Why does the location of sunrise change?
Why does the azimuth of the sunrise position change over the course of the year?
The reason is the tilt of Earth's axis of rotation with respect to the orbital plane. As you know, the axis of rotation is tilted by an angle of 23.5 degrees with respect to the plane in which all the planets go around the Sun. As a result, at some points in the orbit of Earth, the north pole is tilted towards the Sun, and at other points it is tilted away from the Sun. In the first case, the Sun is north of the equator, and in the second case the Sun is south of the equator.
Now, if the Sun were to be directly above the equator (which corresponds to the equinoxes), then it will rise exactly at east. When the Sun is north of the equator, then it will rise at an azimuth north of exact east and when it is south of equator, it will rize at an azimuth south of exact east. As the Earth goes around the Sun, the Sun appears to go in a cycle from equator to north of equator and then back to equator and then to south of equator and then back again to equator (which marks the cycle of the seasons on Earth). Hence, the azimuth of sunrise changes slowly from direct east to north of east and then back to east to south of east and then back again to east.
Thank you for answering my question before about the azimuth, but I was wondering, does the azimuth of the sunrise position change at a uniform rate throughout the year?
No, the change in azimuth is not uniform. If the Earth's orbit were exactly circular, then the change in azimuth will be sinusoidal. It would change slowest during solstices (where the sunrise is most towards north or south) and fastest during equinoxes (where the sunrise is towards exact East).
However, Earth's orbit around the Sun is not an exact circle. It is slightly elliptical with the perihelion (where the Earth is closest to the Sun) occuring near winter solstice (Jan). Hence, the change in sunrise position will not be an exact sinusoid and will change slightly faster around winter solstice compared to summer solstice. This effect is small though.
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