Science: Eclipse Cycles


As described previously, an eclipse occurs when the Moon comes between the Earth and the Sun (a solar eclipse), or the Earth comes between the Moon and the Sun (a lunar eclipse). Since the Moon orbits around the Earth, as we described in The Earth and Moon, it's easy to see how this can occur. However, if it was that simple, there would be a total solar eclipse once every month, at the New Moon, and a total lunar eclipse every Full Moon; and this isn't the case. So, in fact, it must be more complicated than that; and sure enough, it is!

The good news is that it's not too complicated; and in any case, you don't have to understand any of this to enjoy an eclipse! But if you're interested in the mechanics behind an eclipse, read on.

The Earth and the Sun

First, a little terminology. As the Earth circles around the Sun (actually, the Earth's orbit is slightly elliptical, but never mind for now), it stays within a flat plane, known as the ecliptic. When imagining the workings of the Solar System, it is conventional to think of the plane of the ecliptic as being horizontal, with the North Pole of the Earth pointing "up".

Think of it like this: put an orange in the middle of a table to represent the Sun, and a grape towards the side of the table representing the Earth. As the Earth moves in its orbit around the Sun, it stays on the table top; so the table represents the ecliptic.

This is exactly the same arrangement we described in The Earth and Moon; all we've done so far is added the name of the ecliptic plane. Now, though, we have to add one little wrinkle we haven't seen yet -- the Moon's tilted orbit.

The Tilted Moon

Now, you can represent the Moon's orbit by putting a pea near the Earth, circling around it (although the Moon's orbit is actually even less of a circle than the Earth's). Fair enough, it seems; the Moon orbits the Earth in the plane of the ecliptic, just like the Earth orbits the Sun.

Unfortunately, though (for simplicity's sake), this isn't actually true; the Moon's orbit is, in fact, tilted slightly off the ecliptic. The centre of the Moon's orbit is the Earth, of course, which is on the ecliptic; so as the Moon orbits, it alternately dips below, and then rises above, the ecliptic.

Intersecting Planes

This diagram (which is, again, on a wildly exaggerated scale) tries to illustrate this:

Here the ecliptic plane is represented by the translucent green and blue checkerboard, with the Sun in the centre, and the Earth moving in its orbit within the ecliptic; the Earth's orbit is shown in blue. The plane of the Moon's orbit is shown as the tilted red and yellow checkerboard (in reality, it's only tilted by about 5 degrees), with the Earth being the blue and white ball in its centre. The Moon is shown in white, and its orbit is shown as a white line.
 


You'll notice two red blobs drawn on the Moon's orbit. These represent the point where the Moon's orbit crosses the ecliptic plane, and are referred to as nodes. Now, an eclipse can only occur when the Moon is in line with the Earth and Sun; but a line from the Earth to the Sun -- drawn here in purple -- lies along the ecliptic. So, an eclipse can only occur when the Moon is in (or near) the ecliptic; and that means that it has to be at, or near, one of the two nodes, and that node has to be positioned in line with the Earth and the Sun.

As the whole Earth-Moon system orbits around the Sun every year, the two nodes will find themselves aligned with the Earth and Sun (one in between, and one "behind" the Earth) twice a year; this means that there are two times each year when we can get an eclipse. Because the node doesn't have to be exactly lined up to cause an eclipse, there is actually a period of 37 days during which an eclipse can occur. These times -- when one of the Moon's nodes is approximately in line between the Earth and Sun, so there is the possibility of an eclipse -- are called eclipse seasons.

As the Moon goes round the Earth, if it passes through either node during an eclipse season, an eclipse will occur; a solar eclipse if the new Moon passes the node between the Earth and Sun, or a lunar eclipse if the Full Moon passes the other node. Furthermore, if the Moon is (more or less) exactly at that node at the middle of the eclipse season, the eclipse will be total (or maybe annular, for a solar eclipse) as seen from some part of the Earth.

As a matter of fact, the Moon's orbit itself is gradually rotating on its axis, with the effect that the nodes gradually rotate around the Earth. For this reason, an eclipse season happens a little more often than every six months; in fact, every 173 days.

Cycles Within Cycles

OK, so we get eclipses every 6 months (or slightly less), right? Right! But what we don't get is identical, or even similar, eclipses every 6 months. For example, as you can see from my solar eclipse list, the hybrid eclipse of November 3 2013, up in the northern hemisphere, is followed 6 months later by a tiny annular eclipse on April 29 2014, visible in the low southern hemisphere. In general, if you look at the eclipse maps there, you'll see that successive eclipses are scattered all over the globe. So how come?

Well, the answer is that there are even more cycles at work. For example, the time the Moon takes to go from New to New (a Synodic Month) is different (due to the movement of the nodes) from the time it takes to travel from one node, around its orbit, and back to the same node again (a Draconic Month).

The end result of all of this is that these various cycles mesh together to produce the same set of circumstances -- and hence a similar eclipse -- every 18 years and 10 or 11 and a third days. (Whether it's 10 or 11 days depends on how many of the 18 years are leap years). Amazingly enough, this period was actually discovered 2,500 years ago, by Babylonian astronomers; it's called the Saros, meaning "repetition".
You can, if you like, read more about the lunar months, and the cycles behind the Saros.

A Saros series is, then, a series in which similar eclipses happen every 18 years 10/11 and a third days. But of course, eclipses happen more often than that; the explanation is that there are many combinations of circumstances that can produce an eclipse. So, there are, at any one time, 42 Saros cycles running at once; this results in a bit more than 2 eclipses per year.

Each Saros series has a number to identify it -- for example, the August 11 1999 eclipse belongs to Saros series 145. Eclipses within a Saros series are similar to each other, but different to eclipses of other series -- they happen in different parts of the Earth, or are partial as opposed to total, etc. (Even within a Saros series, though, successive eclipses don't occur in the same place; the answer to that is the Triple Saros.)

One last complication -- the Saros cycle itself isn't perfect; the various lunar cycles don't quite mesh up perfectly. For this reason, successive eclipses in a Saros series are shifted slightly either north or south (depending on the particular Saros) from each other. This means that a Saros series is actually of limited duration -- about 70 to 85 eclipses over 1,200 to 1,500 years. Each series starts with a small partial eclipse in either the north or south polar regions; as the shadows of the successive eclipses move farther into the Earth, the first total eclipse will be seen near the polar regions. The eclipses of the series then march down or up the Earth, until the last total eclipse, and then a series of diminishing partial eclipses, occurs at the opposite pole to where the series started; and then it ends.

Eclipses may occur repeatedly, separated by some specific interval of time: this interval is called an eclipse cycle. The series of eclipses is called an eclipse series.

1 General explanation

1.1 Eclipse conditions

Eclipses may occur when the Earth and Moon are on one line with the Sun, and the shadow of one body cast by the Sun falls on the other. So at New Moon (or rather Dark Moon), when the Moon is in conjunction with the Sun, the Moon may pass in front of the Sun as seen from a narrow region on the surface of the Earth. At Full Moon, when the Moon is in opposition with the Sun, the Moon may pass through the shadow of the Earth, which is visible from the night half of the Earth.

Note: conjunction and opposition of the Moon together have a special name: syzygy (from Greek for "junction"), because of the importance of these lunar phases.

Now an eclipse does not happen at every New or Full Moon, because the plane of the orbit of the Moon around the Earth is tilted with respect to the plane of the orbit of the Earth around the Sun (the ecliptic). This inclination is on average about:

I = 5°09'

Compare this with the relevant apparent mean diameters:

Sun: 32' 2"

Moon: 31'37" (as seen from the surface of the Earth right beneath the Moon)

and: 1°23' for the diameter of the shadow of the Earth at the position of the Moon.

So at most New Moons the Earth passes too much North or South of the shadow of the Moon, and at most Full Moons the Moon misses the shadow of the Earth. Also most of the time the Moon will not be able to fully cover the Sun, but because of the elliptic orbit it sometimes is nearer and looks bigger. In any case, the alignment must be perfect to cause an eclipse.

An eclipse can only occur when the Moon is close to the plane of the orbit of the Earth, i.e. when its ecliptic latitude is small. This happens when at the time of the syzygy, the Moon is near one of the two nodes of its orbit on the ecliptic. Of course the Sun is also near a node at that time: the same node in case of a solar eclipse, the opposite node in case of a lunar eclipse.

1.2 Recurrence

Now the time it takes for the Moon to return to a node, the so-called draconic month, is less than the time it takes for the Moon to return to the Sun: the synodic month. The reason is that the orbit of the Moon precessesPrecession (also called gyroscopic precession is the phenomenon by which the axis of a spinning object (e. a part of a gyroscope) "wobbles" when a torque is applied to it. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can backward with respect to the ecliptic, and makes a full circle in somewhat less than 9 years. The difference in period between synodic and draconic month is about 2 + 1/3 days. Likewise, the Sun passes both nodes as it moves over the ecliptic. The period to return to the same node is called eclipse year , and is about 1/9th year shorter than a sidereal yearThe sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. The sidereal year is the orbital period of Earth. A sidereal year equals 365. 2564 mean solar days. The sidereal year is 20 minutes a because of the precession of the nodes of the Moon's orbit in about 9 years.

So if a solar eclipse occurs at one New Moon, so close to a node, then at the next Full Moon the Moon is already over a day past its opposite node, and may or may not miss the Earth's shadow. By the next New Moon it is even further ahead of the node, and it is more unlikely that there will be a solar eclipse somewhere at Earth. By the next month, there will certainly be no event.

However, about 5 or 6 lunations later the New Moon will fall close to the opposite node. In that time (half an eclipse year) the Sun has moved to the opposite node too. Now the circumstances are suitable again for one or more eclipses.

So eclipses can occur in a one- or two-month period twice a year, around the time when the Sun is near the nodes of the Moon's orbit.

1.3 Periodicity

These are still rather vague predictions. However we know that if an eclipse occurred at some moment, then there will occur an eclipse again S synodic months later, if that interval is also D draconic months, where D is an integer number (return to same node), or an integer number + 1/2 (return to opposite node). So an eclipse cycle is any period P for which approximately holds:

P = S×(synodic month length) = D×(draconic month length)

Given an eclipse, then there is likely to be another eclipse after every period P. This remains true for some limited time, because the relation is only approximate.

Another thing to consider is that the motion of the Moon is not a perfect circle. Its orbit is distinctly elliptic, which means that the Moon's distance from the Earth varies. This changes the apparent diameter of the Moon, and therefore influences the chances, duration, and appearance of an eclipse. This orbital period is called the anomalistic month, and together with the synodic month causes the so-called " full moon cycleThe full moon cycle (the abbreviation fumocy was introduced by in the CALNDR-L mailing list in October 2002) is a cycle of about 14 lunations over which full moons vary in apparent size. Also in the same cycle the age of the full moon (time since new moon" of about 14 lunations in the timings and appearances of Full (and New) Moons. The perturbations of the orbit may change the times of the syzygies by up to 14 hours, and change the apparent diameter by about 6% in either direction. An eclipse cycle will have to be close to an integer number of anomalistic months for predicting eclipses well.

The periodicity and recurrence of eclipses is governed by the saros cycle, a period of approximately 6,585.3 days (18 years 11 days 8 hours). It was known to the Chaldeans as a period when lunar eclipses seem to repeat themselves, but the cycle is applicable to solar eclipses as well.

The saros arises from a natural harmony between three of the Moon's orbital periods:


Synodic Month (new moon to new moon) 29.53059 days = 29d 12h 44m


Draconic Month (node to node) 27.21222 days = 27d 05h 06m


Anomalistic Month (perigee to perigee) 27.55455 days = 27d 13h 19m


One saros is equal to 223 synodic months. However, 242 draconic months and 239 anomalistic months are also equal to this same period (to within a couple hours)!

Any two eclipses separated by one saros cycle share very similar geometries. They occur at the same node with the Moon at nearly the same distance from Earth and at the same time of year. Because the saros period is not equal to a whole number of days, its biggest drawback is that subsequent eclipses are visible from different parts of the globe. The extra 1/3 day displacement means that Earth must rotate an additional ~8 hours or ~120º with each cycle. For solar eclipses, this results in the shifting of each successive eclipse path by ~120º westward. Thus, a saros series returns to about the same geographic region every 3 saroses (54 years and 34 days).

A saros series doesn't last indefinitely because the three lunar months are not perfectly commensurate with one another. In particular, the Moon's node shifts eastward by about 0.5º with each cycle. A typical saros series for a solar eclipse begins when new Moon occurs ~18° 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 Earth and a partial eclipse will be visible from the south polar region. On the following return, the umbra will pass ~300 km closer to 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 Earth. Over the course of the next 950 years, a central eclipse occurs every 18.031 years (= 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 occurs near the north pole. The next approximately ten eclipses will be partial with successively smaller magnitudes. Finally, the saros series will end a dozen or more centuries after it began at the opposite pole. Due to the ellipticity of the orbits of the Earth and Moon, the exact duration and number of eclipses in a complete saros is not constant. A series may last 1226 to 1550 years and is comprised of 69 to 87 eclipses, of which about 40 to 60 are central (i.e., total or annular).

Solar eclipses that take place near the Moon's ascending node have odd saros numbers. Each succeeding eclipse in a series shifts progressively southward with respect to the center of the Earth. On the other hand, solar eclipses occurring near the Moon's descending node have even saros numbers. Each succeeding eclipse in a series shifts progressively northward with respect to the center of the Earth. The numbering system used for the saros series was introduced by the Dutch Astronomer G. van den Bergh in his book Periodicity and Variation of Solar (and Lunar) Eclipses (Tjeenk Willink, Haarlem, Netherlands, 1955). He assigned the number 1 to a pair of solar and lunar eclipse series that were in progress during the second millennium BC.

Understanding the numbering sequence of the saros is complicated by the fact that it does not depend on when a series either begins or ends. Instead, the numbering is determined by the order in which each series peaks. In this context, the peak of a series occurs when the umbral shadow axis passes closest to the center of the Earth. Since the duration of each series varies up to several hundred years and the numbering is keyed to the order in which each series peaks, this explains why the first eclipse of a series which peaks later can actually preceed the first eclipse of a series that peaks earlier. From the solar eclipse catalogs, the column labeled Gamma is the parameter that gives the minimum distance (in Earth radii) of the shadow axis from the center of Earth during each eclipse. Gamma is positive or negative depending on whether the shadow axis passes north or south of Earth's center. Looking at any of the saros catalogs (e.g., Saros 145) one can see how the value of gamma changes with each eclipse in a series. When gamma reaches its minimum (absolute) value, the series is then at its peak. In the case of Saros 145, the peak occurs with the eclipse of 2342 Mar 08 (gamma=0.008).

Since there are two to five solar eclipses every year, there are approximately forty different saros series in progress at any one time. 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 beginning and take their places.

To illustrate, the ten central solar eclipses of 1891, 1909, 1927, 1945, 1963, 1981, 1999, 2017, 2035 and 2053 are all members of Saros 145. The series began with a partial eclipse near the north pole in 1639. The first central eclipse of the series was an annular eclipse in 1891. It was followed by another annular in 1909. The next event was the first total eclipse in 1927. The total solar eclipse of 1999 August 11 is number 21 of 77 eclipses in Saros 145, and it is the 5th of 41 total eclipses in the series. Each of the subsequent total eclipses shifts southwards. The last total eclipse occurs in 2648 near the south pole. The last eclipse of the series takes place in 3009. Table of Saros 145 gives details for every eclipse in the series.

The saros cycle for lunar eclipses operates analogously with the solar eclipse saros. For lunar eclipses, the parameter gamma is the Moon's minimum distance measured with respect to the axis of Earth's shadow (units of Earth radii). Note however, that the saros numbering is opposite to that for solar eclipses. Lunar eclipses occurring near the Moon's ascending node have even saros numbers. Each succeeding eclipse in a series shifts progressively southward with respect to the axis of Earth's shadow. Correspondingly, lunar eclipses occurring near the Moon's descending node have odd saros numbers. Each succeeding eclipse in a series shifts progressively northward with respect to the axis of Earth's shadow.

Another significant eclipse cycle is the inex, a period of 358 synodic months (29 years minus about 20 days, or nearly 10,752 days). The inex is useful because it marks the time interval between consecutively numbered saros series. To see a diagram illustrating the relationship between the saros and inex cycles over a period of 26,000 years, visit the Saros-Inex Panorama page.

Baan maan tilted 5 graden en is ook nog eliptisch

As a matter of fact, the Moon's orbit itself is gradually rotating on its axis, with the effect that the nodes gradually rotate around the Earth. For this reason, an eclipse season happens a little more often than every six months; in fact, every 173 days. if you look at the eclipse maps there, you'll see that successive eclipses are scattered all over the globe. So how come?

Well, the answer is that there are even more cycles at work. For example, the time the Moon takes to go from New to New (a Synodic Month) is different (due to the movement of the nodes) from the time it takes to travel from one node, around its orbit, and back to the same node again (a Draconic Month).

The end result of all of this is that these various cycles mesh together to produce the same set of circumstances -- and hence a similar eclipse -- every 18 years and 10 or 11 and a third days.

A lunar eclipse occurs whenever the Moon passes through some portion of the Earth's shadow. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, there is always a full moon the night of a lunar eclipse. The type and length of an eclipse depend upon the Moon's location relative to its orbital nodes. The next total lunar eclipse occurs on December 21, 2010. The next eclipse of the Moon is a penumbral eclipse on July 7, 2009.

The shadow of the Earth can be divided into two distinctive parts: the umbra and penumbra. Within the umbra, there is no direct solar radiation. However, as a result of the Sun's large angular size, solar illumination is only partially blocked in the outer portion of the Earth's shadow, which is given the name penumbra.

A penumbral eclipse occurs when the Moon passes through the Earth's penumbra. The penumbra does not cause any noticeable darkening of the Moon's surface, though some may argue it turns a little yellow. A special type of penumbral eclipse is a total penumbral eclipse, during which the Moon lies exclusively within the Earth's penumbra. Total penumbral eclipses are rare, and when these occur, that portion of the Moon which is closest to the umbra can appear somewhat darker than the rest of the Moon.

A partial lunar eclipse occurs when only a portion of the Moon enters the umbra. When the Moon travels completely into the Earth's umbra, one observes a total lunar eclipse. The Moon's speed through the shadow is about one kilometer per second (2,300 mph), and totality may last up to nearly 107 minutes. Nevertheless, the total time between the Moon's first and last contact with the shadow is much longer, and could last up to 3.8 hours. The relative distance of the Moon from the Earth at the time of an eclipse can affect the eclipse's duration. In particular, when the Moon is near its apogee, the farthest point from the Earth in its orbit, its orbital speed is the slowest. The diameter of the umbra does not decrease much with distance. Thus, a totally-eclipsed Moon occurring near apogee will lengthen the duration of totality.

A selenelion or selenehelion occurs when both the Sun and the eclipsed Moon can be observed at the same time. This can only happen just before sunset or just after sunrise, and both bodies will appear just above the horizon at nearly opposite points in the sky. This arrangement has led to the phenomenon being referred to as a horizontal eclipse. It happens during every lunar eclipse at all those places on the Earth where it is sunrise or sunset at the time. Indeed, the reddened light that reaches the Moon comes from all the simultaneous sunrises and sunsets on the Earth. Although the Moon is in the Earth's geometrical shadow, the Sun and the eclipsed Moon can appear in the sky at the same time because the refraction of light through the Earth's atmosphere causes objects near the horizon to appear higher in the sky than their true geometric position.

The Moon does not completely disappear as it passes through the umbra because of the refraction of sunlight by the Earth's atmosphere into the shadow cone; if the Earth had no atmosphere, the Moon would be completely dark during an eclipse. The red colouring arises because sunlight reaching the Moon must pass through a long and dense layer of the Earth's atmosphere, where it is scattered. Shorter wavelengths are more likely to be scattered by the small particles, and so by the time the light has passed through the atmosphere, the longer wavelengths dominate. This resulting light we perceive as red. This is the same effect that causes sunsets and sunrises to turn the sky a reddish colour; an alternative way of considering the problem is to realise that, as viewed from the Moon, the Sun would appear to be setting (or rising) behind the Earth.

The amount of refracted light depends on the amount of dust or clouds in the atmosphere; this also controls how much light is scattered. In general, the dustier the atmosphere, the more that other wavelengths of light will be removed (compared to red light), leaving the resulting light a deeper red colour. This causes the resulting coppery-red hue of the Moon to vary from one eclipse to the next. Volcanoes are notable for expelling large quantities of dust into the atmosphere, and a large eruption shortly before an eclipse can have a large effect on the resulting colour.

The following scale (the Danjon scale) was devised by André Danjon for rating the overall darkness of lunar eclipses:

L=0: Very dark eclipse. Moon almost invisible, especially at mid-totality.
L=1: Dark Eclipse, gray or brownish in colouration. Details distinguishable only with difficulty.
L=2: Deep red or rust-colored eclipse. Very dark central shadow, while outer edge of umbra is relatively bright.
L=3: Brick-red eclipse. Umbral shadow usually has a bright or yellow rim.
L=4: Very bright copper-red or orange eclipse. Umbral shadow is bluish and has a very bright rim.

Every year there are usually at least two partial lunar eclipses, although total eclipses are significantly less common. If one knows the date and time of an eclipse, it is possible to predict the occurrence of other eclipses using an eclipse cycle like the Saros cycle. Unlike a solar eclipse, which can only be viewed from a certain relatively small area of the world, a lunar eclipse may be viewed from anywhere on the night side of the Earth.


Recent and upcoming lunar eclipse events
March 3, 2007, lunar eclipse - The first total lunar eclipse of 2007 occurred on March 03, 2007, and was partially visible from the Americas, Asia and Australia. The complete event was visible throughout Africa and Europe. The event lasted 01h:15m, began at 20:16 UTC, and reached totality at 22:43 UTC.
August 2007 lunar eclipse - August 28, 2007, saw the second total lunar eclipse of the year. The initial stage began at 07:52 UTC, and reached totality at 09:52 UTC. This eclipse was viewable form Eastern Asia, Australia and New Zealand the Pacific, and the Americas.
February 2008 lunar eclipse - The only total lunar eclipse of 2008 occurred on February 21, 2008, beginning at 01:43 UTC, visible from Europe, the Americas, and Africa.
The next partial eclipse of the Moon will occur on December 31, 2009.
The next total eclipse of the Moon will occur on December 21, 2010.

Posted by AstronomyandScience at 6:44 PM