Selected Questions & Answers From All Experts Astronomy Forum (The Saros Cycle)

Diagram showing conditions for partial and total lunar eclipse.  These, as well as lunar eclipses, can be predicted using the saros cycle.

Question: Can you please explain the saros cycle and how it can be used to predict eclipses? - Rafael G., San Francisco, Calif.

Answer:  The "saros" represents a period which has been used as far back as the ancient Sumerians to predict eclipses.These predictions depend on: (1) Understanding that eclipses can occur in a series, i.e. such as one that commenced in 1599, and (2)An understanding of the relative motions of Earth and Moon and specifically observations of the Moon's period of rotation relative to: (i) the phase (synodic month) and ii) the position of the nodes or the points at which the Moon's and Earth's orbits intersect, and iii) the times of perigee, or the position at which the Moon in its orbit is nearest Earth.

For example, in order to get two identical lunar eclipses the Moon - in each case - would have to be:

a) At the same phase (e.g. full, as shown in diagram A)

b) In the same position in its orbit with respect to the nodes

And:

c) At the same distance from Earth


Now, since the lengths of the months (periods for Moon's rotation) are different, i.e. synodic = 29. 5 days, nodical = 27.3 days and anomalistic = 27.5 days, then the resulting lunar eclipses will be of the same type only if an integral number of synodic months is nearly equal to an integral number of nodical months and an equal number of anomalistic months.

This also applies to solar eclipses. For example, in the diagram shown below:


We easily see why a total solar eclipse would only occur in the lower configuration with New Moon aligned to Earth and Sun as shown. In the upper case, the New Moons are slightly out of alignment because of the difference in synodic (29.5 days) and sidereal (or nodical= 27.3 d) months.  In this best case then we have the geometry:


So as the Moon moves relative to the Earth observer, the phases are observed as seen above.

Now, in the saros period it turns out there are 223 synodic months, 242 nodical months and 239 anomalistic months - each of which add up to approximately 18 years, 11 days.   This is an intervsal of the saros. Thus, at such intervals identical eclipses can be expected to occur. Also, successive eclipses separated by this interval are said to belong to the same "saros series". (Note that because the limits for umbral lunar eclipses are smaller than for solar eclipses, a saros series of lunar eclipses runs through only about 50 cycles, which requires about 870 years.)

Obviously, many differing eclipses can occur during the 18 -odd year period - meaning several distinct series are actually going on at the same time. Call them Series 1, Series 2, Series 3 etc.  Each series takes about 1, 200 years to complete during which time the eclipse paths gradually shift from one pole of the Earth to the other.

From what has been written it should be possible to see that the first solar eclipse in any series belonging to the saros cycle is a partial eclipse that occurs when the Sun and the Moon are at an eastern ecliptic limit.  (An "ecliptic limit" denotes the maximum angular distance the Sun can be from the nodes of the moon's orbit and still cause an eclipse.) 

If it is the descending node the eclipse is just barely visible near the South pole of Earth. If the eclipse is at the eastern limit of the ascending node, it is just visible at the North pole. To fix ideas as to the situation the diagram below is useful.


Note here the Moon's highest and lowest points in its orbit around Earth. The node that intersects the ecliptic plane (the plane of Earth's orbit) on the way up to the highest point is the "ascending node". The node which crosses the ecliptic plan en route to the lowest point is the "descending node".

After 223 synodic months the next eclipse in the series occurs, with the Moon just about 1/30 of a day's journey (or slightly under 1/2 degree), west of the same place relative to the node. Thus the eclipse occurs with the Sun and Moon about 1/2 degree farther inside the ecliptic limit. After about 70 successive eclipses separated by saros intervals, e.g. 70 x 18 yrs. (or about 1200 years) the positions of Sun and Moon at the times of the eclipses have shifted through the node to the western ecliptic limit and the series ends.   The first and last dozen eclipses are always partial ones, visible first at one polar region, then the other.