Need help explaining: shadows and sunlight direction on Artemis 1 footage.

[Patrick Gonzalez]

So Artemis 1 finally made it to the Moon and it has sent some very gorgeous, high-definition images of not only just the Moon, but also its far side. It's fascinating, but like anything related to spaceflight, flat-earthers find a way to deny everything that disproves their worldview. This image has been doing the rounds on flat Earth Twitter:

Pretty cool pic, but I can understand someone getting confused over the lighting angles and the shadows and all that. I feel that if you rotate the image the angles are more intuitive, but I know perspective is playing tricks with my mind. I was hoping if someone had a simulator or something like that that can simulate similar conditions as that in the photograph.

 

[Ravi]

I bet it is a perspective issue.

Here is some interesting reading material if interested:
Perspective shadow

 

[Mendel]

So Artemis 1 finally made it to the Moon and it has sent some very gorgeous, high-definition images of not only just the Moon, but also its far side. [..] This image has been doing the rounds on flat Earth Twitter:
View attachment 56277
Pretty cool pic, but I can understand someone getting confused over the lighting angles and the shadows and all that.

No, people get confused over the red arrows, which don't correspond well to where the light comes from.

First, the moon: it's a ball which is half light and half dark. Since we see mostly light, most of the dark must be on the far side; this means the light source is behind the camera, a little left but pretty high up; similar to a "12 o'clock noon" situation.

Looking at the capsule, the wall is lit, which also means the sun is behind the camera, a little left but pretty high up, again the shadows look pretty much like a "12 noon" situation.

Which means we've worked out where the sun really is, which not where either of the arrows suggest it is.

(I think the most deceptive is the shadow on the sphere—the camera is looking at it "sideways" while it is being lit from far away.)

 

[Ann K]

First, the moon: it's a ball which is half light and half dark. Since we see mostly light, most of the dark must be on the far side; this means the light source is behind the camera, but pretty high up; similar to a "12 o'clock noon" situation.

It's a pity the moon lacks a specular reflection to illustrate that.

 

[Mendel]

Working through this thread may help: https://www.metabunk.org/threads/the-moon-tilt-terminator-illusions.8165/

The thing not mentioned explicitly in that thread is that if you hold the ball away from the moon (in some other direction), you're looking at it from another angle than the angle you're looking at the moon (kinda "sideways"), and the shadows no longer match up ("moon tilt"). The same thing is at play here.

 

[Patrick Gonzalez]

As I said, if you rotate the image 180° it is much more intuitive where the sunlight is coming from. The Sun is behind Orion but the spacecraft is also pointing slightly to the left. It's also approaching the Moon "from above". The shadows would eventually converge due to perspective, is my assumption.

 

[FatPhil]

If you have a not-uniformly-flat surface, you can project the tip of the shadow in all kinds of directions, and add lines connecting endpoints in all kinds of directions - for example, do FE-ers think there are two different suns creating the two shadows I've marked up with yellow lines:

The sun's significantly behind the camera - [edit: insert "were you to face it," here] it's rays will be going "outwards" onto everything. [edit: insert "But as we're facing away from it," here] Light passing over our right shoulder will converge onto the perspective point in opposition to the sun by heading leftwards, and light passing over our left shoulder will converge by heading rightwards.

I don't think the thread that @Mendel referred to is the only one on this illusion, as I do remember 'fessing up to being very susceptible to it in the context of whether the moon tells you that the sun has set or not - it looks like the sun's behind and above you, but in reality it's so far behind you it's long since set.

 

[Mendel]

View attachment 56286

The sun's significantly behind the camera - it's rays will be going "outwards" onto everything. Light passing over our right shoulder will converge onto the perspective point in opposition to the sun by heading leftwards, and light passing over our left shoulder will converge by heading rightwards.

I don't think that's true. I expect that these perspective lines should meet:

 

[FatPhil]

I don't think that's true. I expect that these perspective lines should meet:View attachment 56287

I reformatted the paragraph a few times, and left it unclear. Perhaps my "outwards" was the point of contention. Behind us (the camera), from our perspective, the in-reality almost-entirely-parallel beams of light from the sun will be going outwards, that's the only way they can get past us. Once they've gone past us, they'll converge to the point opposite.

The convergence of the yellow lines below the centre of the frame tells us that the sun is above us. The shadow being on the underside of the moon tells us the same thing. All the shadows we've marked up are still in full agreement with the single distant sun model, even if the lines are pointing in a wide range of directions. If we knew the field of view of that camera, we should even be able to work out from that convergence point the position (elevation/azimuth) of the sun behind us. Measure those angles relative to the moon, and you should get a number that agrees with the amount of it that's lit.

 

[Ann K]

I don't think that's true. I expect that these perspective lines should meet:

I'm not sure about that. I think the two perspective lines on the capsule should meet at a point that is determined by the angle of view of the capsule itself, unrelated to the shadow of the moon. (We must also assume that the body of the capsule is cylindrical rather than some shape that's curved in three dimensions; that seems to be the case.)

One point: your central yellow line drops from a point to its shadow on the angled flange, but as you can see, that's conspicuously different from the line of the shadow on the cylinder.

 

[Z.W. Wolf]

It's just another example of the tired old argument based on the misunderstanding (or willful misunderstanding) about parallel sunrays and perspective.

There's the Apollo Hoax argument about more than one light source on a soundstage:

That one's addressed in this thread:
https://www.metabunk.org/threads/apollo-17-alleged-inconsistency-of-shadows.9188/#post-213944



And the FE argument about a close Sun...

This photo proves that the Sun is very close to the surface of the FE, right? It's just above those clouds... OBVIOUSLY! Not 93 million miles away. Checkmate, Globetards.

This thread addressed that argument:
https://www.metabunk.org/threads/crepuscular-angles-and-the-flat-idea.7360/#post-177041


In the later part of that thread I got objections to my use of crepuscular and anti-crepuscular rays. I'll coin some new terms: Solar point rays and antisolar point rays.

-Solar point rays seem - due to perspective - to be converging toward the Sun.


-Antisolar point rays seem - due to perspective - to be converging toward the antisolar point.


https://personal.math.ubc.ca/~cass/courses/m309-03a/m309-projects/endersby/Antisolarpoint.html

If we look at the ground on a sunny day, the shadow of our head marks the point called the antisolar point, 180° away from the sun. If the sun is in the sky, the antisolar point is below the horizon. If the sun has set, the antisolar point is above the horizon.

These are solar point rays...

These are antisolar point rays...

To keep things as simple as possible:

-Solar point rays occur when the observer is looking toward or mostly toward the Sun.

-Antisolar point rays occur when the observer has the Sun at his back or mostly to his back.



These are antisolar point rays...

The Sun is mostly behind the camera. The sunrays seem - due to perspective - to be converging on the antisolar point.

 

[Mendel]

I'm not sure about that. I think the two perspective lines on the capsule should meet at a point that is determined by the angle of view of the capsule itself, unrelated to the shadow of the moon. (We must also assume that the body of the capsule is cylindrical rather than some shape that's curved in three dimensions; that seems to be the case.)

One point: your central yellow line drops from a point to its shadow on the angled flange, but as you can see, that's conspicuously different from the line of the shadow on the cylinder.

parallel lines always converge
you can define a line by two points
the point on an object and the corresponding point on its shadow define a sun ray
and so does the center of the lit part of the moon and the center of the moon
the geometry of the objects that the shadow is projected on does not matter for this to be true

parallel lines converge (perspective)
if the rays converge, that's what we expect from (almost) parallel sunlight

 

[Ann K]

parallel lines always converge

But this is a three-dimensional structure, and you cannot define what's parallel on a two-dimensional photo.

 

[Mendel]

But this is a three-dimensional structure, and you cannot define what's parallel on a two-dimensional photo.

why not? how is this different to how perspective normally works?

 

[FatPhil]

But this is a three-dimensional structure, and you cannot define what's parallel on a two-dimensional photo.

The point source at infinity (which is what the sun is to first approximation) defines what the parallel lines are on a small scene, such as the craft. As you can see from convergence still agreeing when you introduce the moon, even that can be considered a small scene, as the sun's so far away.

 

[captancourgette]

parallel lines always converge

I don't understand. I thought the deal with parallel lines is they always remain the same distance apart?

 

[Mendel]

I don't understand. I thought the deal with parallel lines is they always remain the same distance apart?

In Euclidean geometry, that's true, yes.
But if you project them onto a 2D plane (such as a photograph), perspective dictates that their projections converge (unless they're parallel to the plane).

Source: https://commons.m.wikimedia.org/wiki/File:Tyabb_railway_station_track_level_south_2018-02-02.jpg

So if you take a photo of parallel lines, they'll usually appear to converge in the photo (though the vanishing point itself is often outside the frame).

 

[FatPhil]

I don't understand. I thought the deal with parallel lines is they always remain the same distance apart?

Are all things which are the same distance apart visually separated to the same extent to you?

 

[Easy Muffin]

Bit late to the party but maybe this can help understand the geometry a bit better.

Recreation of the original picture. The time won't be 100% correct but close enough. The spacecraft is really just a static placeholder so it's not correctly aligned here.

Looking back towards the sun. Those arrows that seem to indicate shadows are really just pointing at the terminator, which might give off a wrong impression of the sun's position due to the curvature of the Moon. If those arrows were correct then the sun would have to be off to the top left in this simulation.

Side view.

Top-down view.

 

[captancourgette]

So if you take a photo of parallel lines, they'll usually appear to converge in the photo (though the vanishing point itself is often outside the frame).

thanks I understand now.
though 2 things I will point out
1. the lines will never actually meet, you can take a better quality photo and will see there is still a gap between them
2. Any two lines (ii.e. parallel lines are a subset of these) will appear to converge if the canvas/fov is big enough

 

[Mendel]

thanks I understand now.
though 2 things I will point out
1. the lines will never actually meet, you can take a better quality photo and will see there is still a gap between them

View attachment 56287
in geometry, a straight line has infinite length, and so they'll come arbitrarily close (no gap).

2. Any two lines (ii.e. parallel lines are a subset of these) will appear to converge if the canvas/fov is big enough

yes (if you equate "intersect" and "converge"), but the thing about parallel lines is that all of them (not just subsets of two) converge on the same point. that's why my sketch shows three lines, and @Z.W. Wolf 's picture shows even more.
View attachment 56298

 

[captancourgette]

in geometry, a straight line has infinite length, and so they'll come arbitrarily close (no gap).

Not sure I agree, my point all lines are the same (parallel lines are a subset of lines) with parallel lines there will always be a gap eg in the above railway photo, you just have to zoom in enough, they will never converge at a point, they may converge at a pixel on the screen but its due to the image's lack of resolution or something. ask micheal angelo (or was it de vinci)
the sun aint a point of light (i.e its not a star! ) stars have near practically zero size, but the sun is the size of the moon, but its 93million km vs how many trillion km to nearest star/s. Even though stars are massive apprently theres one that if it was in place of our sun would exceed mars in its diameter, but viewed for such large distances they are points or light

 

[Gaspa]

Not sure I agree, my point all lines are the same (parallel lines are a subset of lines) with parallel lines there will always be a gap eg in the above railway photo, you just have to zoom in enough, they will never converge at a point, they may converge at a pixel on the screen but its due to the image's lack of resolution or something. ask micheal angelo (or was it de vinci)
the sun aint a point of light (i.e its not a star! ) stars have near practically zero size, but the sun is the size of the moon, but its 93million km vs how many trillion km to nearest star/s. Even though stars are massive apprently theres one that if it was in place of our sun would exceed mars in its diameter, but viewed for such large distances they are points or light

Forgive my bluntness, but you are just wrong and failing to understand an explanation. You don't have to "agree", it's not a matter of opinion, you have to understand.

Parallel lines converge on a single point. It is the first thing you learn when you study perspective. Indeed, go ask Michelangelo, da Vinci.

https://en.wikipedia.org/wiki/Vanishing_point

 

[Ann K]

Forgive my bluntness, but you are just wrong and failing to understand an explanation. You don't have to "agree", it's not a matter of opinion, you have to understand.

Parallel lines converge on a single point. It is the first thing you learn when you study perspective. Indeed, go ask Michelangelo, da Vinci, or any of the other teenage mutant ninja turtles, please.

https://en.wikipedia.org/wiki/Vanishing_point

The problem between your statement and that of @captancourgette is due to the difference between "converge" and "appear to converge". You are both right, but you're talking about different things.

 

[Mendel]

The problem between your statement and that of @captancourgette is due to the difference between "converge" and "appear to converge". You are both right, but you're talking about different things.

Could you explain the difference?

Geometry tells us this:
Take any number of geometric parallel straight lines, of infinite length, in a 3D space.
Do a rectilinear perspective projection onto a 2D plane (e.g. painting or photograph), and then either
a) the 2D projected lines will still all be parallel, or
b) the 2D projected lines will converge on a single point.
That point is the vanishing point; it is not part of any line, but neither is there a gap between the lines. (The width of the "gap" is 0 exactly.)
And this is what it means to converge; same as a number that you keep dividing by 2 will converge to 0. It appears to converge because it converges.

In practice, parallel lines are often not infinite (e.g. actual train tracks); but a sun ray pretty much is, so this convergence does apply in full when we look at the Artemis picture and trace its light ray geometry. (The sun rays are very slightly not straight due to gravity, and very slightly not parallel, and no camera lens is perfectly rectilinear, which makes the model undetectably inaccurate. But that's not Courgette's or your argument.)

 

[FatPhil]

Could you explain the difference?

Lines connecting points in space are virtual, they don't "actually" do anything out in space, as they are abstract concepts in our consciousness. And when we perceive the scene as a perspective view of a three dimensional space, rather than just an abstract line drawing on paper, we intrinsically know that the "convergence" happens "at infinity". At this point in the explanation we're half way there, and I'll hand over the keyboard to Zeno of Elea.

 

[Mick West]

Everyone is kind of correct. The problem (not really an important or useful one) is one of precision in terminology. 3D vs. 2D, line segments (between two points) vs. rays (hypothetical projection of a line segment to infinity).

Lines that are parallel (the same distance apart along their entire length) in the real (3D) world will look like they are converging (getting closer together) in a (2D) photo (unless you take that photo exactly perpendicular to the lines.) I think we can all agree on that basic fact, and the rest seems to be semantics.

 

[Mendel]

And when we perceive the scene as a perspective view of a three dimensional space, rather than just an abstract line drawing on paper, we intrinsically know that the "convergence" happens "at infinity".

In 3D, parallel lines do not converge at all (in Euclidean geometry).
Their 2D perspective projection does, and that 2D convergence target is not at infinity in 2D—but that target would correspond to a point infinitely far away on those parallel lines if such a point existed—it does not.
The word "converge", mathematically, implies "at infinity"—same as f(n+1) := f(n) / 2 converges on 0 at infinity.

 

[Mick West]

A slightly neater illustration of the converging (in 2D) essentially parallel (in 3D) rays

And on lighter note, here's me from a few years ago illustrating how shadows change in 2D as your position changes.

 

[Mendel]

slightly neater

that's very charitable

I had hoped someone would do this when I posted my crude sketch. thank you!

 

[FatPhil]

In 3D, parallel lines do not converge at all (in Euclidean geometry).
Their 2D perspective projection does, and that 2D convergence target is not at infinity in 2D—but that target would correspond to a point infinitely far away on those parallel lines if such a point existed—it does not.
The word "converge", mathematically, implies "at infinity"—same as f(n+1) := f(n) / 2 converges on 0 at infinity.

There is no infinitity to be "at". At least not in the real world. Note that a mathematician wouldn't use the terminology you've chosen. The implications are entirely within the word "converge", no decoration is required. However, also not that mathematicians aren't dealing with the real world, but with abstract concepts.

 

[Mendel]

Note that a mathematician wouldn't use the terminology you've chosen.

Yes. I'm trying to use simple language for since I am not talking to mathematicians. There may also be translation errors in play.

 

[Ranon151]

A slightly neater illustration of the converging (in 2D) essentially parallel (in 3D) rays
View attachment 56339

And on lighter note, here's me from a few years ago illustrating how shadows change in 2D as your position changes.

In the picture below though the lens does seem to be curved, given the bend of the sidewalk edge. How much is that an impact in either image?

 

[Mendel]

In the picture below though the lens does seem to be curved, given the bend of the sidewalk edge. How much is that an impact in either image?

it's a curved gravel walk

if this was lens distortion (which would be highly unusual, to see that much of it), it'd noticeably affect Mick's legs