The Umbra And Penumbra

The shadow cast by the Moon onto the terrestrial surface has a form as sketched in Figure 2-3. The dark central spot is the region

FIGURE 2-3. The umbra (complete shadow) of the Moon on the Earth is a solitary black spot in the middle of the pattern shown here. It is quite small, typically only 60 miles across, whereas the partial shadow or penumbra is over 4,000 miles in diameter, covering a large fraction of the dayside during an eclipse.

FIGURE 2-3. The umbra (complete shadow) of the Moon on the Earth is a solitary black spot in the middle of the pattern shown here. It is quite small, typically only 60 miles across, whereas the partial shadow or penumbra is over 4,000 miles in diameter, covering a large fraction of the dayside during an eclipse.

of totality: the Moon as seen from anywhere within that small region completely covers the solar disk, and this totally shadowed spot is called the umbra. Typically the umbra, or the path of totality, is 60—100 miles wide, although it can have effectively zero width (as in the case of a transition between a total and an annular eclipse), or be intrinsically a little wider in the longer eclipses. There is also a geographical effect: the lunar shadow may be cast

FIGURE 2-4. During the total solar eclipse of August 11, 1999, the crew of the Russian space station Mir photographed the Moon's shadow moving across the Earth's surface.

obliquely onto the Earth's surface, and so the width of the ground track tends to be wider for eclipses in the Arctic or Antarctic.

All around the region of totality the Moon only partially obscures the Sun, and this partial shadow is termed the penumbra. The penumbra is much wider than the umbra. While the umbral spot may have a radius of only tens of miles, the penumbral radius is 2,000—2,200 miles. A partial eclipse will be detectable anywhere within that large area, a grazing touch between lunar and solar disks occurring at its very edge.

Figure 2-4 is a photograph of the Earth obtained looking down from orbit during an eclipse, showing the lunar shadow very clearly. It is the people under this dark central spot who experience totality.

If you were living in Babylon a few thousand years ago, only a tiny fraction of all total solar eclipse paths would cross that city. The penumbra for a total eclipse seen elsewhere would cross Babylon in about a quarter of all cases, because the penumbral circle in Figure 2-3 scans about half of the dayside face of the globe (and half the time you would be on the night side). Mostly the city would lie towards the periphery of that shadow and the Moon would only cover perhaps 10 or 20 percent of the Sun, so that the eclipse might well be missed without foreknowledge. For a society constrained to Mesopotamia and environs, only a small fraction of all solar eclipses would appear in the records, making the discovery of the complex cycles described earlier a near-impossibility.

How, then, were the eclipse cycles unveiled?

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