What is this Sun and moon photographic anomaly?

Question

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.

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:

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.

Answer 1

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):

Answer 2

Here 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.

Answer 3

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 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.

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.

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!

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

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.

Answer 4

When looking at the sky, spherical coordinates are used as a convenience. We turn our head and body in azimuth and altitude to compare the position of objects. In this regards, the sky looks like a sphere. (At least I visualize it as a sphere.) A Cartesian XY (or XYZ) grid cannot be easily used.

The question then becomes: what is the path of a light beam in spherical coordinates? Realizing that light takes the shortest distance from point A to point B, another way to phrase the question is what is the shortest distance between two points in the sky? The answer to the re-phrase question is a great circle.

As Bruzote's Oct 25 2021 answer was indicating, the problem is it is difficult to visualize a great circle on the sky, and the path created by a great circle is not intuitive to most people (including me). Fortunately, you can easily observe where one particular great circle exists and solve the “Moon illumination anomaly” at the same time: go out and observe the Moon! The Moon orbits the Earth in a plane, and the intersection of the orbital plane and the sky is a great circle.

For example, observe the position of the Moon for several days starting a few days after New Moon. Dec 5 through the 13 2022 is a good opportunity. Make the first observation just before or at sunset and observe 4 minutes earlier on each succeeding day. (The 4 minute difference compensates for the Earth's motion around the Sun. Unless your plot of the Moon's position in the sky is precise to a fraction of a degree, you do not need to be so precise with your timing.) If you plot the position of the Moon, it will look something like the following plot: (created from Sky and Telescope's Interactive Sky Chart)

Note that:

1. The “straight line” of the great circle is a curve going across the sky. It does not “feel” straight. (The black line in the figure is the ecliptic, which is the great circle created by the Sun’s apparent path for 1 year. The Moon’s orbit is inclined approximately 6 degrees to the ecliptic -- close enough for reference.)
2. The illuminated face of the Moon points toward the position of the Moon on the previous day.
3. When connected together, the illuminated directions make a “line” (technically a great circle) that connects to the Sun. That is, the illuminated direction is in the plane of the Moon’s orbit and always faces the Sun. (The Moon's great circle crosses the Sun when there is an eclipse. At other times, the great circle may pass above or below the Sun by 6 degrees.)

On May 16 2016, the all-sky plot looks like the following:

When shown in a horizon projection, the image looks like the following. The illumination on the Moon appears to be coming from the upper right because that is the shortest direction to the Sun!

All images are approximations, just like the original photograph, due to projections from 3D onto 2D. The last image is stitched from several images which introduces more distortions.

Answer 5

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.

Answer 6

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.

Answer 7

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.