Cool picture, lek.

Is the answer to the question, "Why is the apparent path of light from the sun to the moon curved?" in any way related to the answer to the question, "Why is that road at the bottom of the picture curved?"

I'm guessing the stretch of road is pretty much straight, even though it appears to curve "down" and then back "up" again, so it seems only logical that a straight path from moon to sun would appear to curve "up" and then back "down" again, doesn't it?

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That's it, and that isn't only something which comes with making the panorama, its what you see if you turn from moon to sun.

Edited to add: If i had a fisheye lense capable of getting both moon and sun in same frame, the terminator would seem perpendicular to direction of sun, but the horizon would be an arc instead of straight line i suppose..

Perfect. That's exactly the "mid-(north)-latitudes" view I was describing and attempting to explain.

Grant Hutchison

If you pointed the camera such that the "straight line" between moon and sun went directly through the center of the field-of-view, I'd imagine.

And in doing so, you'd probably find that the center of the moon-sun line is actually further above the horizon than either the moon or sun.

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Didn't think of that when i wrote it, but yes, that is indeed a necessity.

I disagree. That picture is obviously distorted.

If you were to lie down in the road so you could nod your head from moon to sun, you could see that the straight line from moon to sun was indeed perpendicular to the terminator. It's our perception that is at fault, as I said before. There is no diagram that can show it, without distorting the picture.That's kinda what I was getting at. If you're going to take the surface of a sphere and represent it on a 2D medium, something's going to be distorted. Ask Mercator.

Why dont you go lie down in the snow and start taking pictures


edit: I think you will find that you need to lie down on a spesific slope depending on your location on earth / time of year etc to get the straight line from perpendicular to moons terminator to sun?

Awesome picture, lek! That perfectly illustrates clop's question. How did you do such a nice job stiching? I can always see the lines when I try.

APOD - astronomy picture of the day
EPOD - ?

I think this problem is similar to looking at the flight path from San Francisco to London on a flat map. It looks curved, but if instead of using the equator to bisect the map, you used the flight path, it would become straight and the 2-d representation of the world would re-distort to match.

It wasn't a nice job at stitching by me, it was a case of google free stitching software and then photoshop to remove the "buy this software you git" text from the middle of the pic (30 day trial), thats why it looks edited if you take a good look at the center of the picture

EPOD is "Earth science Picture Of the Day" i think... (for which i don't think this pic is any good since it requires huge resolution to see the "point" and as such not so good candidate for web publishing)

Like hhEb09'1 and others mentioned, this whole issue is indeed about distortion in representing 3d world in 2d, something will look funny no matter how you choose the 2d projection. It isn't any kind of optical illusion, it's just "error" imo.

I'm going to try to duplicate your effort later today, assuming the elements don't discourage me. The sun is shining today, with not a cloud in the sky, but the wind is fierce and cold. I'll try an equatorial mount shot too. And the tennis ball trick

Somehow i don't have any doubt what EQ mount will show

edited to add (im posting way too hastly it seems) Moon was too high to try photographing a ball and moon at the same time, when i was taking pictures... Need to place the "ball" way too far from camera to get the required depth of field, which in this case meant climbing up a tree or something to get the shot...

I think this thread has done a very nice job of showing that clop's question is in fact a good one, and that the answer to the "problem" is an illusion, call it the "horizon illusion", of thinking that straight lines will maintain a fixed angle relative to the horizon. lek's picture shows this quite nicely. This all reminds me of the problem of "parallel transport" that comes up in general relativity, from a perspective looking inside out rather than outside in.

Great picture, lek. Thanks.

Today it will show nothing but heavy rain. 2 hours ago there was not a cloud in the sky >

No, you don't even need to lie down, you just have to be careful to not confuse yourself. I thought it might help to lie down--it works for some.

It cleared up enough to do the ball trick, but not enough for a nice panaroma like lek did.

It was impossible to get both the Moon and the golf ball in focus in the same picture, even at f32. So the 1st image I focused on the golf ball, the 2nd, halfway between the golf ball and the Moon, and the 3rd on the Moon.

Wow. That moon in the foreground has a very regular cratering pattern. I think it could be... artificial!

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That second pic might be worth submitting to APOD, it's pretty nice as a Moon phase explainer!

Well thank you to everyone. At long last I fully understand this problem.

The sky is not flat. When we look at the sky we're essentially looking out at the internal surface of a sphere (like when you're in a planetarium). And when you project a straight line onto the internal surface of a sphere it appears as an arc (unless you happen to be located in one of a special set of locations where the line appears straight, but slightly shorter than it really is). And so the straight line between the moon and the sun appears as an arc in the sky (unless you're near the equator) and the moon's terminator is orthogonal to this arc.

You can demonstrate this arcing of a straight line in the comfort of your own home. Go and stand halfway along a long internal wall in your room, facing the wall and about 30cm away. If you let your eyes follow the straight line of the top of the wall from far left to far right (you're allowed to move your head) your line of sight actually follows an arc through the air, because you have to tilt your head back as the line passes in front of you and then tilt it forwards again as you follow the line to the right. So it's a straight line that appears as an arc.

At least we've discovered that it's got nothing at all to do with large distances or relative distances or relative sizes. It's just cartesian vectors expressed spherically.

Thanks again,

clop

But everybody on earth is standing at one of those special places, to the degree necessary to understand the problem. I think the golf ball photos illustrate that. Your example of standing halfway between two walls shows how the line itself is straight, it is just our perception of it that is at fault. Someone who is familiar with the room would never look at that line and say that it is not straight, just because they have to move their head.It's only an illusion, where we misinterpret what we are actually seeing. Similar to the large moon on the horizon.

No, I mean one of the special places where the terminator does appear orthogonal to the sun even through our optically-deceived eyes. Anywhere close to the equator and reasonably close to an equinox would do, but there are other possibilities. In a planetarium you could observe from any point lying on the vertical plane of the vector between the projector and the projection of a straight vertical line and still perceive a straight vertical line on the dome, but it would be shorter than the actual line, the shortfall depending on your position on the plane.

But clearly, being far from the equator (analogous to being positioned off the plane in the planetarium) makes the line look curved in our field of view, hence the original post.

clop

In my experience (and, I think, as we've shown), the terminator does appear orthogonal to the sun for all observers on the earth. The golf ball pics show that. It's not an optical deception, it is an illusion created by our minds. It is our personal misperception. I disagree, and I've lived near 45 degrees latitude. If you can see both sun and moon, and you trace a straight line (with string, or whatever) between them, the terminator will be perpendicular to the line (string), as near as we can tell. If the earth were transparent, then it would be true even with the sun below the horizon.

But the terminator does not appear orthogonal to the Sun-object
line in a wide range of cases. Perhaps the majority of cases.

Tony's golf ball pictures show that the terminator is very nearly
identical for an object a meter away as it is for the Moon,
385,000 km away. They do not show that the terminator appears
orthogonal to the Sun-object line.

I'd say optical deception = illusion = personal misperception.
Different words, same thing.

I agree with clop: A straight line from Sun to Moon looks
curved. And I agree with you: The terminator is perpendicular
to the straight line.

What Grant said in post #23 on page 1 of this thread clearly
describes the essential cause of the illusion. It is clearly
a problem of perspective. But the description of the cause of
the illusion is just a description, not a complete theory.
We could develop a complete theory.

The most fundamental starting point for such a theory is the
fact that what we are looking at is 3-D, but the retinas of our
eyes are only 2-D. I take this to mean that projective geometry
is the domain of a theory which will explain the illusion.

-- Jeff, in Minneapolis, at 45 degrees latitude

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The sky is a three-dimensional volume.

We see it projected onto the inside surface of a hollow sphere.

And the sky itself, in some vague manner, resembles the inside
surface of a hollow sphere.

-- Jeff, in Minneapolis

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Depends upon the person. It never appears that way to some. It depends upon their perception.If you draw a straight line from the golf ball to the sun, the golf ball "terminator" will be perpendicular to that line. We know that.OK, but the reason that I myself would not use "optical deception" is that it seems to imply that the scene is deceiving us, when in fact it is ourselves deceiving ourselves. Similar to the large moon on the horizon illusion. Similar to other optical illusions, but different from optical deceptions like certain tricks of perspective that are built to be seen with one eye, which make a crooked house look like a normal one.I think you should add that the straight line looks curved to you, not that it looks curved period. It doesn't.

OK hhEb09'1 how about we say it looks curved in a photograph. Maybe then you won't need to be so pedantic about how an optical illusion doesn't affect you as much as it affects almost everyone else. At least you can't argue with the camera idea.

If you take a photograph of the ecliptic (or a straight line projected onto the dome of a planetarium) it will appear curved in the photograph unless the camera is located at one of the special positions i.e. on the plane I described previously, and then it will be straight in the photograph and be shorter than it really is.

clop

Maybe. Even though you say it does not appear curved to you,
I'm not yet convinced that that is so.

Of course. I never suggested otherwise. But Tony's pictures
provide no evidence one way or another on that particular point.

I'm not convinced. When light from the sky refracts through
hot air above a road in the desert, it can look just like water
lying on the road. Is that ourselves deceiving ourselves, or
is that the scene deceiving us? Is there a line between the
two? If so, where do you draw that line?

What is it about the sky that makes it look like the inside
surface of a sphere? Does it look that way to everyone?
All the time?

I'm embarrassed for having given a largely irrelevant and thus
essentially incorrect explanation of the illusion early in the
thread, because I'm pretty well versed in perspective. I have
a fairly good understanding of how it works and how to show it
on a flat sheet of paper. Over the decades I've drawn numerous
pictures of the kind of curvature shown in clop's diagram and
described by Grant-- but in those pictures, I drew objects such
as rows of boxes, in which the curvature is obvious. When there
are only two spherical objects in the scene, with no straight
lines and no right angles, the geometry is very subtly hidden.
I failed to see it for that reason.

When I take clop's suggestion to look at long, straight lines
close-up, whether I see a curve or not depends on what I want
to see. There is a long section of wall in front of me. The
top and bottom edges are straight, horizontal, and parallel.
Yet it is obvious that those edges converge toward the horizon
to my left and right. For that to be possible, the lines must
curve. What do I actually see? Straight lines or curved?
I'm not sure. What does it mean to say that a line looks
straight, or curved? What do I want to see?

I think you are saying what you want to see. Not necessarily
what you actually see.

Define "looks curved". I can't. Not yet, anyhow.

-- Jeff, in Minneapolis

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"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

"If you draw a really straight line (for example using a piece of string as reference like you mentioned earlier) from golfball/moon to sun, the terminator is perpendicular to that line, but that line isn't necessarily seen as straight. That isnt a trick of mind, it is a trick of getting a 2d projection of a 3d world, it can be photographed as not strait, clop's conclusion about imagining the sky as sphere, not flat is exacly the issue.

The moon on the horizon is complitely different, that one exists only in our minds, photos or measurements do not agree with our perception.

If you really are very used to the equatorial vision of world, you may see the line as straight, when majority of people out there would say it's curved.

Right. As suggested by your golf ball photos.

I delibrately neglected the ball-eye distance. That's why I
specified that the deviation should be measured from the center,
when the Sun-observer-Moon angle is 90 degrees, so the distance
is not a factor.
It is maximum at the quarter phases and falls to zero at new
and full phases. But it is always teensy-tiny! Photographing
the ball slightly off-center has a much larger effect. The ball
needs to be smack between the Moon and camera to be precise.

-- Jeff, in Minneapolis

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http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

That makes sense. Just as a footnote, the ball trick does not work for Venus, except when Venus is in the new phase (interior conjunction).