I live at roughly 52.4,-2.1. On a sunny evenings I've often looked at the moon and the sun and noticed that the light part of the moon does not appear to line up with the sun. For example, at about 17:00 GMT on 13 Mar 2011, I noticed the half moon was facing toward a point roughly 10-20 degrees above where the sun appeared to be. Why?
I think it is a parallax effect/optical illusion, and I'm not confident of explaining this clearly but here goes!
The normal vector to the illuminated portion of the moon is pointing generally away from the Earth/moon system towards a point over our horizon. At low altitudes (evenings) the sun will be close to the horizon and this can lead to the brain interpreting it as closer than it is and messing up the geometry. This is similar to the enlarged moon illusion when close to the horizon. Basically the normal vector appears to overshoot the sun as we interpret the sun as closer than it is.
I am puzzled by you question. When one has two points, the sun and the moon, one can always find a line connecting them, by definition of line.
If you mean why the earth is not part of that straight line, it is because the moon has an orbit around the earth, and the angle of the line earth-moon changes. It is the reason the moon has phases. Earth, moon and sun are on the same line during full moon, and the moon rises while the sun sets.
Edit: If as Ted Bun says you mean the bisecting line from the center of the moon, then the drawing given in wikipedia gives an angle because of the motion of the moon around the earth and the motion of the earth around the sun, except at full moon and new moon (if the rays shown are a correct depiction of the sun's direction).
Edit2: If one looks at the drawing In Carl Brannen's answer in combination with the wiki drawing, I think the parallax arises depending on the phase of the moon, because what one sees from the earth is not the total lit up semicircle of the moon. Part of it is hidden from the human observer so the apparent bisector is not the real bisector.
This is what you expect, in terms of the moon pointing towards the sun:
Now the above is a flat drawing. The sky appears curved (i.e. the dome of the starry sky). So that curve may introduce some apparent distortion.
To make a drawing that avoids the curvature issue, consider a drawing that only includes the sun, the moon, and a small amount of sky around the line connecting the two. (By the way, even for the curved bowl of the sky, the shortest line connecting the two is well defined except in the case of a new or full moon.) That drawing is approximately flat and will show the above relation.
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