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I. ASYMMETRY of ECLIPSES. CALENDAR CYCLES Igor Taganov & Ville-V.E

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I. ASYMMETRY of ECLIPSES. CALENDAR CYCLES Igor Taganov & Ville-V.E I. ASYMMETRY OF ECLIPSES. CALENDAR CYCLES Igor Taganov & Ville-V.E. Saari 1.1 Metaphysics of solar eclipses p. 12 1.2 Calendar cycles of solar eclipses p. 20 Literature p. 26 To describe the two main types of solar eclipses in modern astronomy the old Latin terms – umbra, antumbra and penumbra are still used (Fig. 1.1). A “partial eclipse” (c. 35 %) occurs when the Sun and Moon are not exactly in line and the Moon only partially obscures the Sun. The term “central eclipse” (c. 65 %) is often used as a generic term for eclipses when the Sun and Moon are exactly in line. The strict definition of a central eclipse is an eclipse, during which the central line of the Moon’s umbra touches the Earth’s surface. However, extremely rare the part of the Moon’s umbra intersects with Earth, producing an annular or total eclipse, but not its central line. Such event is called a “non-central” total or annular eclipse [2]. Fig. 1.1. Main types of solar eclipses The central solar eclipses are subdivided into three main groups: a “total eclipse” (c. 27 %) occurs when the dark silhouette of the Moon completely obscures the Sun; an “annular eclipse” (c. 33 %) occurs when the Sun and Moon are exactly in line, but the apparent size of the Moon is smaller than that of the Sun; a “hybrid eclipse” or annular/total eclipse (c. 5 %) at certain sites on the Earth’s surface appears as a total eclipse, whereas at other sites it looks as annular. There are more annular solar eclipses than total because on average the Moon moves too far from the Earth to cover the Sun completely. 1 From ancient times several picturesque effects during solar eclipses are known, for example, “Diamond rosary” (Fig 1.2-1), “Diamond ring” (Fig 1.2-2) and “Wedding ring” (Fig 1.2-3). The “Diamond rosary” and “Diamond ring” now astronomers name the “Baily’s beads” in honor of English astronomer Francis Baily (1774–1844) who first published an explanation of these phenomena – the bursts of light appear around the lunar silhouette when during total sun eclipse the sunlight shines through rugged lunar limb in some places. Fig. 1.2. “Diamond rosary” (1) and “Diamond ring” (2) during total sun eclipse on November 25, 2011 [http://www.spacetribe.com/]. “Wedding ring” (3) – the annular sun eclipde on May 20, 2012 [/wikipedia.org/]. A lunar eclipse occurs when the Moon passes behind the Earth into its shadow (umbra). Lunar eclipses occur when the Sun, Earth and Moon are aligned in syzygy (from the Ancient Greek σύζυγος, suzugos, meaning “yoked together”) – a straight-line configuration of all three celestial bodies (Fig. 1.3). The Moon crosses ecliptic – the plane of the Earth’s orbit around the Sun at positions called “nodes” twice every month and when the Full Moon occurs in the same position at the node, a lunar eclipse can occur. These two nodes allow two to five eclipses per year, parted by approximately six months. An eclipse of the Moon can only take place at Full Moon, and only if the Moon passes through some portion of Earth’s shadow, which composed of two cone-shaped parts, one nested inside the other. Fig. 1.3. The geometry of lunar eclipse. Right part: the lunar eclipse on October 27, 2004 (Eclipse Predictions by Fred Espenak, NASA’s GSFC; http://eclipse.gsfc.nasa.gov/. For earthly observer the Moon daily crosses the sky from east to west, however, with respect to the Earth’s shadow cone and the stars it moves from west to east. 2 When the Moon enters into the Earth’s penumbra a partial penumbral eclipse (Fig. 1.4-1) starts with a subtle darkening of the Moon’s surface. When the Moon moves exclusively within the Earth’s penumbra a total penumbral eclipse (Fig. 1.4-2) is visible. Total penumbral eclipses are rare, and when these occur, that area of the Moon which is closest to the umbra can appear somewhat darker than the rest of the Moon. If the entire Moon passes through the umbral shadow, then a total eclipse (Fig. 1.4-3) of the Moon occurs. The type and length of a lunar eclipse depend upon the Moon’s location relative to its orbital nodes. Fig. 1.4. Lunar eclipses: partial (1), total penumbral eclipse (2) and total eclipse (3; the “Blood Moon”). The Moon’s speed through the Earth’s shadow is about one kilometer per second, and total eclipse may last up to more than 100 minutes. However, the total time between the Moon’s first and last contact with the Earth’s shadow is much longer, and could last up to 4 hours. In contrast to a solar eclipse, which can only be viewed from a certain relatively small area of the world, a lunar eclipse may be viewed from anywhere on the night side of the Earth. A lunar eclipse lasts for a few hours, whereas a total solar eclipse lasts for only a few minutes at any given place, due to the smaller size of the Moon’s shadow. A totally eclipsed Moon occurring near Moon’s apogee where its orbital speed is the slowest will lengthen the duration of total eclipse. The inner shadow (umbra) is a region where Earth blocks all direct sunlight from reaching the Moon. The outer shadow (penumbra) is a zone where Earth blocks only part of the Sun’s rays. Though within the umbra the Moon is totally shielded from direct illumination by the Sun, the Moon does not completely disappears as it passes through the umbra because of the refraction of sunlight by the Earth’s atmosphere into the shadow cone. The amount of scattered and refracted light depends on the amount of dust and clouds in the Earth’s atmosphere that influences the color of eclipsed Moon. During an eclipse, the Moon’s disk can take on a dramatically colorful appearance from dark gray or bright orange to coppery- red or dark brown. To describe the color of eclipsed Moon the scale proposed in 1930s by French astronomer André-Louis Danjon (1890–1967) is sometimes used: L=0: Very dark eclipse with Moon almost invisible; L=1: Dark gray or brownish eclipse; L=2: Deep red or rust-colored eclipse; L=3: Brick- red eclipse with the umbral shadow having a bright rim; L=4: Intense copper-red or orange lunar disc having a bright rim and the bluish umbral shadow. A “selenelion” or “horizontal eclipse” occurs when both the Sun and the eclipsed Moon can be observed at the same time, which happens just before sunset or just after sunrise and both bodies will appear just above the horizon at nearly opposite points in the sky. There are a number of high ridges undergoing sunrise or sunset that can see it. Although the Moon is in the Earth’s umbra, the Sun and the eclipsed Moon can both be seen at the same time because the refraction of light through the Earth’s atmosphere causes each of them to appear higher in the sky than their actual geometric positions. The red coloring of eclipsed Moon arises because sunlight reaching the Moon must pass through a long and dense layer of the Earth’s atmosphere, where shorter wavelengths are more likely to be scattered by the air and dust particles, and so by the time the light has passed through the atmosphere, the longer 3 wavelengths dominate. Such scattered light we see as red hues during sunsets and sunrises and it often paints the eclipsed Moon by a reddish color being a cause of the “Blood Moon” phenomenon. Eclipse season is the only time during which the Sun is close enough to one of the Moon’s nodes to allow for an eclipse to occur (Fig. 1.7). During the Eclipse season, whenever there is a Full Moon a lunar eclipse will occur and whenever there is a New Moon a solar eclipse will occur. Each season lasts from 31 to 37 days, returning about every 6 months (173.31 days – half of an Eclipse year). At least two – one solar and one lunar, in any order, and at most three eclipses – solar, lunar, then solar again, or vice versa, will occur during every Eclipse season. Since it is about 15 days between Full Moon and New Moon, if there is an eclipse at the very beginning of the Eclipse season, then there is enough time for two more eclipses. If the last eclipse of an Eclipse season occurs at the very beginning of a calendar year, it is possible for seven eclipses to occur since there is still time before the end of the calendar year for two full Eclipse seasons, each having up to three eclipses. Occasionally 4 total lunar eclipses occur in a sequence with intervals of 6 lunations (the average time for one lunar phase cycle i.e., the synodic period of the Moon, or the period from one New Moon to the next). Such remarkable lunar eclipse series is called the “Tetrad”. Italian astronomer and science historian Giovanni Schiaparelli (1835–1910) noticed that there are eras when Tetrads occur comparatively frequently, interrupted by eras when they are rare and later Dutch astronomer Antonie Pannekoek (1873– 1960) explained Tetrad phenomenon and found a period of 591 years. Recently Tudor Hughes explained the Tetrad period variation by secular changes in the eccentricity of the Earth’s orbit and estimated the current period as about 565 years.
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