From the perspective of the AE map: The sun circles the earth. Every complete circle it makes is approximately one day. However, the sun is not always on the circle of the equator. It spirals inward from the equator to the tropic of cancer, and outward from the equator to the tropic of capricorn.
Let's assume the year starts at the spring equinox (about March 20th). At that point the sun is circling the equator. Around 3 months later (summer solstice) the sun has spiraled inward and is now at the tropic of cancer. Around 3 months later again (fall equinox) the sun has spiraled outward and is back at the equator. Around 3 months later (winter solstice) the sun has spiraled outward further and is at the tropic of capricorn. Around 3 months later (back at spring equinox again) the sun has spiraled inward and returned to the equator again. The year is complete.
My question is, how does one find the equation of the spiral of the sun for the AE map? If this equation is found, you could calculate the exact position of the sun at any given point of time on the AE map (which is ultimately the goal).
