The Moon Tilt & Terminator Illusions

[Eburacum]

Define your axis, your plane, and your radius, and then we can talk orthodromes

Now I come to think of it, we can define these values fairly easily. The plane is the plane that bisects the illuminated part of the Moon exactly; this plane will also bisect the Sun, and the observer. The axis is 90 degrees normal to this plane, and the radius is infinity, with the observer at the centre.

Note I'm not trying to explain the phase of the Moon, but the angle of tilt; the phase is dependent on distance, as AmberRobot notes in this post.
https://www.metabunk.org/threads/cl...a-evidence-for-distant-sun.12918/#post-289025

 

[Z.W. Wolf]

Here's the 'great Circle' path of the sunlight, superimposed onto Trailblazer's image. This corresponds to the brim of FatPhil's hat.

This covers a decent amount of degrees. I'm not sure how many. So what kind of camera, what kind of lens, and how was it cropped? The aspect ratio of the photo leads me to believe that it has been cropped.

Are we sure this anomaly is not due to non-rectilinear barrel distortion or post-processing artifacts?

I know about barrel distortion. The Sun and Moon are at the top of the frame and the far edges of the frame. The Moon is in prime real estate for anomalous tilt due to barrel distortion. Couldn't the "great circle" rather be tracing the upper edge of this kind of thing? Note the tilt of the buildings on the far left of the frame.

The barrel distortion would be less severe than this, of course. This is was taken with a very short focal length lens. But I exaggerate to clarify.


How has the photo been cropped? If the frame was cropped through the center, we wouldn't see the barrel distortion on the new bottom of the frame. The relatively undistorted center of the frame would become the bottom of the frame. In other words the barrel distortion would only be evident at the top of the frame because the distorted bottom of the frame was eliminated.


But I doubt things are this simple. It might be true with a film camera, but that's not likely the kind of camera in use here.

I suspect there's a more complicated explanation that involves the optics of digital cameras and how things are processed by the camera, or post processing.


Full disclosure. I don't know anything about "stitching" so I uploaded the photo to GPT 4o and asked my electronic friend: "In this photo the terminator of the Moon seems to be tilted the wrong way. In other words the illuminated portion of the Moon doesn't seem to be pointed at the Sun. Could this be an example of post processing of the wide angle photo which has attempted to eliminate distortion but has introduced this anomaly as a side effect?"

Post-processing Artifacts (in panoramic stitching or lens correction)
What it is: When stitching a wide-angle or panoramic image, software often performs:

Perspective correction

Lens distortion removal

Field flattening

Effect on geometry: While these steps aim to make the image appear natural to the human eye, they alter angular relationships between objects. A straight "great circle" path between Sun and Moon can appear curved or misaligned as a result.

Relevance here: The image appears to have been stitched or post-processed to reduce lens distortion, but as a side effect, it may have introduced non-linearities in the alignment between celestial bodies.

I have no way of evaluating this answer. If someone here has the knowledge base to evaluate the answer, my mind's wide open.

 

[FatPhil]

However, I expect you fully understand how the light follows a great circle in this situation;.

I don't think it does. All the great circles that I can think of on earth are ones below my feet. Curves connecting arbitrary points in the sky - which in three-dimensional reality are straightlines - do not satisfy the definition of a great circle. They would if spherically projected onto the earth, but then they'd be below my feet.

 

[FatPhil]

Now I come to think of it, we can define these values fairly easily. The plane is the plane that bisects the illuminated part of the Moon exactly;

That's progress, but it tells me making progress will be a slow proces. An infinitude of planes bisect the illuminated part of the moon exactly. They all share the moon-sun vector as a common axis. Did you mean the one that also includes the earth observer, I can't think of any other one that would have any relevance at all? However, I don't see even that as a relevant plane for creating a useful great circle. What sphere are you trying to create a great circle on, I don't even get that at the moment? (It's not necessary for specifying a great circle, which is why I didn't ask for one before, but clearly me skipping out the parts you can throw away later is causing confusion. Smaller steps might work.)

 

[Eburacum]

What sphere are you trying to create a great circle on, I don't even get that at the moment?

Apologies for being unclear. The sphere that constrains this great circle is the 360 celestial sphere, surrounding the observer at infinity. By including the line that bisects the illuminated side of the moon, the Sun, and the observer, we have defined a triangle that also defines the plane of this great circle.

Standing on the surface of the Earth, this circle looks like a curve, but (as Mick West mentioned in post #2) it is really a straight line. Light always follows a geodesic, which is a straight line (except in a very strong gravity field, which is irrelevant here).

 

[Eburacum]

Sorry to bang on about this, but the Moon Tilt illusion blew my mind when I first saw it, way back in 1978. I really didn't understand it until I started drawing imaginary great circles on the sky.

If I'd thought of your hat-brim analogy, I might have understood it more quickly.

 

[Z.W. Wolf]

I've found more clarity.

Stitching means putting together separate shots, which can cause "panorama distortion."

Panorama distortion refers to the visual warping or stretching of objects in a panoramic image, often appearing as curved lines or stretched proportions, especially at the edges of the image. This distortion is a common side effect of creating wide-angle panoramas by stitching together multiple images.

Post processing a single image with distortion is different. I'm too busy to look into it just now.

 

[Z.W. Wolf]

I've rethought this whole line of enquiry. I don't want to get out in the weeds about optics. We did that all here:

https://www.metabunk.org/threads/ex...-not-fake-just-perspective.11724/#post-248260

The bottom line for me is that people don't "see" the way cameras see. Visual perceptions don't necessarily have a strict connection to optics and geometry.

I'll look at a daylight gibbous Moon again and give the illusion another chance.

 

[Trailblazer]

I've rethought this whole line of enquiry. I don't want to get out in the weeds about optics. We did that all here:

https://www.metabunk.org/threads/ex...-not-fake-just-perspective.11724/#post-248260

The bottom line for me is that people don't "see" the way cameras see. Visual perceptions don't necessarily have a strict connection to optics and geometry.

I'll look at a daylight gibbous Moon again and give the illusion another chance.

Try this, which I posted 9 years ago in this thread and shows that the illusion isn't just seen with cameras. Look up at the corners of a rectangular room and you can see that the two ends of the straight line which connects one with the other don't appear to "line up" if you look at them in isolation.

Yes, right. I think we are saying the same thing, I just meant you don't only see it in photos.

If I look into the top left corner of the room, the line of the ceiling seems to be angled upwards from left to right. If I look at the top right corner, the line of the ceiling seems to be angled downwards left to right.

View attachment 22807

View attachment 22808

Clearly that is actually a straight line, and yet if you projected either end off in a "straight line" then it wouldn't meet the other end.

If you imagine the moon being placed in the top left corner with the terminator perpendicular to that line then you can see that it would not point at the sun in the top right corner.

View attachment 22811

 

[Ann K]

The bottom line for me is that people don't "see" the way cameras see. Visual perceptions don't necessarily have a strict connection to optics and geometry.

Absolutely! When I was first taking art lessons years ago, I was once drawing a building that was very close to me. I studied each portion and made sure the angles drawn on the paper matched the angles I saw. I ended up with a picture that looked like a photo taken with a fish-eye lens.

 

[FatPhil]

Absolutely! When I was first taking art lessons years ago, I was once drawing a building that was very close to me. I studied each portion and made sure the angles drawn on the paper matched the angles I saw. I ended up with a picture that looked like a photo taken with a fish-eye lens.

Yup. It shares the property of mapping straight lines to circles that this does:

image link: https://en.wikipedia.org/wiki/File:CartesianStereoProj.png
via: https://en.wikipedia.org/wiki/Stereographic_projection

but in mathematical honesty, that's a representation of the inverse of the transform, but nobody needs to know that!
It's close enough because they are both just Moebius transforms ( https://en.wikipedia.org/wiki/Möbius_transformation ), so could be considered the same.

Technically, to preserve verity, you should have been painting on a convex hemispherical canvas, but those are awfully difficult to keep taut on the frame.

 

[Mechanik]

I have noticed this phenomenon in the past and completely understand the technical explanations, but I enjoy practical demonstrations. When I read this yesterday, i went out to observe the moon and sun at sunrise.

To my eyes, the lit portion of the moon was clearly "pointing" at a position "above" the sun. However, if I changed my position so that my eyes were aligned to the orientation of the moon, facing the sun, the apparent divergence went away. (to the extent of the error bars introduced by blocking the sun with a neighbor's roof peak). The angle may be small enough that I can't see the difference.

I suspect this would not work as well during a waxing moon, but I'll give it a try in a few weeks. The "divergence" today was noticeably smaller than yesterday as the angle between sun and moon is noticeably less.

Today, just for fun, I related the above, then put on a very wide and flat-brimmed gardening hat and can confirm that, with the brim aligned with the sun and moon, regardless of any head tiling or viewing angle, the moon aligns perfectly with the brim's Great Circle.

This has been a fun thread. Thanks!