Eclipse Cycles

Eclipses occur in a long series
called the saros, and are about 18 years apart from one another. The word saros
originated as a Babylonian word meaning ‘repetitive’. Saros has become a term
that is applicable to both lunar and solar cycles of the 18-year duration. The
saros lasts exactly 223 synodic months. Each series of eclipse is separated by
an 18 year 11-1/3 cycle. This series of eclipses is known as a saros series.
The saros also coincides closely with 19 eclipse years. Eclipses occur
repeatedly, separated by a specific interval of time. This interval is called
an eclipse cycle. The repetition of eclipses tends to follow a very regular
pattern.

Both the
Sun and the Moon subtend significant angles. This means that for an eclipse to
occur, they do not need to be exactly at the nodes along the Line of Nodes. In
addition, an observer's position on the surface of the Earth introduces a
sizable parallax of 2° in ecliptic latitude. These factors, combined with the
fact that the Sun is within 18.5° of a node, make a solar eclipse possible. The
Sun travels about 1° per day along the ecliptic, requiring around 37 days to
travel across through the eclipse zone centred on each node. As the New Moon
takes place about every 29- 1/2 day, at least one eclipse can occur in the
process of each of the Sun’s node crossings. . The period during which the Sun
is near a node is called an eclipse season. There are two eclipse seasons in a
year.

If the line of nodes were fixed in space, eclipse seasons
will take place at the same time each year, six months apart from the previous.
In actual fact, the line of nodes drifts westward slowly at a rate of about 19
degrees a year. Thus, eclipse seasons will occur every 173.3 days and two eclipse
seasons will constitute to an eclipse year of 346.6 days, which is 18.6 days
less than a solar year but equal to the time required for the Sun to cross the
same node 2 times. In order to find a periodicity in the mechanics of solar
eclipses, there must be commensurability between the synodic
month and the eclipse year. Fortunately, 19 eclipse years are almost exactly
equal to 223 synodic months; they differ by only 11 hours. The coincidence is
all the more remarkable when compared to a period known as the anomalistic
month. This is also the time required for the Moon to pass from perigee to
perigee in approximately 27 1/2 days. The anomalistic month is important
because the Moon's geocentric distance is the main factor that determines the
annular or total nature of a solar eclipse. 239 anomalistic months are also
equal to 223 synodic months to within 6 hours. This is the origin of the famous
Saros cycle of 6585 1/3 days or 18 years. 11 days and 8 hours.

Any two eclipses separated by one
Saros cycle share very similar mechanical characteristics. They occur at the
same node with the Moon at the same distance from Earth and at the same time of
year. Because the Saros does not contain an integral number of days, its
biggest drawback is that subsequent eclipses are visible from different parts
of the globe. Although the 1/3 day displacement shifts the eclipse path 120°
westward with each cycle, the series goes back to the same geographic region
every 3 Saroses or 56 years and 34 days.

A Saros series does not last
indefinitely because the various periods are not perfectly commensurate with
one another. Particularly, 19 eclipse years are 1/2 day longer than the Saros.
This results in the node shifting eastward by about 0.5° with each cycle. A
typical Saros series commences when New Moon takes place at about 18 degrees
east of a node. If the first eclipse occurs at the Moon's descending node, the
Moon's umbral shadow will pass 3500 km below the Earth resulting in a partial
eclipse that may be visible from the South Polar region. On the following
return, the umbra will pass about 300 km closer to the Earth and a partial
eclipse of slightly larger magnitude will result. After ten or eleven Saros
cycles (about 200 years), the first central eclipse will occur near the south
pole of the Earth. Over the course of the next 950 years, a central eclipse
will occur at each Saros but will be displaced northward by an average of 300
km. Halfway through this period, eclipses of long duration will occur near the
equator. The last central eclipse of the series will occur near the North Pole.
The next ten eclipses will be partial with successively smaller magnitudes.
Finally, the Saros series will end some 13 centuries after it began at the
opposite pole. A typical series may comprise of 70 to 80 eclipses, among which
about 50 are central.

If a Saros series begins near the
ascending node, the first eclipse will be partial from the northern polar
region and the previous sequence of events is reversed. Since at least two
solar eclipses occur every year, there are obviously many different Saros
series in progress simultaneously. For instance, during the later half of the
twentieth century, there are 41 individual series and 26 of them are producing
central eclipses. As old series terminate, new ones are always beginning and
take their places. For instance, the total solar eclipses of 1925, 1943,1961,
1979, 1997, 2015 and 2033 are all members of Saros 120. The series began with a
partial eclipse at the South Pole in 915 AD. The 2033 event is the last central
eclipse of the series. Note that the paths of the last four eclipses grow
progressively broader as the umbral shadow cone passes closer to the limb of
the Earth. The next eclipse in the series will be a partial eclipse in 2051.
Saros 120 will end with a partial eclipse near the North Pole in 2195.