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Below is a photo that my son took in Scotland showing the sun and moon at the same time. I immediately noticed this anomaly that the light illuminating the moon could not possibly come from the sun. I sent the photo to 4 University astronomy departments and only one responded and that was Cambridge University which is near where I live. The response came from the department librarian (not an astronomer) who said he had never heard of this before. He gave me two possible solutions, one was was from an engineer (not an astronomer) in which he got confused between perspective and light ray tracing and the other was referring to Einstein's theory of light bending by gravity. I check out Einstein and the effect was so small as to be almost immeasurable.

enter image description here

I have looked at the various 'complex' explanations for what to me is a very simple model. What need is there to introduce 'curved planes' and 'starry sky domes' all of which do not exist in reality? It is only referred to as an 'illusion' because observation doesn't fit the conventional model hence the complex explanations to try and make it work. The anomaly is acknowledged to exist with or without photos. Since everyone believes that the moon is illuminated by the sun then simple normal physics do not seem to work. Either the physics is wrong or the sun does not illuminate the moon. I realise that is a heavy statement!

Therefore I state once again:

  1. The sun and the moon are two objects (like a torch and a football) that are suspended in a 3 dimensional space and size should not matter.
  2. The moon/football are illuminated by the sun/torch and a perpendicular line or light ray can be drawn between them.
  3. It doesn't matter where in space you choose to view them, a perpendicular line or light ray can still be drawn between them.

This drawing explains my doubts:

enter image description here

I'm very surprised that some of you have never noticed it before hence the suggestion asking me to post a video. This is a very common occurrence and I have seen it many many times as I go for my morning walk at about 8.00am every morning. I have never thought of actually tabulating my observations.

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  • $\begingroup$ One thing that just stood out to me... is that the moon seems more lit than I'd expect from being as close to the sun as the picture hints visually. I did find in further investigation that the moon on 5/16/16 should've been roughly 135 degrees from the sun in the sky (suncalc path, mooncalc path). $\endgroup$ Aug 8 '18 at 13:36
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    $\begingroup$ Given the picture has some vertical tilt (up)... I would think the image should have a curved ground if a panorama, or is using some sort of lens to adjust the curvature maybe? I wonder if that might be a key factor? $\endgroup$ Aug 8 '18 at 13:37
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    $\begingroup$ The reason this question isn't getting much attention here might be that there is a separate Astronomy Stack Exchange site. It might suite better there... $\endgroup$
    – Communisty
    Aug 23 '18 at 13:45
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    $\begingroup$ Did you mean to say "do not seem"? Good to remember that the ultimate goal of this site isn't discussion, but to make the ultimate answers easily digestible, so people can quickly learn (especially useful on computer programming related questions, where I constantly find the site invaluable... but also has its benefits in preventing questions ending up being opinions.) It still awaits a definitive answer unfortunately... but it's a little rough you're dismissive of most attempts at answering. Many times in life I've thought people wrong only to later finally better understand what they said $\endgroup$ Aug 26 '18 at 18:28
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    $\begingroup$ The "direction of illumination" arrow you have drawn is wrong... the arrow should be pointing directly at the observer (us), perpendicular to the image... not pointing "left" as if the sun was next to the Earth/Moon system. The sun is 93 million miles away... and it's really big. $\endgroup$
    – f.thorpe
    Oct 16 at 0:06
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The apparent anomaly, known as the Lunar Terminator or Moon Tilt Illusion, is indeed a matter of perspective. A brief explanation can be found here: http://chrisjones.id.au/MoonIllusion/

The essence: 'The illusion occurs when the moon and sun are separated by a wide angle, so that they are perceived relative to the horizon, as if in a panorama. A panoramic photograph is a cylindrical projection. In this projection, most straight lines project as sinusoidal curves. The moon-sun line is curved, unless the moon and sun are on the horizon or directly above one another.'

A long, technical explananation is in the PDF The moon tilt illusion. Quoting from page 21:

Modern cameras use lenses whose properties are designed to deliver a rectilinear or curvilinear image. Rectilinear lenses reduce barrel or pincushion distortion from the image but such lenses are difficult to manufacture for the wide angles (90° and above) needed to record both the sun and the moon on a single photograph. A photograph [3] of the moon and sun at an azimuth difference of 80° containing a leaning tower and unnaturally leaning trees illustrates the difficulty of eliminating distortion in a wide-angle photograph

That reference [3] is to A Different Moon Illusion on Jerry Lodriguss astrophotography site Catching the light where he shows and explains the exact same situation (picture taken from there):

enter image description here

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  • $\begingroup$ Since the phenomena can be clearly seen by the naked eye it is therefore a real phenomena and that appeals to photographic optical illusions are not necessary. If you were to draw on a blackboard what was observed then optical illusions are ruled out. $\endgroup$
    – Jackamus
    Aug 8 '18 at 16:47
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    $\begingroup$ A phenomenon that you observe, incorrectly, with the naked eye is the definition of an optical illusion. This answer explains how the illusion occurs, in spite of what you think you are seeing. $\endgroup$
    – haresfur
    Aug 28 '18 at 21:53
  • $\begingroup$ If a torch were placed on a pole coincident with the sun and a football also on a pole and coincident with the moon, the torch would not illuminate the football. I think the reason it is called an illusion is because it doesn't fit the standard paradigm. $\endgroup$
    – Jackamus
    Oct 6 '18 at 17:15
  • $\begingroup$ The idea that this is being called an illusion is because it doesn't fit the official narrative because everyone and his dog KNOWS the Sun illuminates the Moon. It is impossible for this accepted Moon-Sun system to be viewed in any other way than the way I have been maintaining. A bright light illuminating a distant smaller spherical object can only behave in the way that a smaller light (torch) and smaller closer spherical object (football). $\endgroup$
    – Jackamus
    Oct 28 at 20:03
  • $\begingroup$ Out there in space there are no curved planes or celestial spheres on which to build an explanation to try and compensate for the obvious anomaly. In space there is no up or down or left or right. Whatever you observe is what is actually there. Viewing it from a position here on Earth will make no difference to what is observed - a light shining on a sphere. $\endgroup$
    – Jackamus
    Oct 28 at 20:04
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enter image description hereHere my wife holds a globe with the moon in view. I carefully processed in a bit-mode to find the curve of light on the globe and drew perpendicular lines. Plainly we can see that the moon-lite side is facing the sun in the same direction of my globe.

The illusion is due to the sun being so far that the difference in angles shown in the drawing would not be noticeable. Imagine two planes where both of them contain the sun and moon, the level plane would be how an observer would see the moon when both the moon and the sun were at the horizon. The tilted plane is how an observer would normally see the moon high in the sky even though the sun was at the horizon during sunset. The observers on both planes would see the same half-moon shape even though the relative heights in the sky vary greatly. This construct might only work for quarter moon illuminated.enter image description here

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  • $\begingroup$ You seem to agree that one would expect the moon to be tilted more towards the sun but it isn't. The moon's illumination seems to be coming from another direction. I realise that what I am saying goes against what everyone believes but that may be the problem - it is a 'belief' that the sun illuminates the moon and not a fact. $\endgroup$
    – Jackamus
    Oct 18 at 16:19
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    $\begingroup$ @Jackamus It is very much fact that the moon is illuminated by the sun. livescience.com/45979-why-does-the-moon-shine.html $\endgroup$ Oct 20 at 7:33
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    $\begingroup$ Humans can't judge linear metrics beyond 8km. So, when a person visualizes the location of a light source illuminating the moon, the problem is 2D only, involving ORTHOGONAL ANGULAR DISPLACEMENTS (e.g, right ascension/declination, altitude/azimuth, etc.). One traces a "line" from the moon's day/night terminator, orthogonal to its midpoint. This "line" is actually a 2-D "HALF-INFINITE" TRIANGULAR PLANAR SECTION which continues from moon to the light source, with the observer at the vertex. In this case, the moon is on the left edge, and the section continues rightward UNTIL a light source! $\endgroup$
    – Bruzote
    Oct 26 at 23:14
  • $\begingroup$ @Jackamus, per my previous comment, one's eyes cannot perceive distance. Thus, it is only an optical illusion that leads to one to think one perceives that an imaginary "line" from the moon is receding into a point in space. One can only see in angles at astronomical distances. So, where would one stop when sweeping from the terminator in the direction of the light source? Well, one stops at the light source! One must not stop before then, because literally there is no justification to stop. Any perception of a "line" in 3-D space that has terminated is a self-imposed illusion. $\endgroup$
    – Bruzote
    Oct 26 at 23:22
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    $\begingroup$ A further comment to Bruzote - You are trying to complicate a very simple property of physics with complicated geometry which finishes up, not demonstrating anything but stating it is an illusion. You are trying to use scale as a 'Get out of jail card'. Supposing I showed you a photo of a half illuminated sphere without any reference to its size (football or planet). How would you go about determining the line that would lead you to the light source? $\endgroup$
    – Jackamus
    Oct 27 at 20:17
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You can see this effect on the powerline above the railroad tracks in the picture you posted too, it doesn't look straight, even though it likely was in reality! The straight line between the sun and the moon is just even more curved. Just like what you see at http://chrisjones.id.au/MoonIllusion/ , like the top answer already posted. If you accept that the curvature of the powerline on this picture is just an optical illusion/distortion introduced by the camera, then so is the sun-moon illumation!

the picture curves straight lines

The error in your diagram is that you assume a rectangular and linear (0, 1 or 2 point foreshortening) perspective. As you can see in this VSauce video, straight lines in our surroundings actually become curved lines from a single eye (or photocamera) perspective. After you've seen the VSauce video, you can check that this holds true for you too: if you rotate your head, you'll notice that the place where your wall and ceiling meet will curve when you're moving from side to side. Straight lines, when viewed from below from left to right cease to be straight! A 5-point curved perspective better captures the way straight lines appear to us.

5 point perspective

Note, by the way, that even from a "torch" perspective, as you insist, and without any optical illusion, we can get the moon shining "upward". Consider the following overview picture: the moon (left object) is illuminated by the sun (right object) in exactly the way you expect. Now, however, consider that you are an observer (where the two red lines converge), in particular, that you are standing below the sun and moon. As you know, if you stand below things, you cannot see what is on top -- and similarly, you can see more of what is on the bottom of that object. That is what's drawn in the dotted lines from the observer view: they tangentially hit the moon on the dark side on the bottom, and cannot observe the top of the moon. Just because we're below that object.

Overview picture of moon and sun

Thus, if you place yourself in the position of the observer, the objects will appear as if they have both rotated away from the horizon, because we can see both bottoms of the objects!

If you put the two effects together (one, the strange effects of panning from left to right to lines above us; and the effect of being located below the moon), we end up with the following effect, where it appears that the "moon" is facing upwards to the right in the first few frames when we're looking to the left, but once we zoom out you can see that the sun is actually level with the moon!

sun-moon system

The effect nearly disappears entirely once I add a line connecting the two bodies:

sun-moon system with added lines

Now the effect looks like it isn't even there anymore, because somehow our brains are able to make sense of the perspective. Note how in every single picture, the lines are all straight (so, no trickery with wide-angle or fish-eye lenses), but when we rotate from left to right, they seem to "change direction" from pointing northeast to northwest and back.

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    $\begingroup$ @Jackamus: Okay, so I have replaced the two animations with two new ones, which hopefully show the full effect. You can see a moon (on the left) that appears to "point upwards", but when zooming out the effect disappears. Even if the sun/moon are level with the camera (so, we're still looking up, but they are positioned in the center line of vision) as in imgur.com/a/W1aVBEy, you can see that the effect persists. $\endgroup$
    – Erik
    Oct 23 at 7:41
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    $\begingroup$ I think those new animations are the most intuitive answer I've seen on here (and they match the answer I never got around to posting 3 years ago). Note you can easily reproduce this effect IRL by looking up at a wall/ceiling join through a directors viewfinder formed by your hands and then swivelling. $\endgroup$
    – Deditos
    Oct 23 at 10:19
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    $\begingroup$ @Jackamus It'd be helpful to make sure you agree (or not) on two points first. (1) do you agree that the powerline in your picture appears more curved than it would be in real life? (2) do you agree that in the zoomed-in perspective (without lines present) it kind of looks like the "moon" is illuminated from above-right rather than from just from the right? These are relevant points for me! $\endgroup$
    – Erik
    Oct 24 at 8:16
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    $\begingroup$ @Jackamus I agree that the moon should be (and is) illuminated by straight rays following the shortest path from the sun to the moon. Just like a torch and a football. But doesn't the animation show that the moon (or football) might seem to be lit from above (from a zoomed in perspective below the object, looking to the side), even when it really is lit from the side only (as visible from a zoomed out perspective)? To me, the animation [and curved power line] confirms that your picture is an optical illusion: a stitched-together picture of the zoomed-in perspective on the moon. $\endgroup$
    – Erik
    Oct 25 at 13:54
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    $\begingroup$ @Jackamus from seas.upenn.edu/~amyers/MoonPaperOnline.pdf, “...the line connecting the horns of the moon, between its first quarter and full moon, for instance, does not appear to be at all perpendicular to the direction from sun to moon; we apparently think of this direction as being a curved line. Fix this direction by stretching a piece of string taut in front of your eye; however unlikely it may have seemed to you at first you will now perceive that the condition of perpendicularity is satisfied” $\endgroup$
    – Erik
    Oct 25 at 17:12
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EDIT: I am making two simplifications which still display the "anomaly".

  1. I consider the 2 dimensional case.
  2. Sunbeams (blue lines) are nearly parallel, since the Sun is so far away.

At sunset the observer can see the unlit part of the Moon at the bottom, so it appears illuminated from above. enter image description here

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  • $\begingroup$ Sorry but no. The observer will see exactly what you have drawn. The light coming from the right is perpendicular to the illumination of the moon. The place of observation will make no difference to what is observed. In your drawing a second observer is observing the first observer and what that first observer sees. $\endgroup$
    – Jackamus
    Oct 17 at 10:07
  • $\begingroup$ The observer will see the shaded portion of the moon at the bottom. The new moon always appears illuminated at the bottom at sunrise or sunset, for the same reason. $\endgroup$ Oct 17 at 15:43
  • $\begingroup$ You still seem to be missing the point. It doesn't make any difference where I view the moon from. If it is being illuminated by the sun then there will be a perpendicular between the moon and the sun. I cannot understand why this is not obvious to you as indeed you would have to agree that a football and a torch would look just the same. The problem is, with the greatest respect, 'cognitive dissonance'. You are being shown an observable fact that conflicts with what you believe. $\endgroup$
    – Jackamus
    Oct 18 at 16:11
  • $\begingroup$ "there will be a perpendicular between the moon and the sun" Usually we speak of a line perpendicular to another line (or perhaps a plane). What do you mean by this? $\endgroup$ Oct 18 at 16:45
  • $\begingroup$ By 'perpendicular I mean a straight line drawn between the centre of the Moon and the centre of the Sun. $\endgroup$
    – Jackamus
    Oct 19 at 18:29
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Here is what you do. Look at the moon. See which way the sunlit face of the moon is pointing, not in a picture but in a real-life view of the moon. Using your own perception, trace a line INCREMENTALLY through space that goes out in the direction "pointed to" by the lit side is pointing. Keep tracing that line until your line hits an object bright enough to light the moon OR until the line extends past the horizon. This process ill eventually lead you across the sky to the sun or in the direction of the sun at the horizon. Every. Single. Time.

If you find otherwise, then you have an insufficient sense of three-dimensional direction and that requires either some kind of skills therapy or else just acceptance that you can't accurately imagine 3-D line tracing in the real world.

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    $\begingroup$ The issue is a "straight" line in the sky is not straight; for example, a line from the Moon to the Sun. A straight line in the sky is a great circle, and a great circle "arcs across the sky". This is the phenomenon that needs to be explained. The light from the Sun to the Moon is in the plane of the ecliptic (within 6 degrees of the ecliptic), and the ecliptic projected onto the sky is curve. After removing the distortions due to photographic lenses, the curving line of the ecliptic is exactly like the original photo. The illuminated part of the Moon points in the ecliptic plane to the Sun. $\endgroup$
    – JohnHoltz
    Oct 25 at 16:38
  • $\begingroup$ @JphnHoltz - You are right. I realized that after my comment. Still, Jackamus should follow a great circle across the sky. Unfortunately, she doesn't seem to intuit why she should do that. Instead, she uses fallacies to discredit explanations that she will not understand. She clearly demonstrates frustration with explanations that are not convenient for her. The reality is she simply doesn't "get" how she is confusing 2-D and 3-D geometry and line tracing. Further, she seems to want only validation of her emotions, not a logical explanation of her misperception. $\endgroup$
    – Bruzote
    Oct 25 at 16:59
  • $\begingroup$ With a name like 'Jackamus' I would have thought that my gender was obvious - Male! Regarding the 'Great circle' it doesn't exist - there is no celestial sphere. I said this in earlier comments when someone mentioned it. The celestial sphere is simply a convenient way to plot stars with respect to each other. BTW I was a technical illustrator for over 30 years and part training was understanding perspective geometry and light ray tracing. So I do know the difference. $\endgroup$
    – Jackamus
    Oct 26 at 16:27
  • $\begingroup$ Jackamus,- You have a good handle on perspective? Fine. Then see my explanatory comment under Eric Reiter's answer. Hopefully it puts to rest your confusion. $\endgroup$
    – Bruzote
    Oct 26 at 22:50
  • $\begingroup$ Would someone care to explain to me why appeals to the 'celestial sphere' and the 'great circle' are constantly made when we all know it doesn't exist. It only enables you to plot on star relative to another star using spherical coordinates for the sake of convenience. It cannot be used to answer my Moon-Sun anomaly. Would someone please confirm this? $\endgroup$
    – Jackamus
    Oct 27 at 20:25
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I agree that this problem is very counterintuitive! However, the answer is very simple: the horizon is curved (it is actually a circle that passes behind us as well as in front of us).

Although it is curved, we generally perceive it as straight unless we specifically look for the curvature. This "correction" in our brains is what makes the angles seem wrong. You can see the curvature of the Earth anywhere there is a wide angle of open water (greater than 90 degrees is best) reaching the horizon. If you were standing on the moon and the moon's surface was smooth instead of mountainous, the curvature would be more apparent.

The apparent direction the lit side of the moon is facing will always be higher than the apparent position of the sun due to the convex nature of the horizon. The greater the angular distance between the sun and the moon, the greater the effect.

Another optical illusion explained the same way is that the apparent angles make it seem that the sun is as close as, or closer than the moon in your photo since the moon is at least half illuminated by the sun.

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  • $\begingroup$ I think you are trying to make the facts fit the theory. Why can't you compare the anomaly with a torch shining on a football? Surely it is only a matter of scale. $\endgroup$
    – Jackamus
    Jan 24 '19 at 12:34
  • $\begingroup$ @Jackamus It's more like a nuclear blast shining on a grain of sand 1000 miles away. $\endgroup$
    – f.thorpe
    Oct 16 at 0:10
  • $\begingroup$ Light travels in a straight line and the grain of sand will still be illuminated on a perpendicular line from the nuclear blast. The moon does not appear to be illuminated in this way. $\endgroup$
    – Jackamus
    Oct 17 at 10:00

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