sun varies. We sometimes get annular eclipses where the Sun is not totally covered.
The moon is 400 times smaller than the sun, but the sun is 400 times farther away, so they appear to be the same size. The solar eclipse we see, with the moon obscuring the sun but just allowing light around the edges the way it does, may be a very uncommon phenomena.
It’s more like, if the moon were much farther away then total solar eclipses wouldn’t happen at all. But the opposite is not true. If it were closer than total solar eclipses would be more common.
It is an interesting coincidence. But the statistician in me feels like calculating the probability is a bit spurious. For one, not all combinations of distance and size are equally likely, and running physical simulations to try and get decent Monte Carlo estimates of the odds feels a bit suspect - I imagine a decent chunk of what you’d be measuring is the influence of parameters whose values are empirically unknowable.
But, even more than that, it comes from the same place that requires me, when a cashier sees the total is exactly $50 and asks, “What are the chances of that?” to actively suppress the urge to say, “About the same as for $59.37.”
Im not trying to be mean but nothing you said made any sense, possibly because I wasnt clear.
I do appreciate your time and your feedback and Im not great at patience but Im going to try because I am dim in many subjects.
I meant an exact solar eclipse where the Sun and the moon seem to match perfectly.
As such the math odds are low.
Finally, if I ever went to a shop and I was charged a round number like $50, or in my case even $3 I would immediately assume I am being scammed, as that is rare given the context. ( which incidentally happened to me once in Barcelona due to a local spanish barman trying to charge me a tourist tax ).
But I am grumpy and it is late, please forgive coarseness of my reply.
I think it's easier to understand if you consider the opposite case: how could the moon never be on the Sun-Earth ray? It would have to orbit Earth around the Sun-Earth ray. But the Sun-Earth ray changes direction as Earth orbits the sun, so the Moon's orbit would have to change with it. People in the northern hemisphere would not be able to see the moon at the same time as people in the southern hemisphere for significant portions of the Lunar cycle, and we would always see a half-moon.
That the Earth-Moon orbital axis is not incidental with the Sun-Earth orbital ray means we'd always, eventually, have solar and lunar eclipses.
Perhaps if Earth were in a tidally locked orbit with the Sun, the Moon could be in a tidally locked orbit with the Sun while also orbiting the Earth. But then half the planet would be frozen and the other half would be completely baked and we wouldn't be having this conversation.
It is never a bad moment to mention this. For planets with a single moon, the probability of such an occurrence has been estimated at 4% [1]. I like to think that this is what extraterrestrials would find most fascinating about our world.
[1] https://medium.com/@asorlik/the-probability-of-total-solar-e...
It’s also transient. In a few million years, the Moon will have drifted far enough away that it cannot fully eclipse the sun. Long ago, the Moon was so close you wouldn’t have been able to clearly see the Sun’s corona during a total eclipse.
Over 600 million years left! Complex life may be gone by then (see silicate weathering).
It's simply a huge, beautiful coincidence. If the galaxy was teeming with life capable of interstellar travel, our planet would be famous for its perfect eclipses.
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).
Well sure. Yeah. Do you find this explanation clear and satisfying though? Can you use it to answer a question like "at sunset, during a half-moon, can you see an upward-facing moon"? Maybe you're much smarter than me, but I had to write the simulator to figure out the answer. Claude and gemini never wrote the simulator, so they consistently answer that question incorrectly :)
No, you will not see an "upward facing" moon. At sunset, the west side of a half the moon will be illuminated. I think you are getting your self tangled with terms like "upward" and "downward" and "facing"
Makes perfect sense to me. When starting the shortest path for a flight from San Francisco to Tokyo, you don't point the plane toward Japan, you point it towards Alaska.
Well, you also point it at Japan.
Was expecting time travelling moon robots. :(
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...
I think you're overstating your case. I never said this was novel. I didn't vibe code any of this. Two balls and a lamp were not sufficient to make this clear to me, but writing the simulator was.
The LLMs have read all of the internet, and are thus quite good at answering questions like this, and I have zero problems asking them about it. In THIS case, the answers available on the internet kinda suck, which made the LLM suck as well.
Perhaps I was too harsh, sorry. I’ve seen a huge amount of vibe coded solutions to more trivial questions than this and assumed it was more of the same.
...have done this many times for friends! A torch and a yoga ball work nicely ;)
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
Omg this paradox has bothered me for so long. I’m thrilled to have it finally explained.
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?
If it rose to the zenith, it would. This is the paradox.
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.
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.
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.
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