is 2 longitude lines and 2 latitude lines that are "tangent" to a circle projected onto a sphere. I did latitude last night, but longitude is another story.
Now it's really a matter of finding the relationship between the circle and where the longitude lines touch it as was said last night.
I thought about it last night, and I have some thoughts, though no solution. Now, if we have a circle with radius delta-r, then the longitude lines are going to be touching close to the diameter until the edge of the circle gets very close the poles, at which point the chord length goes to zero. Thinking about this, I am sure this is not a linear relationship (big surprise there).
Now if we have some circle with radius r, then when the radius is at the equator, we have longitude lines touching on the same diameter. As the circle moves up (north), the points at which the longitude lines touch form a chord that moves toward "top" of the circle. Then the two points finally meet at the pole.
Now, we know that this has to be some nonlinear relationship between the radius of the circle, the location of the center point of the circle (theta), the radius of the sphere. Feel free to add any I missed. Now to figure out what it is.
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