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Originally Posted by TheDon
... yar i hate noticing things like this once you take calculus .. it kinda looks like an upside down "witch of agnesi curve"
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That's probably pretty close but I think it maybe four unrelated curves.
The first is the Earth's curvature, the second is the Earth's rotation, the third is the Earth's tilt and the fourth is the Earth's orbit around the Sun. Each of these is integrated to give the lit (and unlit) area of the Earth at a certain time of day and date. The derivative would be the problem of position for navigation.
Bot