Gravitational deflection of the Sun's apparent position is too slight to be visible to the unaided eye. If it were visible, it would make the Sun's apparent position slightly higher than the true position, just as does the much larger atmospheric refraction near the horizon.

Yes, relativistic bending of sunlight would definitely not be a factor in the observation. Atmospheric refraction could be, but I think that that is still at most a single degree--which also wouldn't account for the observation. I think it is just an optical illusion.

If you were to draw a truly straight line (actually great circle in the sky) connecting the Sun and the Moon, the Moon’s terminator would appear perpendicular to that line. The problem is that people tend to get confused when the Sun and Moon appear rather far apart, and draw an imaginary line across the sky that is actually curved. This is similar to the manner in which the mind is fooled by optical illusions.

__________________
Curt Renz - "Centaur"
For monthly astronomical calendar visit:
www.CurtRenz.com/astronomical

So, are we starting this thread over again?

-- 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

Maybe so. New user barry carrick-white resurrected the three-year-old thread to ask about the importance of relativistic bending in the phenomenon, which I'm pretty sure wasn't originally discussed in the rest of the thread.

Centaur did respond to the OP, though.

I think this thread was well worth resurrecting after three years, because there may be many new readers here who are just as perplexed as clop was back then. Following is a link to post #22 in which he posted drawings of what he expected and what he actually saw.

Why does the moon's terminator not appear orthogonal to the direction of the sun?

I just now went out and looked at the Moon as it was due south at sunset. The terminator was angled upward, strikingly contrary to the intuitive expectation when the Sun, far around to the right, clearly is on the horizon and at a much lower elevation. I understand clop's conundrum perfectly. The visual booby trap is the inherent distortion we get when imaging the celestial sphere in any sort of optical device, including our eyes.

In my view today, the Moon's elevation was about half of the difference in azimuth between it and the Sun. I held a yardstick up with the left end aligned with the Moon, and angled it down on about a 50% slope, as expected intuitively. It came nowhere near the Sun, but met the horizon far to the left of the Sun's position. Then I moved the stick until its ends were aligned with the Sun and the Moon. When I looked right at the Moon, that end of the stick was inclined upward for a few inches, but as I moved my eyes along the stick it leveled off and then started approaching the horizon as I continued sweeping my eyes toward the Sun end. The stick was clearly perpendicular to the Moon's terminator.

When I looked at the horizon under the Moon and swept my eyes to the right, the stick, now in my upper peripheral vision, looked arched rather than straight, just as the ecliptic does in the pictures in post #22. When I looked directly at the stick and swept end to end in a similar manner, the horizon, now in my lower peripheral vision, looked concave rather than straight. It appears that this visual action is creating a sensation similar to a Mercator map, in which great circles other than the equator or the meridians are projected as curves rather than straight lines.

I am suggesting that the illusion occurs because the Sun is appearing lower in the sky in the early morning than it actually is. So ignoring the moon, I enclose a crude and exagerrated picture of what I meant about the sunlight being bent around the Earth by the Earth's gravity.
The view is looking down from the North pole; it is early morning; the observer is looking east towards the Sun and is seeing the Sun lower than it really is because the Sun's rays that he/she is seeing have actually reached the Earth over the horizon to the east and then been curved around the earth entering the observer's eye at a lower angle than the true direction to the Sun.
If it were possible to draw a line from the Sun to the observer's eye then a ray beginning its passage from the Sun down that path would never reach the observer's eye and in effect would be deflected in a curve somewhere overhead.

Would the gravitational effect be enough to bend light? Well it is light coming very close to the surface (in fact, initially on a "collision" course) and we know little about this, I would guess, as the famous 1919 experiment to measure the bending of starlight passing near the Sun was carried-out when the Moon eclipsed the Sun and due to difficulties with the corona was measured some way out from the Sun. Another point is that the way that light is bent around the Sun, the actual path, is surely theoretical; the light could be curved around at its closest as partially orbital or just as is surmised in conventional diagrams of the phenomenon deflected in a longer, shallower, bow-like curve. Wouldn't the effect observed from Earth appear the same?

Incidentally, this is nothing to do with refraction caused by the Earth's atmosphere which, if it were occuring would have the opposite effect of the Sun appearing higher than it really is.

I apologise if I am mucking up your thread.

Barry

Attached Images

Moon_Terminator_theory.bmp (96.1 KB, 7 views)

Hello, Barry!

All of the effects you talk about are very well known, and have been
measured to very high precision for decades. Radar and space probes
have been invented since 1919, which allow us to do a lot of things
that we couldn't do back then.

Your diagram shows the effect of Earth's gravity backwards. The actual
effect of Earth's gravity on the path of light is to bend the path downward,
toward the Earth, the same as atmospheric refraction. So any object in
the sky near the horizon appears higher than it actually is, due both to
atmospheric refraction and gravitational refraction.

However, the amount of gravitational bending of light caused by Earth's
gravity is extremely tiny. It is vastly less than the bending caused by
atmospheric refraction. It is a tiny fraction of a second of arc -- an
angle far, far smaller than any eye can discern. In fact it is too small
to be detected from the Earth's surface even with instruments designed
for the purpose. The only way to detect it is to go a long distance from
the Earth so that the bent light path can move a significant distance
across the field of view. That is how we detect the much larger bending
caused by the Sun's far stronger gravity field.

* * * *
I looked at the "misplaced terminator" effect yesterday. It was striking.
The terminator appeared to be slanted very strongly relative to the
direction to the Sun.

The time was about 7 pm. The Sun was about 20 degrees above the
horizon to the west-northwest, and the Moon was about 45 degrees
above the horizon to the southeast. The Moon was gibbous -- between
first quarter and full.

I took a long piece of string and held it overhead so that it was stretched
tight, from the Moon to the Sun in my field of view. The Moon was on my
left and the Sun on my right, far enough apart that I couldn't see either
of them clearly when they were both in my field of view simultaneously,
so I had to turn my head to look toward the Moon and then toward the
Sun, while being careful not to move the string.

The string was indeed perpendicular to the terminator. As it crossed the
face of the Moon, on my left, the string was angled sharply upward, away
from the horizon. Looking to my right, the string angled downward toward
the Sun, and back down to the horizon.

All of this can be explained in terms of projective geometry. It is not a
matter of the light paths being altered, nor distortion of the image in the
observer's eye, nor is it entirely an illusion. I'd say it's a wrong expectation
of what a straight line should look like, that occurs when the straight line
is not actually visible, as is the case when I'm not holding the string up.
I interpret a straight line as looking like a curve, if I have no other clues --
such as the taut string -- telling me that it really is a straight line.

The line where the wall in front of me joins the ceiling runs straight from
left to right. On my left, the line angles down toward the horizon. On my
right, the line also angles down toward the horizon. That is perspective,
an application of projective geometry, and exactly the same phenomenon
as causes the Moon illusion.

-- 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

Isn't that the classic definition of an illusion though?

Here is a Crazy Line Illusion, where two straight lines appear to some people to be curved, because of the enviromental clues, but can be made to be seen as straight if a ruler is placed upon them.

That makes three of us in this thread who have performed the experiment. Happily, we've all obtained the same results.

(Hmmm ... not sure what the precision on our experiment is --- probably at least +/- 10% in estimating the 90 degree perpendicular angle

Maybe, but I don't think so. The lines in the real world really are
straight. The lines in the projection may or may not be straight.
Whether the lines in the projection are straight or not, they should
not be considerd to be distorted, because the imaging system is
functioning as it is designed to function. Yet if I notice the curvature,
or fail to interpret the curved projected lines as representing straight
lines in the real world, that could be considered a misinterpretation,
and thus an illusion. So I dunno, ya know?

I spent at least two minutes thinking about how to say what I meant
when I wrote "nor is it entirely an illusion". And I was only tentatively
satisfied with the result. I just knew you would raise this question.

Worse than my uncertainty about whether to classify it as an illusion
is my mumbo-jumbo about the line not actually being visible, so that
I have no other clues. Even if the line is there, it can still look
curved. When I look up at the line joining the wall in front of me to
the ceiling, I can see it as straight or as curved either down or up
toward the ends. It is much easier to see it as curved down if I put
the center of my vision below the line, and curved up if the center
of my vision is above the line, but nomatter where I look, I am able
to interpret it as curved in either direction. Actually, after a couple
of minutes of staring at it, I'm now having a hard time seeing it as
anything but straight....

That is definitely an illusion of classic pedigree.

-- 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

Would you at least consider it like a forced perspective?

__________________
Numbers are not case sensitive. (me)

Forced perspective is an illusion, right?

Shhh , I was trying for the subtle inference.

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Numbers are not case sensitive. (me)

Why is the light being bent away from the Earth?

First, all of you, thanks for tolerating my very layman's view -- I'm just a guy in the street who happened to look up in the air and was puzzled by this phenomenon.

With regard to Amber Robot's Q. as to why is the light in my crude diagram being bent away from the Earth I actually meant that the light rather than bending shallowly around the Earth instead kind of goes into orbit around part of the surface and then off at a slightly different angle to the linear approach direction on the side of the Earth away from the Sun, but the diagram doesn't show this. Anyway, that's irrelevant now as I accept Jeff Root's explanation -- that the effect would be far too small -- and thank him for such a lengthy consideration of my comments.

Another point which you have probably all noticed is that you need a really low horizon below the Sun (i.e. if there is a nearby hill below the Sun you don't see the effect as the Sun is really too high). Indeed it helps if the observer is on a hill.

I think that I shall try the stick and string experiment.
Best regards,
Barry

Actually, depending on the height of the observation, atmospheric refraction can result in up to several degrees of error, which must be accounted for when shooting celestial observations for navigational purposes.

__________________
If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

The Wikipedia page on atmospheric refraction says it is just over half a
degree at the horizon. Half a degree is the diameter of the Sun and Moon.

-- 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

As a celestial navigator, I'm...

...forgetting the difference between minutes and degrees! You're right, it's 35 minutes (0.5833... degrees) with an Ho of 0 degrees.

__________________
If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.