Do the maths for the southern hemisphere and compare: It is my belief due to axial tilt AND the solar rotation period and solar distance, the effects aren't ent

Do the maths for the southern hemisphere and compare: It is my belief due to axial tilt AND the solar rotation period and solar distance, the effects aren't entirely equal north and south pole. Do the maths for the dusk side of the story. Dawn is good, but how this behaves in the rate of sun appearance and rate of sun disappearance also has a shift, the two event peaks aren't aligned. Again, a function (I believe) of the axial tilt. So its a system with differences, with multiple inputs, with complex maths. I love it!