Eclipse cycle

An eclipse cycle, the repetition of solar eclipses or lunar eclipses is as a regular series of events that with a certain same time interval - are related to each other - the relevant darkness period. Different batches of the same characteristic period belong to the same cycle type, but may each comprise a different number of events darkness and run consecutively or overlapping.

Seen for the Earth as a whole, not earlier than 15 days just about an eclipse to occur, or vice versa after a lunar eclipse; and the earliest after about just 30 days - a lunation - may be followed by a lunar eclipse again a lunar eclipse or a solar eclipse, the next solar eclipse.

In general, however elapse between two suns or two lunar eclipses around six synodic months, and this period gives the semester cycle from solar or lunar eclipses. Before one ending its ranks, often an additional eclipse takes place after five synodic months, with a new series begins.

All events listed in the Canon of eclipses according to their temporal sequence can be assigned to the first semester cycle. The excerpt shown on the left shows selected data sets of each semester a series of forming solar eclipse dates.

The other darkness cycles are longer; they represent as readout cycles with a longer period selected rows is from the sequence of all eclipses and also refer a greater number of successive events, which are also of times to times only slightly different from each other.

4.1 Preset sizes
4.2 Node Distance change in the semester cycle
4.3 eclipse cycle number and duration of the semester cycle ( eclipses )

Special feature of darkness cycles

In a " pure" temporal cycle, repeat the events over an indefinite period. An example is the cycle of weekdays: Each of the seven days of the week is repeated with a period of seven days without limitation in the future.

A darkness cycle consists of series of events which are limited in time length and number of events. Such rows there are unlimited. Follow up, or made with more ( read- darkness cycles ) or less ( half cycle) overlap at the same time. The time offset is a deviant from the darkness period interval.

Unfortunately, both the parent darkness cycle, whose characteristic is the effective single rows within its darkness period, and each of these individual series is called the certain darkness cycle. Confusion are therefore not excluded. In the known Saros cycle, one tries to deal with the by each of its individual rows contains its own number. The solar eclipse of 11 August 1999 there was, for example, in the series with the number 145, briefly: the Saros cycle 145

Formation of read cycles

The principle of the formation of a readout cycle for solar and lunar eclipses the same. In the following sections first cycles of solar eclipses, and then features of eclipse cycles are treated.

The period of a readout cycle is an integer multiple of the synodic months. With increasing darkness period each row also contains a higher number of dark events, all of which are covered with the same period without interrupting each other. With increasing period, the respective difference to an integer multiple of half drakonitischen months is decreasing, that is, the change in the distance between the nodes is smaller individual events, and the events are thus similar to each other. The greater the darkness period was chosen, the more such long rows with the same period of time run parallel to each other.

With the eclipse period, the number of skipped darkness grows. Read-out condition is that the period contains an integer number as possible of a synodic months integer drakonitischer half months. Since eclipses can occur at close to the moon at each of the two nodes, the condition also applies to an integer drakonitischen months plus one half. In such cycles, the eclipses will find successively alternately held in proximity to the ascending or descending node. Suitable pairs of numbers of synodic months and drakonitischen can be found with continued fraction calculations.

A read cycle can start with any of darkness. For this reason there of a cycle with a certain period at the same time as many rows in addition darkness, like the darkness were not counted in the relevant readout. When Saros there are about 38 individual cycles at the same time, each provided with a different number. Principle, be recognized as a component of any cycle type any darkness, and be related to other eclipses with different certain period length. Read cycles can be arbitrarily large. There is no theoretical limit.

The following two figures show, for example, the Saros cycle compared to the semester cycle, the result of such selection.

Saros cycle

The number of eclipses contained in a series increases proportionally with the period, the duration of a series but is growing disproportionately and soon exceeds a human life significantly. Of the larger cycles of the Saros cycle still has practical significance (period 18.03 years, range with an average of 71 distributed over approximately 1270 years eclipses ), although an observer can see only five to six eclipses this cycle. An astronomer at the time of antiquity could at least watch three of them and carry out scientific assessments. Three Saros periods are the period of the Exeligmos ( Triple Saros ). Much of the importance of the Saros cycle is that with him the similarity of consecutive eclipses is not determined solely by the relatively small node distance change, but that the Saros is also nearly an integer multiple of anomalistic month, the moon So then each similarly Distance stands for ground.

For more read cycles

The marked ( *) cycles, the eclipses will find successively held alternately in proximity to on - or descending node.

Between semesters *) and Saros cycles Hepton *) (period 41 synodic months), Octon (47) Anonymos *) (88) and tritos *) ( 135 ) to order.

After the Saros follows the very large Inexzyklus *). Its period consists of 358 synodic months ( 28.95 years ). A Inexreihe contains about 23,400 years distributed solar eclipses, on average, 809. The Knotenditanz amounts to only 0.041 °.

Already in ancient times known long-period cycles are for example a cycle of the Maya ( 405 synodic months equal to 3 Tritosperioden equal to about 33 years old) and one of the Greeks (939 synodic months equal to just under 76 years ).

Assumptions and accuracy

The links provided are based on the assumption each a circular rather than an elliptical orbit of the earth and the moon and average values for their orbital periods. Thus, the values given for the period, number of eclipses and duration of the cycle are also mean values that are not sufficient for the detailed calculation of an eclipse, for the abstraction of the periodicity in cycles but adequate. The auxiliary variables node distance ( ecliptic angular distance between new or full moon and nodes) and darkness limit ( node distance, up to the can an eclipse occur ) are also averages.

The theoretical mean values are compared with statistical averages. The latter vary according to the evaluated in the statistics eclipses what is to be observed in the use of specimens taken from the literature values. As each new darkness never resembles an older, working with mean values is anyway not a free radical to arbitrariness.

Some calculations

Preset sizes

During a synodic month ( 29.53059 days ) the earth moves in its orbit 29.1067 ° (360 ° to 365.2422 days ), the line of nodes rotates in this time -1.5638 ° to the ecliptic (360 ° in 18,613 years ):

( D ÷ 29.53059 365.2422 d) · 360 ° = 29.1067 °,
( 29.53059 d ÷ ( 18,613 · 365.2422 d) ) · 360 ° = 1.5638 °.

Node distance change during semester cycle

After 6 synodic months, the Earth has come in its orbit 174.6402 ° ahead, the line of nodes has turned -9.3828 °. The new or full moon is 4.0230 ° (node distance change, ecliptic angle) come over the counter node addition:

174.6402 ° - ( -9.3828 ° ) - 180 ° = 4.0230 °.

Darkness cycle number and duration of the semester cycle ( eclipses )

With the eclipse limit ± 16.6 ° (average value, see entry in this figure) is the darkness index, on average 9.25, the cycle duration on average 4.5 years:

( 2.16 6 ° ÷ 4.023 ° ) 1 ≈ 9.25 ( 1, Because the number of interval boundaries = number of intervals 1 )
9.25 · 6 · 29.53059 d ≈ 4.5 years.

Geographical aspect of solar eclipses

The first and the last of a series eclipses are partial and are held in one of the two polar regions of the earth. In between, they are central ( total or annular) and are shifting gradually over all latitudes, until they stop in the opposite polar region. Find the darkness, alternating with the on - or descending node (*) instead, there is a series of two nested sub-series, the one from south to north, the other runs north to the south of those.

For a negative value for the node distance change the darkness series runs in a westerly direction with respect to the node. On Earth, its course between the polar regions is reversed to a number of positive nodes distance change.

Total and annular solar eclipses total -

The darkness in the middle of a row are total or annular. The majority are either total or annular, when the period is an integer multiple of the anomalistic month (mean of 27.55455 d) is also approximate. This condition is well fulfilled when Hepton and the Saros:

Hepton: 41 · 29.53059 d = 1210.7542 d ≈ 43.94 anomalistic months,
Saros: 223 · 29.53059 d = 6585.3216 d ≈ 238.99 anomalistic months.

This property owes the Saros his goodness and awareness, it repeated very similar eclipses.

Cycle data in Summary

Multiples of darkness periods

The Mayan darkness known period of about 33 years is three times the Tritosperiode.

An integer extension of the Saros period leads to Exeligmos or Triple Saros periods with a duration of about 54 years ( 3.18 03 years ). Its importance lies in the fact that then a darkness almost at the same time of the day takes place as another 54 years before, because 669 synodic months are almost a whole number of days ( 669.29, 53059 d = 19'755, 965 d ≈ 19'756 d). The repetition of such eclipses is therefore observable from the same place, there is the maximum of the eclipse but about the same longitude. This fact was already known in ancient Greece. The important for the formation of lunisolar calendars moon circle shows a period of 235 synodic months, which is close to five times the period of the Octon with 47 synodic months. Because of this coincidence, the moon circles is often regarded as darkness cycle. But compared to the Saros period with similar length, it is an insignificant short cycle with only four or five eclipses. In extension of Octon period ( the average of 22.9 Eclipses contains ) to five times only every fifth darkness is counted namely. The moon circles thus covers only about half as many events as the otherwise darkness shortest cycle that semester.

The multiplication of the period reduces the number of darkness in the cycle set by the same factor.

Lunar eclipse cycles

Unlike eclipses by the umbra of the earth's penumbral lunar eclipses are not easily identify with the naked eye. In the Canon of Lunar Eclipses of Theodor Oppolzer they are therefore not listed ( see figure at right ). By contrast, the astronomical term covers both types of lunar eclipse and therefore the events of a barely perceptible darkening of the moon through the penumbra of the earth are in newer lineups also included.

The darkness has limit including the penumbral lunar eclipses with approximately ± 16.7 ° about the same value as that for solar eclipses, including the partial solar eclipses ( approximately ± 16.6 °). Cycles of lunar eclipses and those from solar eclipses are therefore approximately the same length and contain approximately the same number of events.

The darkness limit is approximately ± 10.6 ° is much smaller and the time window corresponding to close when the penumbral lunar eclipses are not counted. A lunar eclipse cycle number from the easily recognizable core shadow eclipses thus contains only about two-thirds of the events and is about a third shorter than a number, in which also the less visible eclipses will be counted. For the semester cycle, for example, this leads to a reduction to 5-6 eclipse events per row ( see figure at right ), instead of the otherwise 8-10 lunar eclipses counting rows (which may overlap similar to the semester cycle for solar eclipses, see figure at the top).

335292