Eclipses and Eclipse Cycles

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).

  • Solar eclipses are much more extraordinary to see than lunar eclipses.

    Frequency of Solar Eclipses

    There will be 18 solar eclipses from 1996-2020 for which the eclipses are total on some part of the Earth's surface. The common perception that eclipses are infrequent is because the observation of a total eclipse from a given point on the surface of the Earth is not a common occurrence. For example, it will be two decades before the next total solar eclipse visible in North America occurs.

    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 geometry associated with solar eclipses is illustrated in the following figure (which, like many figures is illustrative and not to scale).

    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.

    Types of Solar Eclipses

    The preceding figure allows three general classes of solar eclipses (as observed from any particular point on the Earth) to be defined:
    1. 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.

    2. PARTIAL SOLAR ECLIPSES occur when the part of the penumbra and part of the umbra of the moon's shadow passes over a region on the Earth's surface. To an observer, the moon only partially blocks the sun.

    3. ANNULAR SOLAR ECLIPSES occur when a region on the Earth's surface is in line with the umbra, but the distances are such that the tip of the umbra does not reach the Earth's surface.
    As illustrated in the figure, in a total eclipse the surface of the sun is completely blocked by the moon, in a partial eclipse it is only partially blocked, and in an annular eclipse the eclipse is partial, but such that the apparent diameter of the moon can be seen completely against the (larger) apparent diameter of 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.

    Angular Diameter of Sun and Moon

    It turns out that the richness of the solar eclipse spectacle is made possible because the moon and the sun have nearly the same angular diameter on the sky. (Recall that we discussed the angular diameter of an object in the sky in lecture 1).

    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.

    Total Solar Eclipses

    Total solar eclipses occur only in the NEW MOON phase.

    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.

    Appearance of a Total Solar Eclipse

    If you are in the path of totality the eclipse begins with a partial phase in which the moon gradually covers more and more of the sun. This typically lasts for about an hour until the moon completely covers the sun and the total eclipse begins. The duration of totality can be as short as a few seconds, or as long as about 8 minutes, depending on the details.

    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.

  • Note that one is warned not to look directly at the sun. This is because one is because the copious IR (infra-red) radiation can fry our retinas. However, this is still true in a partial solar eclipse when only part of the sun is covered. The warnings that are given are to remind people that this is not safe, but of course, its not more dangerous than looking at the sun during any other circumstance. Apparently people get confused on this point.

  • A safe way to look at an eclipse is through a piece of paper with a pinhole. Then put another piece of paper below it for the projection. (Fig 3-15 in text).

    Annular Eclipse

    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.

    Partial Eclipse

    Christmas Day 2000, photographed in North Carolina. Single exposure 11 am to 1:30 pm:

    Patterns of Eclipses

    There are about 1 or 2 total or annular eclipses per year which can be seen someplace on the Earth.


    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:

  • The orbit of the moon is tipped with respect to the plane of the Earth's orbit, so we see the moon follow the path tipped by that angle with respect to the ecliptic.

  • The moon crosses the ecliptic plane at two points each month called NODES. The moon crosses one node going south, and the other node going north two weeks later.

  • Eclipses only occur when the sun is near one of the nodes of the moon's orbit. Most of the time, new moons pass too far north or south of the ecliptic to form an eclipse. Similarly, lunar eclipses don't happen every full moon since full moons usually pass to far north or south of the ecliptic.

    There are thus two arrangements for an eclipse:

    1. If the moon is at one node and the sun is at the other, and the moon is full we have a lunar eclipse.

    2. If the moon is at one node and the sun is at the same node and the moon is new we have a solar eclipse.
    An ECLIPSE SEASON is the period when the sun is close enough to a node so that an eclipse can occur. An eclipse season for solar eclipses is about 32 days and any new moon in this period will produce a solar eclipse. The lunar eclipse period is 22 days.

    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.

  • If you stand in the same place for 54 years, you will be able to see the exact same eclipse. If you are impatient and wait only 18 years 11 days, you will have to travel for 8 hours west to see the same eclipse because of the extra 1/3 of a day.