## Lunar Eclipse Phenomena

What basic phenomena occur during a lunar eclipse? A longitudinal section through the shadow cast by the Earth is shown in Figure A-12. If the Sun were a point object then the planet would produce only a complete shadow (termed the umbra), but the Sun is actually over half a degree wide. This makes the shadow fuzzy around the edges, producing a region called the penumbra.

This effect is easy to demonstrate in your back garden on any sunny day. Hold a sheet of paper up close to a shadow, such as that cast by the leaves of a tree. Near the leaves their shadows appear to have sharp, well-defined edges, but as you pull the paper back further they become less and less distinct. This is due to the finite size of the Sun.

Now consider the Earth in space rather than a leaf in your garden. The distance that the shadow is projected is immense. Figure A-12 is drawn in a much-compacted form: the angles between the straight lines are actually very small (about 0.533 degrees, that being the Sun's average angular diameter). This produces a conical shadow zone with the apex at point A, a distance 850,000 miles from the Earth.

If the Moon has a node close to opposition it will pass through

850,000 miles

Path of Moon

FIGURE A-12. The Earth casts a conical shadow that is about 850,000 miles long, to its apex labeled A here. When the Moon passes somewhere through the shadow a lunar eclipse occurs (not to scale).

that shadow, and an eclipse will occur. The mean geocentric distance of the Moon (238,850 miles) is about 28 percent of the distance to the apex of the shadow. As a result the umbra is 72 percent the diameter of the Earth at the position of the Moon, or about 5,700 miles across. Recall that the Moon is 2,160 miles in diameter, and so the umbra can easily envelop it. That is, a total lunar eclipse is easily achieved, and will last for some time as the Moon slowly moves through the umbra. On the other hand the penumbra is about 128 percent the planet's width at the lunar position, a diameter of close to 10,150 miles, and so almost five times the extent of the Moon. The sizes of the umbra and penumbra are portrayed to scale in Figure A-13 as slices through the terrestrial shadow, to show how total, partial, and penumbral lunar eclipses may occur.

Penumbra

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