What? I'm only disagreeing with the "proofs"I think I already have "argued" with the camera idea. Any photo that shows a 180 degree view is going to be distorted. A distorted photo should not be offered as proof.This is not true. The camera does not have to be at a special place. The tracking of the camera just has to go from moon to sun, and then be stitched together. Same technique as was used before. The photographer could have gone to the left from the moon--then the lit side of the moon would look like it was away from the sun, not just above the sun.Smile when you say that.That is an effect of refraction or reflection, and affects everyone similarly.Actually, this subject came up a long time ago, and I had heard of the illusion. I too tried to explain it using diagrams but when I could not do that, to answer the question I just went outside and looked. I'm only telling you what I saw.The moon on the horizon can be zoomed in, so that the photo actually shows it larger on the horizon than higher in the sky. That's a distortion that is similar to the photo that appears in this thread--because if care is taken to not distort the image, the line can appear straight even in the photo.

I can take a series of pictures of a bus starting with the right front wheel, proceed over the bus to the left rear wheel, and stitch them together. The result would show both wheels visible, but that is only because of the distortion of the photo, and is not something that we can actually see.

I need photography lessons from lek, but here's my equatorial-mount panorama. It's not a true ecliptic mount.
I just shortened 1 leg on my camera tripod until it was pointing at what was my best guess as to where Polaris is.

In the panaroma the Moon is noticable, but too small to tell phase. I've labeled the Moon and the approximate position of the Sun.
I can't tell exactly where the Sun is because a large cloud moved in front of it about a minute earlier.

Panaroma:


And this is the portion of the panorama that contains the Moon, zoomed in so you can see phase.

I think you should say it doesn't look curved to you. Perhaps you also think a pencil half in a glass of water doesn't look bent, because you can mentally compensate for the refractive indices.

I have said that. I've also shown how it is not actually curved.We've already mentioned refraction effects. It's not a matter of "thinking" in this case--the line between the sun and moon is not curved. It's not a matter of refraction or reflection or optical distortion of any sort. It just looks curved to some people. I'm not denying that there are refraction effects in the atmosphere, there are--but not at the level that we are discussing.

I understand how perspective works--parallel lines appear to converge at infinity. But this is not the same thing. The line can even appear in a photograph to not be curved--if the pan is along the line, which is as it should be if we didn't want to distort the line.

This bab about moving the camera along a curved line and stitching the shots together to produce a final photograph showing a straight line is total crap. Jesus, I could take lots of photographs of the circumference of a circle, turning the camera slightly between each shot, and then stitch them together to make the circle look like a straight line. It's a trivial and worthless claim. Wow I could even make a zig-zag line look straight as long as I turn the camera properly and stitch the shots together just right.

I maintain that if the sun and moon are close enough together in the sky for you to take a single photograph with both of them in the frame, the straight line between them (the ecliptic) would have to be drawn as an arc on the photograph, it would not be a straight line on the photograph, unless you're under the ecliptic.

clop

But that's my point. Stitching the photos together can distort the view--I mentioned doing it to both sides of a bus.The sun follows the ecliptic, the moon does not.

But what we are discussing here is the straight line between the sun and moon (which would be a straight line in such a picture, ignoring distortion) and whether it would be perpendicular to the terminator. It would.

The moon follows the ecliptic closely enough for us to use the approximation.

If the sun and moon had been closer in the sky (or if he'd had a slightly wider angle lens) he could have taken a single photograph with them both in the frame. No stitching. No distortion. And a straight line drawn between the sun and moon on the photograph would not have been perpendicular to the moon's terminator. Would you like me to draw a line on Lek's photograph for you?

clop

Five degrees then is our allowed error

But what you say below cuts to the heart of the matter and makes the ecliptic issue irrelevant.I think that is a clear and simple declaration of the situation. And I disagree, I would say it would have been perpendicular.As near as I can tell, lek posted only one photo, and it was stitched together, so I don't think it qualifies. In the next post he even says:On the basis of that, I would have said lek disagrees with you, but then SeanF posted and lek answeredlek is wrong there, though, it is not a necessity. For instance, a pinhole camera would do it without the need for the line going through the center of view.

PS: If we are talking about getting both bodies in the same frame. Looking at those posts again, lek is talking about a situation where we cannot get both bodies in the same frame, unless he uses a fisheye lens--which distorts the images. So, lek was not wrong, but he is talking about a situation that doesn't pertain to our basic disagreement there.

I was trying too hard to untangle the thread. I like the single statement, agree or disagree better:

If the sun and moon had been closer in the sky (or if he'd had a slightly wider angle lens) he could have taken a single photograph with them both in the frame. No stitching. No distortion. And a straight line drawn between the sun and moon on the photograph would not have been perpendicular to the moon's terminator.¹

You agree with it.

I disagree.

1. source

The notion has been suggested that a photograph taken with a
fisheye lens is distorted, while one taken with a normal lens
is not distorted. I've thought about this question and related
questions for many years. (Which is a good reason for me to
feel embarrassed at having given an incorrect explanation of
the illusion early in the thread.)

All representations of three-dimensional objects in 3-D space
on two-dimensional surfaces are distorted. The question is
whether you notice the distortion.

Any image projected on the eye's retina is curved. Some shapes
and figures can seem less curved than others, depending on the
detail they contain, how they are positioned on the retina, and
whether the person is trying to see the curvature. I notice it
if the detail makes it possible and I want to see it. I do not
notice it if I'm not looking for it.

All that is also true of photographs. In addition, changing
focal length or film size or cropping alter the size of the
field. Generally, the larger the field, the greater the
curvature, and the more noticeable the curvature is. Fisheye
lenses have particularly large fields and large curvature from
edge-to edge. Panoramic cameras capture wide fields without
such obvious curvature, but introduce other distortions, which
is evidenced by, for example, the ability of a single person
to show up in more than one place in a single photo!

-- Jeff, in Minneapolis

__________________
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

Additional details:

Pinhole cameras distort as much as any other. If the image is
projected onto a flat surface, it is distorted progressively
more away from the center, like a camera with a lens. If it
is projected onto the inside of a sphere, the resulting image
is essentially distortion-free when viewed from the pinhole
location, but that is the same as an imge made by a camera
with a lens when viewed from the position of the lens. Viewed
from any other position, of course, the image will be highly
distorted.

A straight line which passes through the center of the field
is not distorted from side-to-side, but it is distorted from
end-to end. Imagine a straight line with tick marks on it at
equal intervals. The tick marks appear widely-separated near
the center of the field, and closely-packed near the edges.

-- Jeff, in Minneapolis

__________________
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's more or less my point.

Perspective cannot be blamed for this illusion. Lines get mapped to lines.

So how does that work, if you're standing between two parallel railway lines, that stretch from the horizon on your left to the horizon on your right? They meet at the horizon on both sides of you, but if you look down they pass each side of your feet, maybe twenty degrees apart.
Zero degrees apart; twenty degrees apart; zero degrees apart.
I think you'd be hard pressed to process the converging lines to your left and the converging lines to your right as forming parts of the same pair of straight lines inside your head. It certainly doesn't work for me.

Grant Hutchison

That's my point. It is inside your head.

That's what makes it an illusion, rather than something physical. In the case of either line, if you draw a straight line along it, it stays along it. Some people can look at rail lines and not be convinced that they actually converge.

Which is my point, referring to your remark "Perspective cannot be blamed for this illusion."
Surely perspective is inside your head, rather than something physical? And the apparent curvature is part of the process of perceiving perspective, just as the apparent convergence is.

Grant Hutchison

Perception is inside your head, yes, and vision too, but that is not what I meant by the remark. I just meant that there is no trick of geometry that causes the misperception. If you look to your left, the left rail looks straight. If you look to your right, the right rail looks straight. If I look at the moon and the sun, the line between them looks straight, and perpendicular to the terminator. Things in the scene may cause an illusion--similar to the optical illusions that were brought up before, straight lines drawn across a field of curved lines sort of thing that create an illusion that the straight lines are not straight.

Then you're in something of a minority, I think, since the illusion as described by the OP is well reported. It's certainly very striking to me.
Do you do a lot of sky-watching? (I'm wondering if the habit of orientating yourself along great circles might make you better at seeing straight lines as running straight over arcs wider than your central visual field.)

Grant Hutchison

All of us here do a lot of skywatching, no?

But I'd say from my experience, it's engineers that have a developed three dimensional sense. Astronomers too maybe. And mathematicians. Taxi drivers. And artists. Hunters. Climbers. I suppose I could fit in any of those groups. Also pilots I'd imagine. But I'm not convinced it's necessary.

Yes, okay, but do you do a lot?

Grant Hutchison

No, I only do a lot.

To expand on that, one of the exercises could have been to take a picture of the golf ball and sun in the same frame. The ball's terminator would be perpendicular to the ball/sun line (I claim, others may disagree), but a series of photos could be taken and stitched together so that the ball and sun appeared in the result, with 300 degrees of sky between them. Then, in that photo, the sun would appear to be illuminating the side of the ball facing away from the sun.

Can somebody please take a photograph of the moon and sun in the same frame and show hhEb09'1 that he's sadly wrong. The moon is more or less full now but should be a nice quarter crescent and only 45 degrees from the sun in about 10 days time. That should allow them both to appear in the frame using a 50mm lens, which closely represents the magnification of the eye, so there shouldn't be any distortion due to wide-angle or telephoto lensing.

The clock is ticking hhEb09'1. Maybe you'd like to place a wager?

clop

I'll check with the mods to see if that's allowed

A 50 mm lens on a 35 mm camera doesn't have a wide enough field
to capture Sun and Moon in one frame when 45 degrees apart.

A 50 mm lens on a 35 mm camera doesn't guarantee elimination
of distortion. It does minimize distortion to a large extent,
but it is only an approximation. The human mind accomodates
a considerable amount of distortion without noticing it. So
the distortion in a photograph has to be quite large before
you think, "That doesn't look quite right."

As I said previously, a straight line through the center of any
lens should be undistorted from side-to-side. A straight line
drawn in the sky from Sun to Moon, and photographed so that the
image of the line passes through the center of the lens, should
be perpendicular to the Moon's terminator in the photo.

-- Jeff, in Minneapolis

__________________
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

Well then we'll just have to wait and see won't we. No matter how hard I try I can't imagine a photograph of the ecliptic projected in a planetarium showing a straight line, even if the image of the line passes through the centre of the lens (which is a pretty pointless requirement in my opinion - good quality camera lenses around 50mm do not distort straight lines very much, even at the edge of the frame), unless you have the camera in the plane of the ecliptic.

hhEb09'1 I bet you AU$10.

clop

I quite by coincidence took an image on 8 March that illustrates the illusion.

http://members.ozemail.com.au/~mlewi...gonalmoon.html

Martin Lewicki

That isn't relevant. A straight line between the Sun and Moon
is a straight line nomatter where you view it from.

I'm not sure why you talk about lines on a planetarium dome.
A planetarium dome is a poor simulation of the sky, because
the sky is not a dome! It resembles a dome in some ways,
but only some.

I agree with Grant's analysis, based in part on your excellent
diagrams. A straight line between the Sun and Moon can be made
by, for example, a yardstick or a piece of string stretched
between your hands. That straight line is the thick, gray line
in your diagrams. It is curved in your diagrams because of the
way it is projected onto the diagrams. And it actually looks
curved in exactly the same way as your diagrams. (If they were
drawn to accurate scale and so forth. You just drew them by
eye, which was accurate enough for the purpose.)

If you want to accurately draw a straight line across the sky,
you need to hold up a yardstick, or a piece of string, or hire
a skywriter to make a trail on a windless day, or get lucky
and see crepuscular rays which stretch all the way from the
Sun to a point on the far side of the sky. Such a line will
look straight or curved depending on how you look at it.

-- Jeff, in Minneapolis

__________________
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

Hello, Martin!

I think you posted the wrong link. I'd like to see your photo
when you get the link straightened out.

-- Jeff, in Minneapolis

__________________
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

Done!

http://members.ozemail.com.au/~mlewi...gonalmoon.html

Martin

I respect your explanation but in my eyes it is not the correct answer, or maybe not all of the answer. With the sun above the horizon the apparent location of the sun is the actual location of the sun, and you could describe a plane on which lies the sun, the moon and you, and the sun's rays will travel along this plane to reach the moon, and your view of the moon should be symmetrical about this plane, and in fact, it is. The problem is simply that the plane cuts our sky in an apparent arc, and there only appears to be a problem if you try to project the line of the plane through the sky onto a two-dimensional surface (i.e. our retina or a camera film). In actual fact if you look at your photograph and rotate your head to the left so that the illuminated fraction of the moon is uppermost in your vision and then tilt your head back and let your vision follow the terminator's bisector as it passes over your head it comes down behind you an meets the sun. This is independent of the relative distances of the moon and sun. It would work with footballs hanging from the ceiling in your living room. But when you have both objects in your field of view, and try to map them in cartesian coordinates on your retina or in a camera, the straight bisector becomes an arc, and this is what we will prove in 10 days time when the moon is in last quarter, though it would be easier to photograph a week later in first quarter when it sets after the sun.

clop