Sunrise Time: Likewise sunrise is defined as the point when the leading edge of the sun is first visible even though this is some minutes before the sun actually rises above the horizon. You ask where the sun really is: when the sun sets and rises it is about one solar diameter below where it appears to be, i.e. about half a degree.
Most people know that the Sun "rises in the east and sets in the west". However, most people don't realize that is a generalization. Actually, the Sun only rises due east and sets due west on 2 days of the year -- the spring and fall equinoxes! On other days, the Sun rises either north or south of "due east" and sets north or south of "due west."
Each day the rising and setting points change slightly. At the summer solstice, the Sun rises as far to the northeast as it ever does, and sets as far to the northwest. Every day after that, the Sun rises a tiny bit further south.
At the fall equinox, the Sun rises due east and sets due west. It continues on it's journey southward until, at the winter solstice, the Sun rises are far to the south as it ever does, and sets as far to the southwest.
Many, if not most, prehistoric cultures tracked these Sunrise Time and settings points with great detail. If they had jagged mountains along the horizon, the exact points could be readily remembered. Without a suitably interesting horizon, standing stones could be arranged to line up with the various rising and setting points. Or, tree poles could replace the standing stones. Or, rock cairns could be used.
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