Hello guys. I recently recieved an assignment for my Modern Geometry course to create a solar clock capable of determining the week of the year and the hour of the day.
I understand how on any given day the shadow of a point in space projected on the plane travels along a unique conic section (assuming the earth doesnt move during one day) and so the process would require to find all the conic sections for each week. (26 curves since after each equinox the curves overlap)
Weve seen in class how the eccentricity of the conic sections depends on the angle between the north pole's plane and the plane on where we stand, just like the two planes considered in the Dandelin Spheres to proof the definition of a conic section according to its eccentricity.
I was wondering if anyone here has ever run into a book detailing the calculations required for this process since there are many details the teacher overlooked and we must formulate.