The paths are all parallel to each other, but are slanting at 21 degrees to the horizon. It will also be noticed that the horizon divides the total path of the Sun into equal periods only on the first days of spring and fall, i. In summer, the portion of the Sun's path above the horizon is much greater than the night portion, and the reverse is true in the winter.
This illustrates the geographical effect , which depends on the observer's latitude. Figure 8 and 8a below. The daily path of the Sun as seen from Hawai'i on the first day of spring, summer, fall, and winter. The equinoxes and the directions of sunset show why. The equinoxes occur when the sun sets due west, and the days and nights are virtually of equal length everywhere on Earth.
So, in its yearly journey along the ecliptic, there are only two days when the sun crosses the equator. Which means that the ecliptic and equator must be in different planes, and must intersect at the equinoxes. Like the Babylonians and others before them, the Greeks wanted to be able to keep track of the stars and planets, in order to study the ways of the deities who ruled them, and also to help with navigation.
Ptolemy reasoned as follows. At the equinoxes — when the direction of the sunset is halfway between the most northerly and southerly sunset points — the sun is at the point of intersection of the ecliptic and the celestial equator, as I mentioned.
So the angle between these two intersecting planes must be half the difference between the summer and winter solstice solar altitudes, which exhibit the same symmetry. It was an incredible deduction, even if Ptolemy did believe that the planets and stars, including the sun, literally moved around the Earth. Today, of course, we believe it's the Earth that's moving in the plane of the ecliptic, not the sun. Astronomers also have a more up-to-date figure for the angle of tilt, If there were no tilt, the Earth would revolve around the sun with its north pole pointing upwards, and the ecliptic and equator would be in the same plane.
And, like his famous contemporary Galileo Galilei, Harriot was also a Copernican. So, at the equinoxes, when the declination is zero and therefore so is its sine, the deviation of the direction of sunset is also zero, and the sun sets due west as expected. So the deviation from due west is just the declination of the sun on that day.
It wouldn't rise high in the sky, and would be up for only about 6 or 7 hours, making your days short on daylight and cold. At the Spring and the Fall equinoxes, the Sun would rise at the east end of the middle track and set at the west end. Build your own Sun Track Diorama What about the stars? The rising points of the stars don't change as much as the Sun's because they are so very far away. So the rising points of stars on the horizon were not as critical to ancient cultures.
However, the rising times of stars change by 4 minutes each day, so any particular star would rise at different times during the year. For about half the time, the star would rise during the daytime and thus be blocked by the huge light of our Sun.
There was something called the "heliacal" or dawn rise of a star -- and this happened on only one day of the year. Thus these dawn rising were extremely useful for keeping track of exact days. For an explanation and examples of heliacal or dawn risings of stars, see Show Me a Heliacal Rising. Image credits: Medicine Wheel sunset photograph by Tom Melham. The Tom Melham picture appeared in the National Geographic.
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