The main effect in shifting latest sunrise several days after the shortest day of the year is an oscillation of the time of day when the sun reaches its highest elevation in the sky. This time oscillates about noon throughout the year in a sine wave with an amplitude of 8.8 minutes (at latitude 45 degrees) and with a period of 6 months. At the solstices and equinoxes, highest elevation is at noon. Sunrises and sunsets each day occur equally before and after the time of sun’s highest elevation. If, for the moment, we redefine morning and afternoon to be those intervals, then at the winter solstice, the length of morning is minimum and so changes very little for a few days. But although the time of sun’s highest elevation is noon at the solstice, that time gets later quite quickly and shifts sunrise to be later for a few days. After that few days, morning begins to get longer and overwhelms the 8.8 minute sine wave so we get earlier sunrises again.
The changes in the time of sunrise and sunset, and the length of days, do depend on the seasons. And the changes of seasons are caused by the relationship of the axis of the Earth in relation to the Sun.
The axis of spin of the Earth is not vertical to the plane between the Earth and the Sun.
Even though the Earth spins on that axis, and rotates around the Sun, the tilt of the axis never changes. Because of this, the Northern and Southern hemispheres are exposed to more or less sunlight at different times.
As a result, when the top of the Earth is in a position where it is closer to the Sun, the Sun’s light rays strike well above the Equator, resulting in Summer, and longer days.
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