Metonic Research Articles

Examining the Impact of the Book of Enoch, Sefer Yetzirah, and Greek Civilization on the Jewish Calendar System: An Islamic Astronomical Law Perspective

This article analyzes changes in the reference system of the Jewish Calendar. Initially, the Jewish Calendar reference was based on the movement of the Sun. However, the calendar system used by the Jewish community worldwide now refers to two celestial objects, the Sun and the Moon. This study is literature research with a qualitative approach and uses the Book of Enoch and the Sefer Yetzirah as primary sources. The authors found that the first reference system of the Jewish Calendar, which was based on the movement of the Sun (Solar), follows the description in the Book of Enoch and the Sefer Yetzirah. These two books explain the calendar system used by Prophet Idris to Prophet Moses. The Solar Calendar reference system was later replaced with the Lunar Calendar in the second century BCE. Six centuries later, the Jewish Calendar returned to using a Solar Calendar combined with the Lunar Calendar, known as the Lunisolar Calendar. The latest reference system is a mathematical calendar with the Metonic cycle that refers to the movement of the Sun and Moon. The authors argue that the influence of the Greek civilization and the adjustment of the difference between the Lunar and Solar Year caused the changes in the reference system of the Jewish Calendar.

Revisiting the Spawning Pattern of Nyale Worms (Eunicidae) Using the Metonic Cycle

Mass spawning dates of nyale worms (Eunicidae) have been scientifically predictable since 2019. The month of spawning is consistently following the pattern of the February full moon, while the date of spawning is consistently on the 20th of the lunar calendar. There are particular years with February only spawning, March only spawning, and split spawning in both February and March. The existing prediction of the split spawning, however, was constructed with very little available data. The present study aimed to revisit the split spawning prediction using the Metonic cycle, a 19-year lunisolar cycle. The results show that the spawning prediction very much follows the Metonic Cycle. There are minor dates on split spawning to be revised, when February full moon rises on 14th February. The revised hypothesis is that split spawning is very likely to occur when the full moon rises between the 7th to 13th of February. When February full moon appears before the 7th of February, single spawning will take place on the fifth day after the March full moon. When February full moon befalls after the 13th of February, single spawning will occur on the fifth day after the February full moon. The revised prediction method has only 2 (two) deviances in 114 years of simulation dates. The present study is the first to suggest the link between Polychaete spawning patterns and the Metonic Cycle.

Introduction of a New Cycle in Replacement of Metonic: An Ideal Solution towards a Deviation Free Luni-Solar Calendar

Molad is simply an interval between two successive new moon timelines with respect to the line joining the Sun and the Earth i.e., with respect to the Sun as seen from the Earth, which in scientific terms is referred as lunation or “synodic lunar month”. Though synodic lunar month may vary by up to ±0.7 days locally, the length of mean synodic lunar month is constant over a long period of time and is a crucial value in determining the luni-solar calendar’s new months similar to Hebrew calendar’s “Rashei Hodesh”. Based on the Metonic cycle the luni-solar Hebrew calendar adds 07 intercalary months in 19 solar years. This hypothesis proposes a new cycle instead of the Metonic cycle towards eliminating the deviation of the calendar incurred in the long course of time. The research analyzed that application of the conventional Metonic cycle to luni-solar calendar is erroneous, which theoretically leads Hebrew calendar to absorb extra 11 days (approx.) by 2053 years after inception. The study pointed out that through the application of 2116 - 2053 lunar-solar years cycle instead of 235 - 228 lunar-solar months based Metonic cycle, formulation of a far better high precession luni-solar calendar is possible and also both lunar and solar sides of the luni-solar calendar became fully balanced and harmonized.

Farmers in the Marsh: Lessons from History and Case Studies for the Future by Susan C. Adamowicz and others

Salt marshes across coastal New England are undergoing rapid change characterized by increased areas of saturation resulting in shifts in vegetation communities, large areas of vegetation dieback, and increases in shallow standing water. In the early 2000s, gently sloped leading edges of salt marshes (“low marsh” dominated by Spartina alterniflora and flooded daily) began to be lost from Maine to Connecticut. More marsh edges are now “cliff-faced” with steep, vertical edges often characterized by peat calving. In many places, the “high marsh” (the irregularly flooded marsh platform normally dominated by Spartina patens, Distichlis spicata, and Juncus gerardii, as well as forbs) has been overtaken by short- (<0.10 m) to intermediate- (>0.60m – 1.0 m) form S. alterniflora, bare patches, and large areas of shallow standing water. The marsh platform between the ubiquitous ditches has subsided. In extreme cases, the marsh has ‘collapsed’ and now holds shallow water in a mega-pool with the only vegetation occurring along the ditch margins, in a “waffle-maple syrup” pattern. Elsewhere, the mega-pool becomes large and amorphous or interlocking in a jig-saw puzzle fashion suggestive of northern patterned fens with strings and flarks. While a few researchers have documented traits and trajectories of “natural” pools, the relatively sudden appearance and geographic extent of these changes suggests large-scale drivers. At the same time, research into historical salt marsh alterations for farming purposes dating as far back as the 1600s with large corporate works in the 1800s, has led this team to realize that remnant infrastructure from past agriculture coupled with accelerated sea-level rise is driving wide-scale salt marsh degradation. Tidal marsh obligate birds, such as the saltmarsh sparrow, which nest in narrow portions of “high marsh”, are at increasing peril from the loss of marsh elevation due to subsidence trajectories exacerbated by a heretofore largely unrecognized historical agricultural infrastructure. With species extinction modelled at 2050 and a metonic cycle shifting toward increasing tide ranges in 2024, it is imperative to halt subsidence trajectories by re-balancing marsh hydrology to optimize vegetation, accretion, and elevation gain. Obligate wildlife species and their habitats can then be supported over the long-term through the development of strategic management plans for each salt marsh system. Following a review of the historical literature, which documents the breadth of standardized farming practices, we identify these features on several sites, then present a four-step process to restore hydrologic function using innovative restoration practices at two case studies located in Rhode Island and Massachusetts, USA.

Lunisolar Calendars, the Antikythera Mechanism, the Halieia of Rhodes and some thoughts on the Calendars of Rhodes and Kos

This paper will discuss the logic, history and development of lunisolar calendars, including the octaëteris, the Metonic Cycle and Callippic Cycle periods (particularly how the latter two are employed on the Antikythera Mechanism), as well as the years, season, history and events of the Halieia games of Rhodes (which are also attested on the Antikythera Mechanism). It will also discuss the order and seasons of the months and the day-nomenclature of the calendars of Rhodes and Kos as well as their semester systems. Here it will be argued that there were two separate calendars in operation with different starting points at both these city-states an Eponymous Calendar-Year and a Bouleutic Calendar-Year. The paper will also discuss the intercalary month Πάναμος δεύτερος at Rhodes along with various theories concerning the Διπανάμια festival there. Finally, the paper will conclude by analyzing the years in which several Rhodian festivals were celebrated, based upon which several Rhodian inscriptions will be redated.

The influence of Hipparchus in Antikythera mechanism

Around 1900, a group of sponge divers, pulled out from an ancient Roman shipwreck, near the Antikythera island, a piece of a hardly distinguishable geared mechanism which is known since then as “The Antikythera mechanism”. Until now the exact use of some of its survived gears is investigated and there are speculations about its missing parts. In 2005 two revolutionary technical methods were applied on Antikythera mechanism. The first is known as : (3D) X-ray computed tomography (CT) by X-Tek Systems Ltd, with the use of which many hidden details under the corrosion, came to light. The second is known as : Polynomial Texture Mapping (PTM) which was applied by HP Labs, revealing engraved symbols and letters on Antikythera mechanism surfaces. After all these years of research, a more comprehensive picture of this machinery was built, leading to the conclusion that it was used as a multi functional “astronomical calculator” according to Freeth et al. (2006b) with many impressive capabilities such as:•a prediction of upcoming Solar and Lunar eclipses•a calculator of the four astronomical cycles (Metonic cycle, Callippic cycle, Saros cycle, Exeligmos cycle)•moon phases indication•Sun and Moon position in zodiacThe whole mechanical construction seemed covered by a wooden case with a front and a back door with engraved inscriptions on them. According to Freeth et al. (2006b) “The inscriptions support suggestions of mechanical display of planetary positions” proving the existence of a missing planetary subsystem. In this decrypted text, according to Freeth et al. (2006b), astronomical terms have been recognized like stations ▪ like statio,conjunctions and according to Jones (2017), there are references about the names of the five known planets. Researchers are trying for years to present planetary activity on their models suggesting different solutions with a common characteristic. In all models of planetary motion, the epicyclic theory is applied. Although this theory is precise enough for planets with negligible eccentricity, fails to demonstrate the real recorded apparent orbit of planets with significant eccentricity, like Mercury’s which is 0.205. On the other hand in Antikythera mechanism remains, there is an advanced device, known as the “pin & slot”, which simulates the non-uniform motion of the moon. According to Moussas (2009)...The difference between Kepler’s predictions on the angular velocity of the Moon during the month and the mechanism’s prediction is of the order 1/400 .... So if the constructor used a specialized gearing to model the moon’s orbit eccentricity which is 0.0549 why not do the same for Mercury’s case with an eccentricity of 3.7 times bigger? Many speculations about the Antikythera mechanism’s purpose have already been expressed, but nevertheless, accuracy is its undeniable feature which should be reflected in the mechanism’s astronomical indications. So, there’s a question that might be answered. ”Is it possible, the planets eccentricity can be simulated using the pin & slot device?”. This research tries to find an answer and proposes a feasible epicyclic gearing which can simulate the geocentric apparent path of Mercury. The construction is taking seriously the planet’s eccentricity, trying to minimize the discrepancy between expected and indicated measurements. Our proposal is based on theories known at the time Antikythera mechanism was constructed.

Regional Particularities of the Metonic Meteorological Cycle on Earth

Abstract This paper intends to demonstrate that, on Terra's surface, there are cycles of air's temperature and of other meteorological elements having a duration of 19 years (the Metonic cycle). These 19-year cycles are recorded on every continent, especially in temperate climate areas where the (planetary) Rossby waves exhibit very clearly. As in the case of other cycles of meteorological elements, the atmospheric tides play a very important role in their occurrence. In the case of this cycle, the atmospheric tides are also generated mainly by Moon’s and Sun’s attraction.

Analysis of Two-Segment Lunar Free-Return Trajectories

A precise and convenient procedure for designing the two-segment lunar free-return trajectory is presented in this paper. The trajectory characteristics are analyzed to support the lunar mission design associated with the higher inclination lunar approaches and safer returns from the moon. The concise procedure is established based on the matched conic model. An analytical algorithm is developed to compute the spacecraft state at the lunar sphere of influence to complete the conic matching. An iteration process is then adopted to generate favorable initial solutions that satisfy the constraints at injection, perilune, and Earth-entry interface. Orbital launch windows for departure from Earth, lunar encounter, and returns to Earth are established in the years 2024 and 2034. These years are chosen due to the moon’s inclination reaching a maximum in 2024 and it reaching a minimum in 2034 during a Metonic cycle. This novel trajectory enables greater lunar surface coverage than standard free-return trajectories. The trajectory can be used to lower the fuel consumption for high-latitude lunar orbiting and landing. In case a mission should be aborted in the lunar approach stage, the spacecraft can safely return without additional maneuvering. The initial trajectory is modified in a high-fidelity gravitational model and the results indicate that the difference is small and convergence is rapid.

A New Constellation Configuration Scheme for Communicating Architecture in Cislunar Space

A new constellation configuration is proposed to provide near-constant communications between any two points in the cislunar space. Four satellites were allocated on some natural orbits near points by a multiple shooting corrector numerically. The revisiting intervals between the successive revisits on specified points by the constellation are demonstrated both on the geographical maps of the Earth and the Moon, with a consideration of equatorial inclinations with respect to the Earth-Moon orbital plane. Moreover, the coverage periodicity on the Moon is induced by Metonic cycle of 19 years. Cost analysis on stationkeeping and launching is implemented for this constellation in detail. Finally, some aspects about communications, such as satellite links, delays, ground stations, and communication devices, are surveyed preliminarily.

The Metonic Cycle, Number Symbolism, and the Placement of Psalms 19 and 119 in the MT Psalter

This study explores the possibility that the scribe responsible for the final redaction of the MT Psalter knew about the Metonic Cycle, a 19-year calendrical system that synchronized the lunar and solar years, attributed a symbolic significance to the number 19 related to this number’s role in creating cosmological harmony in that system, and then used 19 as a symbolic number to inform the placement of Psalms 19 and 119 in the final redaction of the MT Psalter. A discussion of the contrastive content of Psalm 19 provides some warrant for looking to a number symbolism derived from the Metonic Cycle. Both the Metonic Cycle and Psalm 19 are thematically similar in that they harmonize two apparently different but cosmologically significant entities (sun and moon / creation and Torah). The proposal outlined in this study provides a theologically significant reason for the precise position of Psalms 19 and 119 in the MT Psalter and offers a suggestion for how this position may have subtly contributed to the Torah’s cosmological exaltation within the Psalter as a whole.

Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism

Previous research on the Antikythera Mechanism established a highly complex ancient Greek geared mechanism with front and back output dials. The upper back dial is a 19-year calendar, based on the Metonic cycle, arranged as a five-turn spiral. The lower back dial is a Saros eclipse-prediction dial, arranged as a four-turn spiral of 223 lunar months, with glyphs indicating eclipse predictions. Here we add surprising findings concerning these back dials. Though no month names on the Metonic calendar were previously known, we have now identified all 12 months, which are unexpectedly of Corinthian origin. The Corinthian colonies of northwestern Greece or Syracuse in Sicily are leading contenders-the latter suggesting a heritage going back to Archimedes. Calendars with excluded days to regulate month lengths, described in a first century bc source, have hitherto been dismissed as implausible. We demonstrate their existence in the Antikythera calendar, and in the process establish why the Metonic dial has five turns. The upper subsidiary dial is not a 76-year Callippic dial as previously thought, but follows the four-year cycle of the Olympiad and its associated Panhellenic Games. Newly identified index letters in each glyph on the Saros dial show that a previous reconstruction needs modification. We explore models for generating the unusual glyph distribution, and show how the eclipse times appear to be contradictory. We explain the four turns of the Saros dial in terms of the full moon cycle and the Exeligmos dial as indicating a necessary correction to the predicted eclipse times. The new results on the Metonic calendar, Olympiad dial and eclipse prediction link the cycles of human institutions with the celestial cycles embedded in the Mechanism's gearwork.

The Jewish Calendar \-\- A Mix of Astronomy and Theology

The lunisolar Jewish calendar is an example par excellence of "time engineering." It is based on the relation between the mean period of the lunar motion about the earth and the mean period of the earth about the sun (the tropical year). This relation is that, to six places of decimals, the number of days in 19 tropical years is equal to the number of days in 235 lunar cycles and is known as the metonic cycle. Moreover, the Jewish calendar, unlike our civil calendar, for example, is intertwined with the days of the week by virtue of the first day of Tishri (Rosh Hashanah) being allowed—for religious reasons—only to occur on Monday, Tuesday, Thursday, and Saturday. Because the metonic-cycle relation is not exact, there will eventually be a significant seasonal drift in holidays such as Passover unless the calendar construction is modified appropriately.

The hydrology of Piermont Marsh, a reference for tidal marsh restoration in the Hudson river estuary, New York

The topography, hydroperiod, water table, and selected edaphic characteristics are described for Piermont Marsh, an irregularly flooded tidal marsh in the Hudson River Estuary, New York, USA. Despite variations in microtopography, overall the marsh is flat, and although the observations were conducted at a high point in the Estuary's 18.6 year metonic cycle, its surface was only inundated 10–12 times a month. Observations of spatial differences in the saturated hydraulic conductivity and surface infiltration rates are also discussed. ‘Edge’ portions of the marsh are characterized by a slightly higher, more uniform, more structured, less organic, and less hydrologically conductive substrate than found in the marsh interior. Preferential flow is facilitated by macropores in the creekbank wall. The water table is close to the marsh surface for a lesser percentage of the lunar month in the marsh ‘edge’ when compared to the interior, where it is almost always within 10 cm of the surface. The extent to which the spatial variability of these hydrologic characteristics determines the marsh's ability to provide various ecosystem services is also discussed and the implications of these observations on tidal marsh restoration efforts briefly presented.

Accuracy of the Hebrew calendar

The present Hebrew (Jewish) calendar was put into effect by Hillel II in the year 358 C.E. [1]. Prior to that time, various sages imparted fundamental astronomical data with regard to the lengths of the lunation (synodic lunar month). The elders of the ruling judicial system established the calculations upon which (with corroborations by witnesses) declarations of the new moon were based. The destruction wrought by the Romans and dispersion of the people produced the need for a permanent calendar whose basis could be taught to skilled laymen. It still is complex, since the calendar months are lunar and yet, for example, Passover must occur in the Spring, a solar event. Thus, the Hebrew calendar must be in harmony with both the lunar and solar cycles. The fact that 19 mean solar years contain almost precisely 235 lunar months (the Metonic cycle) makes such a lunar/solar calendar possible. The accuracy of this calendar is examined. It is shown that despite the approximations necessary to provide a fixed calendar, the Hebrew calendar's mean lunar month duration discrepancy from current astronomical values (a small positive number) amounts to only one day in 14,000 years. More remarkable yet is that this error was less in the past, since there has been a decrease (very small) in the orbital period of the moon. Several research issues are formulated.

The Cuneiform Conception of Celestial Space and Time

The significance to the modern world of Mesopotamian celestial divination and astronomy cannot be overstated. The names and the ‘ominous’ values assigned to the heavenly bodies by the Mesopotamians underlie Western astrology, and have also influenced Indian astrology. Many of the key features in the astronomy of Hipparchus and Ptolemy, which later passed into the astronomy of the medieval world, were borrowed from the astronomers of Babylon and Uruk. The zodiac, the Metonic cycle, horoscopy, and a variety of astrological techniques are all first attested in Mesopotamia. The same goes for units, notably those divisions of space and time which are now used throughout the world (such as 60 minutes in an hour and 360° in a circle) which can be traced back to cuneiform antecedents.

Metonic Intercalations in Athens

~W~7~JHEN I published in 1940 the only known Attic decree naming in its preamble v v at least part of the name and demotic of the secretary of 298/7 I suggested that the calendar equation indicated an ordinary year of twelve months.' This determination was taken over by Pritchett and Meritt in Chronology of Hellenistic Athens (p. xvi), by Pritchett and Neugebauer in Calendars of Athens (p. 80), and by Meritt in The Athenian Year (p. 232). There is one consideration which at the time did not seem so important as it does now and which I wish to discuss here. The incentive to a reconsideration has been the observation that the sequence of ordinary and intercalary years which called for OOIOI in 299/8-295/4 rather than OIOOI at the beginning of the 8th Metonic cycle was the first apparent deviation from Meton's norm for possibly a hundred years, except for the anomaly in 307/6 which had valid and obvious historical reasons and which could be amply explained.2 I noted, as a comment on the cycles, that the eighth cycle has only the transposition of IO to OI in the years 298/7 and 297/6. 8 Otherwise the cycle in the festival calendar of Athens followed faithfully the normal Metonic cycle of intercalation. In the text of Hesperia, IX, 1940, pp. 80-83 (13), as now restored with a stoichedon line of 29 letters, the equation reads:

The Archonship of Charikles (196/5)

T HE archonship of Charikles (196/5) was intercalary in the festival calendar KaT' apxov1a of Athens.1 The evidence that it should be ordinary in the Metonic calendar KaaTa OEoIv was set forth in 1964,2 but the crucial evidence for the nature of the calendar KaT' a'pxovra was overlooked, and the assumption was made that the year was ordinary both Kar' a'pXovTa and KaTa OEOv. This, of course, is impossible in view of the explicit mention of the intercalated Posideon in I.G., II2, 785. For a time I thought that the calendar equations of this year could all be restored for an ordinary year Kcara ov, reading the date by month in I.G., IJ2, 785, as Ilocrt8EWvoa 4,83oX4ov V [EL KaLt vat], and assuming a late start (late by one month) for the Ka-&a IEo9v calendar. But an examination of the stone in Athens, kindly undertakenfor me by Malcolm McGregor, shows a trace of delta after the published letters epsilon nu. The date was Posideon II 11, and the prytanies were scaled to this intercalary year KaT' a'pXovTa. Such a relationship was frequent during the third and second centuries, diverging from the intercalations in the Metonic cycle. The three known equations of the year 196/5 are:

イラン暦の諸問題

There are three calendars of ancient Iran: the Old Avestan, Young Avestan and Old Persian calendars.Gathic people were aware of the lunar year as well as the solar and settled five important turns of season on the ecliptic while they made them adjust the solar vague year. It is probable that even a Metonic cycle was known to some extent.The young Avestan and the Old Persian calendars are the complex of the solar, lunar and lunisolar calendars.Problems of months of the beginning of the year, the five-day stolen month and the ten-day fravardigan at the end of the year, the Zoroastrian weeks, and the Hamaspathmaedaya feast are illustrated.

A Note on the Metonic Cycle

A Note on the Metonic Cycle

Did the Maya Know the Metonic Cycle?

Did the Maya Know the Metonic Cycle?