Celestial phenomena form the basis for most cardinal and ordinal directional systems and the same was true anciently.Fact #1. In temperate and tropical latitudes (south of the Arctic Circle, north of the Antarctic Circle), the sun rises in the east and sets in the west. On a flat horizon, sunrise will be due east and sunset due west twice a year, on the vernal equinox (near March 21) and the autumnal equinox (near September 21). The site of Dzibilchaltun in Yucatan is justifiably famous with tourists partly because of spectacular site alignments on equinox sunrise.
 |
| Equinox sunrise, Dzibilchaltun |
This is the same structure on vernal equinox about 30 minutes after sunrise.
 |
| Equinox sunrise + 30, Dzibilchaltun near Merida |
Even more renowned among tourists is the serpent of light that appears on the steps of the Temple of Kukulcan (El Castillo) at Chichen Itza on the afternoon of each equinox.
 |
| Serpent image created by the equinoctial afternoon sun |
Fact #2. The earth's spin axis is tilted 23.5 degrees from the plane of the ecliptic, the hypothetical plane that intersects both the earth and the sun. This tilt causes the seasons as days in the northern hemisphere lengthen toward summer solstice (near June 21) and shorten toward winter solstice (near December 21).
 |
| Visual representation of earth's tilted axis |
At the equator on a flat horizon, the sun will rise on the summer solstice at a point 23.5 degrees north of due east. On the winter solstice that point will be 23.5 degrees south of due east. So, at the equator throughout one solar year, the sunrise point will vary across 47 degrees of a 360 degree arc, with that variation centered on due east. As one moves north or south of the equator, variation in solstitial sunrise points increases according to the formula 23.5/cosign(latitude). So, for example, the solstitial variation between sunrise points at Guatemala City (15.5 degrees north latitude) is 48.76 degrees on a flat horizon, slightly more than at the equator. The solstitial variation between sunrise points at Mexico City (19 degrees north latitude) is 49.68 degrees on a flat horizon. Mexico City (Teotihuacan) is about the northern extreme of New World locations that could plausibly be referenced in the Book of Mormon text. So, when the Nephites observed sunrise or sunset, they were looking at points on the horizon within 24.84 degrees of due east or due west. As with the equinoxes, solstice sunrise points were important in ancient architectural layouts. This, for example, is the entrance to the famous Temple of Karnak in Egypt on the winter solstice sunrise.
 |
| Entryway, Temple of Karnak, Winter Solstice |
Moonrise and moonset points follow a more complex but ultimately similar pattern. The new moon rises due east and sets due west on the spring and fall equinoxes, just as the sun does. The full moon does the same. The waxing moon rises due east and sets due west on the summer and winter solstices, which is opposite the sun's behavior. The waning moon does the same. As the moon goes through its phases, it will rise and set at points on the horizon that vary (at the equator) by the 23.5 degrees of the earth's tilt + the 5 degrees of the moon's own tilt. Like sunrise and sunset points, the amount of moonrise/set variation north and south of due east/west increases as one moves from the equator to higher latitudes. This graph from Paul Middents of the Battle Point Astronomical Association shows lunar rise/set point variation on the horizon relative to solar rise/set point variation across the 18.6 years of a Draconic Cycle.
 |
| Variation in moonrise points on the horizon relative to sunrise points |
As the graph shows, some years the variation in moonrise points will be up to 5 degrees smaller than the variation in corresponding sunrise points. Some years the variation in moonrise points will be up to 5 degrees greater. Like the sun, the apparent movement of the moon will always center on due east and due west.
Venus, the evening and morning star, exhibits similar predictable behavior in the sky rising and setting on the horizon at points in between the solar and lunar maximums. The apparent motion of Venus is affected by its sidereal period (225 days), its synodic period (583.9 days), the tilt of its axis (2.7 degrees away from the plane of the ecliptic) and its interaction with earth's sidereal period (365.256 solar days). The ancient Assyrians were careful observers of the planet's movements as shown in the Venus Tablet of Ammisaduqa on display in the British Museum. This 7th century B.C. copy of a 17th century B.C. text was in the library at Nineveh.
الفقرة السابقة
أول 