**Chronos**, I’m not sure I see how great circles would come into it. The sky isn’t really spherical, it’s just this vast three dimensional space that we’re hanging out in. A straight line from the moon to the sun will appear to be a straight line, regardless of your viewing angle; there will be no curve.

Thinking about it a little more, I think I see what the problem could be, but it may be a little difficult to explain; it boils down to three-dimensions vs. two-dimensions, and a little confusion there.

So you’re looking at the moon, trying to pick out the perpendicular bisector…got it. But what may not be so easy to pick out is the third dimension (or “orientation” may be a better word) of the line. For example, picture in your mind a thin crescent moon, sitting *right next* to the sun. Now picture a line going straight through the center of the moon, pointed straight at **you** (this line would actually appear to you as a point, since you’re looking right down it). Fix the point of the line at the center of the moon, and rotate the line about this point a tiny amount, in the direction so that in now appears to “bisect” the lit surface of the moon. In fact, there’s an *entire plane* that you can rotate this line through so that the line always appears to bisect the lit surface of the moon (so basically what I’m saying is that there isn’t a *line* that bisects the lit surface (to your perspective), but a *plane[/]). Obviously not all of those lines will point to the sun.

So the bottom line is that, not only do you have to pick the perpendicular bisector of the moon, but you also have to consider how it should be *rotated/oriented*. If you look at the full moon, that line will be going (“almost”) right through you to point to the sun. If the moon is a little shy from full, the line isn’t pointing to the side out from the moon, it’s pointing in your general direction on it’s way to the sun. Conversely, for a nearly new moon, the line is pointing almost directly away from you towards the sun.

I hope that description made sense. Anyway, the final point being that failure to account for this when trying to picture the line may account for the distortion you saw.