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Originally Posted by hhEb09'1
I just looked at Jeff Root's diagram too, and I don't like it
either. The top half says it shows what your eyes see--but the
text seems to indicate that the observer is under the moon,
rather than away from it. I don't think you can explain this
one with diagrams--it's just an illusion, it's not a real
effect, just like the moon illusion.
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It is an illusion, but I'm confident that a diagram can show
how the illusion is caused. My diagram is lacking in that it
is only two-dimensional, rather than three-dimensional. I'm
pretty sure that if you consider the geometry in 3-D, it will
fully explain the illusion.
I don't understand what you meant by my text indicating that
"the observer is under the moon, rather than away from it."
What does that mean?
The geometry I depicted is with the Sun and Moon 90 degrees
apart in the sky. I did that simply because a right angle
is familiar to everyone, and easy to visualize.
The observer is at the top of the Earth. That is where all
observers always are! The Moon is shown directly above the
Earth and the Sun is to your left. Observers in the northern
hemisphere can interpret that to mean that the Moon is on your
meridian directly south of you, shortly after sunrise. Those
in the southern hemisphere can interpret it to mean the Moon
is directly north of you, shortly before sunset. The Moon
could be low in the sky, or high in the sky.
None of that is important.
What is important is that there is a definite angle from the
Sun to you to the Moon (90 degrees in the diagram). Given that
the Sun and Moon appear to be roughly the same distance away,
your visual system interprets the angle of the path of light
from Sun to Moon as about 45 degrees (for the case diagrammed),
though it is actually well under one degree.
I think the diagram needs to be 3-D to be complete.
-- Jeff, in Minneapolis