When you say orthogonal are you projecting the line between the Moon and Sun as a straight line? If so that may be the source of youir confusion.
Remember, the Moon and the sun follow a path that appears from our point of view to be an arc. In the attached jpeg I've drawn a rough diagram that I believe represents the situation. The Moon's terminator is perpendicular to the path it traces. The arrow represents the direction you assume the sun to be in by projecting a line perpendicular to the terminator.
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"The very powerful and the very stupid have one thing in common: They don't alter their views to fit the facts, they alter the facts to fit their views." The Doctor, Doctor Who: The Face of Evil.
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