Note that a lunar eclipse can only occur when the moon is in the FULL phase. It represents the blockage of the sun's light by the Earth. Thus the Earth is in between the moon and the sun. Here the moon passes through the shadow cast by the Earth.
In addition though, the moon can shadow the sun's light as viewed from the Earth, and thus the Earth passes through the shadow of the moon, blocking the sun. this is a SOLAR ECLIPSE. Again, the small tilt of the moon's orbit with respect to the plane of the ecliptic and the small eccentricity of the lunar orbit make such eclipses much less common than they would be otherwise, but partial or eclipses are frequent (both solar and lunar).
The next total solar eclipse will be June 21 2001, with the PATH OF TOTALITY crossing South Africa and Madagascar.
|Geometry of solar eclipses
The arrows point to the location of the Earth for the various types of eclipses.
The shadow cast by the moon can be divided by geometry again into the completely shadowed UMBRA and the partially shadowed PENUMBRA.
TOTAL SOLAR ECLIPSES occur when the umbra of the moon's shadow touches a region on the surface of the Earth. To an observer standing in that region, the moon totally blocks the sun.
A given solar eclipse may be all three of the above for different observers. For example, in the PATH OF TOTALITY (the track of the umbra on the Earth's surface) the eclipse will be total, in a band on either side of the path of totality the shadow cast by the penumbra leads to a partial eclipse, and in some eclipses the path of totality extends into a path associated with an annular eclipse because for that part of the path the umbra does not reach the Earth's surface.
If we take an object of fixed LINEAR DIAMETER (the actual diameter we would measure with a ruler placed on the surface of the object) and imagine it to be moved farther and farther away from us, we would see the angular diameter decrease. This tells us that the angular diameter is related to the distance and the linear diameter of the object. For small angular diameters, ( those << 60 degrees) The relation we use is
(angular diameter in arc seconds / 206265" ) = (linear diameter / distance)
where 206265 is the number of radians per arc second.
(This relation is easy to derive for those interested in doing so: Recall that for a circle centered at the Earth, traced by the orbit of the moon or sun, the circumference of the orbit is 2 x Pi x distance. The linear diameter of the object is approximately the fraction of that circumference traced out not by (2)(Pi), but by the angular diameter of the source. I leave the details to the interested.)
We can use the formula to find the angular diameter of the moon if we know the distance and the linear diameter. That is plugging in we have:
(angular diameter in arc seconds / 206265" ) = (3476 km/ 384,000km)
Then we multiply both sides by 206265 to get 1870 arc seconds (1870"). If we divide this by 60 we get 31 arc minutes (31') and divide be 60 again we get 0.5 degrees. (Recall that there are 60" in 1' and 60' in 1 degree).
If we do the same for the sun we get about the same number. This means that the factor by which the sun is farther from the moon is nearly equal to the factor by which its linear size is larger than that of the moon.
Solar eclipses would not very interesting if the angular diameter of the moon were smaller than the sun's. They are extra interesting not just because the moon's angular size is large enough to block the sun, but because the sizes nearly match.
A total solar eclipse requires the umbra of the moon's shadow to touch the surface of the Earth. Because of the relative sizes of the moon and sun and their relative distances from Earth, the path of totality is usually very narrow (hundreds of kilometers, usually about 270 km). The following figure illustrates the path of totality produced by the umbra of the moon's shadow. (We do not show the penumbra, which will produce a partial eclipse in a much larger region on either side of the path of totality; we also illustrate in this figure the umbra of the Earth's shadow, which will be responsible for total lunar eclipses to be discussed in the next section.)
|Solar eclipse (not to scale)
As noted above, the images that we show in discussing eclipses are illustrative but not drawn to scale. The true relative sizes of the sun and Earth and moon, and their distances, are very different than in the above figure.
As totality approaches the sky becomes dark and a twilight that can only be described as eerie begins to descend. Just before totality waves of shadow rushing rapidly from horizon to horizon may be visible. In the final instants before totality light shining through valleys in the moon's surface gives the impression of beads on the periphery of the moon (a phenomenon called Bailey's Beads). The last flash of light from the surface of the sun as it disappears from view behind the moon gives the appearance of a diamond ring and is called, appropriately, the diamond ring effect (image at right).
As totality begins, the PHOTOSPHERE (lighted outer surface) begins to get covered. The SOLAR CORONA corona (extended outer atmosphere of the sun) blazes into view. The corona is a million times fainter than the surface of the sun; thus only when the eclipse is total can it be seen; if even a tiny fraction of the solar surface is still visible it drowns out the light of the corona. At this point the sky is sufficiently dark that planets and brighter stars are visible, and if the sun is active one can typically see solar PROMINENCES and FLARES around the limb of the moon, even without a telescope (see image at left).
The period of totality ends when the motion of the moon begins to uncover the surface of the sun, and the eclipse proceeds through partial phases for approximately an hour until the sun is once again completely uncovered. The duration of the totality (total covering) is less than 7.5 minutes.
A partial solar eclipse is interesting; a total solar eclipse is, by all accounts, a remarkable sight. If you have an opportunity to observe a total solar eclipse, go for it! As I mention above, June 21 in Madagascar is the place to be.
Although the moon's orbit is nearly circular, there is some small ellipticity. Because the angular sizes of the sun and moon are so close, the slight ellipticity in the moon's orbit means that at APOGEE (the farthest point in the moons orbit) the moon's angular size is smallest and does not fully cover the sun. Then one gets an annular eclipses.
DESCRIBING THE CONDITIONS FOR AN ECLIPSE TO OCCUR:
Because solar eclipses are the result of periodic motion of the moon about the Earth, there are regularities in the timing of eclipses that give cycles of related eclipses. These cycles were known and used to predict eclipses long before there was a detailed scientific understanding of what causes eclipses. For example, the ancient Babylonians understood one such set of cycles called the Saros, and were able to predict eclipses based on this knowledge.
Now we know more:
There are thus two arrangements for an eclipse:
To see all of this more explicitly look at figure 3-21. Not the precession of the moon's orbit with respect to the ecliptic plane (this is represented by the fact that the 5 degree inclination of the moon's orbit varies the location of the above and below portions of this orbit with respect to the direction to the sun.)
The precession affects the time scale for repetition of favorable alignment of the line of nodes for an eclipse. The precession rotates the line of nodes rotate westward 19.4 degrees per year so a full rotation takes 18.6 years. The sun then returns to the line of nodes every 347 days, so the eclipse season begins 19 days earlier every year.
It turns out that all of the above means that after every 18 years 11 and 1/3 days, the eclipse cycles completely repeat. The ancients notices this pattern called the SAROS CYCLE. One saros is 223 lunar months. The moon therefore returns to same phase. In addition the sun returns to the same place with respect to the nodes of the moons orbit.