Take the crescent moon. Draw a straight line connecting its two points (or horns, or whatever you wanna call them). Presumably, a second line perpendicular to and bisecting that line should continue on to the center of the Sun. But sometimes when the Sun and Moon are in the sky together, you can see it ain’t so. It’s appears as if there’s light coming from where there’s no Sun (if you will), and light coming from the Sun that isn’t lighting up some of the moon.
It is always so. If it looks like it isn’t, that’s due to some form of optical illusion or another. At a guess, I’d say that the most likely culprit is that you’re trying to draw your “straight line” in the sky at a constant distance above the horizon, rather than along a great circle.
A line connecting the horns is not the right model, it is a 2D idea applied to a 3D situation. You need a plane that cuts through the sphere of the moon along the twilight zone (or whatever the correct name is…I forget). Then draw a line from the center of the moon, orthogonal to that plane, and that will intersect the moon.
For a half moon, you will see just the edge of the plane, but for a crescent moon you would see some of the face of the plane that is away from the sun.
No matter where you are, the moon looks pretty much the same, as long as you’re on the part of the earth that can see the moon. But your orientation changes, depending on your location. So to someone in, say, New York City the moon would look about the same as someone in, say, Paris . . . but due to their location on earth, it would “point” in a different direction.
Like, garygnu, I agree with this. Take this example: Sunset with a 1st quarter moon. The moon is due south (for those of us in the northern hemisphere) with the moon’s lighted part pointing horizontally due west (to the right), yet the sun is down on the horizon. But a straight line due west at the moon immediately starts to curve downward along a great circle to the sun.
In The Flying Circus of Physics, Jearl Walker claims it’s because you mentally misinterporet the shape of the sky “dome” when you’re drawing your bisector through the illuminated moon. Thatr would be consistent with the way M. Minnaert draws our supposed mental image of the sky “dome” in his classic book The Nature of Light and Color in the Open Air.
According to botyh sources, we really ought to view the sky as a hemispherical dome, but “really” perceive it as a much flattened non-hemispherical concave surface. This may all be true (and would account for the incorrect visualizsation that causes the OP’s problem, as well as other effects like the apparently larger size of the moon on the horizon), but I’m not familiar with any original work on the topic, or psychological studies.
As I think about this more, The OP’s construction should work in the 2D view. The Terminator is a little fuzzy, so there is some ambiguity about where exactly the points of the horns lie, but this should only introduce a few degrees of miss when projecting a line to the sun.
For a gibbous moon, the ambiguity is much larger, and the sun’s apparent position is much farther from the moon as well, and I can see that generating a significant miss.
When we look at objects in the sky we tend to vastly underestimate the size and scale of what we are seeing. Our brains are hard wired to perceive things at the scale we are familiar with on Earth.
I have seen similar observations to what the OP is talking about - most notably at dusk when the sun just passes below the horizon and the illumination on the moon doesn’t seem to point directly towards the sun. The problem with my perception was that I wanted to place everything too close to me; the angles I expected would only be right if the moon and sun were just barely above me in the sky.
I noticed exactly what the OP was talking about - the angle with which the sun lights up the moon seems to different than the angle that the sun was lighting up me. I assumed it was because the earth is tilted, so indeed the angle is different (from the perspective of an earth-bound observer). From a non-earthbound observer of course, the effect would not exist.
If I’m understanding correctly, this is happening because you tend (at least I do) to believe that the sun and the moon are at about the same distance from the earth, meaning that the triangle composed of the centers of the earth, sun, and moon is isosceles. But they’re not, and the sun is always “behind” the moon in some sense, which would mean that the line you create from the moon should generally point father back, away, from you than it would be if that triangle were in fact isosceles.