Article

The Length of the Lunar Month

Authors:
To read the full-text of this research, you can request a copy directly from the author.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the author.

... In Figure 2, one pixel corresponds to 21" of degree. This value corresponds to half of the angular resolution of the average human eye, 42", for typical lunar [35] surface brightness. The diameter of the Earth's shadow-innermost circle-is about 2.67 of the Moon diameter. ...
... Moreover, segmented sleep is also present in the Bible [20]. In the New Testament, some parables seem to refer to segmented sleep: at midnight someone could knock at a friend's door for borrowing three loaves of bread (Luke 11, 5), or five girls could be invited to go to the store-in the middle of the night!-to buy some oil for their lamps (Mt 25, 9-10), or watchful servants, suitably dressed and with lamps lit, are waiting just at midnight, or before the sunset, for their master to come back from a wedding feast (Lk 12, [35][36][37][38]. Jesus was arrested in the middle of the night, and part of the Sanhedrin readily gathered in the house of the High Priest to judge him, a reunion difficult to imagine in a society such as ours, where segmented sleep is not practiced. ...
... The full Moon, seen from the Earth, subtends an angle of about 0.5 • (i.e., it is seen under an angle of 30 arcminutes). By the naked eyes it is seen with an angular resolution of 42 arcsec (60 arcseconds make 1 arcminute, 3600 arcseconds make a degree), corresponding to a visual acuity of 3600/42 ∼ = 86 cycles per degree [35]. At the Nyquist angular frequency, samples must be taken every 21 arcsec, therefore the diameter of the Moon requires only 1800/21 ∼ = 86 pixels to simulate how it would be seen by naked eyes, much fewer than the digital resolution allowed by a digital camera. ...
Article
Full-text available
We have re-examined and discussed all chronological, historical and astronomical elements which can be referred to the year of Herod the Great’s death, which occurred—according to Josephus—after a lunar eclipse and before Passover. Since the XIX century, most scholars still assume the eclipse occurred on 13 March 4 BC, so that Dionysius Exiguus was wrong in calculating the beginning of the Christian era—by four years at least—because Herod the Great must have been alive when Jesus was born. We have solved the apparent incompatibility of the events narrated by Josephus, occurring between the eclipse of 13 March 4BC and a too-near Passover (12 April 4 BC), by determining another date after studying all eclipses visible from Jerusalem in near years. This analysis—supported by a novel simulation of naked–eye visibility of partial lunar eclipses—has shown that the most eligible eclipse associable to Herod’s death occurred in the night of 8–9 November 2 AD. Besides this astronomical finding, our conclusion is also supported by significant correlation between segmented sleep and eclipse intervals; by its compatibility with the long sequence of events narrated by Josephus and with the rabbinic tradition about Herod’s death. This dating also agrees with other historical facts connected to Roman and Jewish history. In conclusion, Herod the Great must have died in the first month of 3 AD and, very likely, Dionysius Exiguus was correct.
... We have found table 2 with Maunder's criterion. Schaefer (1992), using the physical method developed in the LunarCal software (Schaefer, 1990), reaches the same conclusion: the months are 29 or 30 days for observers located in what we have called the central zone. We warn that this rule may not be fulfilled for places at high latitudes; this will occur if the observer far to the north or far south sees the crescent two or more days after the earliest sight. ...
... We have found table 2 with Maunder's criterion. Schaefer (1992), using the physical method developed in the LunarCal software (Schaefer, 1990), reaches the same conclusion: the months are 29 or 30 days for observers located in what we have called the central zone. We warn that this rule may not be fulfilled for places at high latitudes; this will occur if the observer far to the north or far south sees the crescent two or more days after the earliest sight. ...
... a) Positive declination and observation in the northern hemisphere. There are latitudes for which the Sun is always above the horizon, at least for one day; therefore, there is no sunset, this occurs when 180º H   and cos 1 H    , then by (10)     sin sin sin 1 cos sin 50 89º 10 cos cos ...
Preprint
Full-text available
For the central zone of the Earth (approximately 50ºN-50ºS), Islamic months have lengths of 29 and 30 days depending on the place of Earth from where we observe the first lunar crescent. We verify that all the lunar months have two durations for the central zone, one of 29 days and the other of 30 days. For higher latitudes (50º N or S to 61.5º N or S), we find that months can have 28 and 31 days lengths. We determine the length of the lunar months using the Month Change Line concept, applying the extended Maunder criterion.
... Los nevados del Aconquija como sitio de frontera y espacio de observación lunar, Tucumán, noroeste de Argentina incide en la fórmula para calcular la pascua cristiana en Occidente, coincidiendo con el domingo y primera luna llena después del equinoccio de marzo (Schaefer 1992). ...
... Porque contaron los meses por lunas, como luego diremos, y no por días y, aunque dieron a cada año doze lunas, como el año solar ecceda al año lunar como en onze días, no sabiendo ajustar el un año con el otro, tenían cuenta con el movimiento del Sol por los solsticios, para ajustar el año y contarlo, y no con las lunas. Y desta manera dividían el un año del otro rigiéndose para sus sembrados por el año solar, y no por el lunar"(de la Vega 1945(de la Vega [1609: 111, en Bauer y Dearborn 1998: 57).Su ciclo de fases, igual a 29,53 días, promediado en números enteros de 29 y 30(Schaefer 1992;Stern 2008; Steele 2010), ha servido como un parámetro indicativo del tiempo social, al menos desde el Paleolítico Superior europeo en el sitio de Abri Blanchard, en Dordoña (Francia, con fechas cercanas al 29000 AC(Marshack 1972), y la Venus de Laussel (diosa de la fertilidad) con representaciones de 13 ciclos lunares dentro de un año, con fecha del 20000 AC (da Silva 2010, citando a Joseph 2010). 360°), tras lo cual aparece como una delgada creciente por el oeste, cerca de donde se está ocultando el sol. ...
... Se plantea también la posibilidad de otro marcador al poniente, 54° al sur del cerro Las Cuevas en un nevado (no identificado), donde se tienen noticias de "grandes montones de leña", para la puesta del sol en el solsticio de diciembre. Según cálculos realizados por Hyslop, este evento ocurriría 2°30' al norte del nevado Hauthal (5340 msnm), coincidiendo con la falda oriental, del que se asume, es el cerro de Las Minas (5500 msnm)(Beorchia 2001: 205).La observación de ciclos lunaresDesde tiempos remotos, la observación de los ciclos de la luna ha sido el fenómeno de la naturaleza más fácil de registrar, sirviendo como base para la estructura de distintos calendarios como el babilónico, el árabe, el hindú, el judío-hebreo y el chino(Schaefer 1992;King 1993;Montgomery 1999;Stern 2008; da Silva 2010). Estos sistemas calendáricos asumen períodos de tiempo (fijo) a partir de la combinación de los ciclos sinódico y sideral de la luna, constituyendo también base para los distintos sistemas de creencias a través de la creación de constelaciones, mitos y deidades lunares. ...
Article
Full-text available
We present social aspects related to the concepts of border, ushnu and lunar observation at the inca site of La Ciudacita, Tucuman province, northwestern Argentina. The analysis focused on the possibility of observing the lunistice or major lunar standstill, in relation to concepts of geographical latitude, architecture and horizon landmarks from the perspective of cultural astronomy. Our hypothesis is that the ushnu serves as a representation of the Moon at the zenith, south of the Tropic of Capricorn, highlighting its utility for following and predicting eclipses. Results show that the relationship between the ushnu and gnomon in observing the Moon's phases was possibly linked to relations of power and the expansion of Tawantinsuyu, circa.
... They used a standard criterion to predict the moon's sight, which was sufficient for that purpose. Other civilizations, such as Indians and Chinese, also used lunar sight and still do to this day, although use different criteria to determine the start of a lunar month [2]. Jewish people also still use the moon cycle to indicate the start of the months in their lunisolar calendar, although they use arithmetic calculation rather than moon sighting. ...
... They are Fasting-Breakfasting "Siam-Fitr", Pilgrimage "Hajj", and Alms "Zakat". The first two pillars are performed in a specific lunar month in a year, while the third is performed once in the first month of each lunar year [2]. Reckoning of the first crescent moon after the conjunction is an essential indication for Muslims to begin their lunar months and perform their religious duties. ...
Article
Full-text available
Various theories have been proposed since in last century to predict the first sighting of a new crescent moon. None of them uses the concept of machine and deep learning to process, interpret and simulate patterns hidden in databases. Many of these theories use interpolation and extrapolation techniques to identify sighting regions through such data. In this study, a pattern recognizer artificial neural network was trained to distinguish between visibility regions. Essential parameters of crescent moon sighting were collected from moon sight datasets and used to build an intelligent system of pattern recognition to predict the crescent sight conditions. The proposed ANN learned the datasets with an accuracy of more than 72% in comparison to the actual observational results. ANN simulation gives a clear insight into three crescent moon visibility regions: invisible (I), probably visible (P), and certainly visible (V). The proposed ANN is suitable for building lunar calendars, so it was used to build a four-year calendar on the horizon of Baghdad. The built calendar was compared with the official Hijri calendar in Iraq.
Preprint
Full-text available
We show that in high geographic latitudes (approximately > 50º north or south), the lunar months of 28 and 31 days are possible.
Conference Paper
Full-text available
Software has become a necessity in calculating new moon visibility data. The software must have certain qualities which are: 1) accuracy of data; and 2) user-friendly. By analysing the current quality models and observing the available new moon calculation software, we came out with the set of quality parameters model that acts as a mold or guidelines for new developers in new moon calculation software. After a thorough revision with current software quality models, it is concluded that none of the quality model fits with all type of application, considering every one of them has different classification. Thus there is an absence of any kind of metrics that could help use the evaluating quality characteristic objectively, particularly when the software involving new moon calculation. The quality parameter suggested will covers some limitation that found in the existing models and ignores the quality aspect from existing model that not applicable to New Moon Calculation Software.
Article
Full-text available
This research aim to analyze of the data generating a modern empirical visibility criterion called Indonesia visibility criteria (RHI criteria) in the form aD ³ 0,099 DAz2-1,490 DAz + 10,382. Although based on a local database, but these criterion are consistent with the international visibility databases such as Yallop and ICOP, along selected only for data sourced from the tropical region. These criterion also were consistent when compared to the tropical visibility database not from Indonesia. So this criteria is the national visibility criterion (for Indonesia) and also regional visibility criterion (tropical region). Comparative analysis showed that although different in form than modern visibility criterion that have similar variables as Fotheringham-Maunder and Bruin criterion, but the form of the Indonesia visibility criterion (RHI criterion) may still be accepted because it is supported by the recent observation data. The difference in shape is due to the Indonesia visibility criterion (RHI criterion) does not distinguish between optical aid-based observations with naked-eye observations.
Article
This article considers three questions associated with Ptolemaic-Roman lunar chronology: did the temple service begin on Lunar Day 2; were lunar phases determined by observation and/or cyclically; how accurate were lunar observations? In the introduction, Babylonian and modern observations of old and new crescents are analyzed to obtain empirical visibility lines applicable to Egyptian lunar observations.
Article
Given that the cause for the strong increase in 14C in AD 774/5 in Japanese and German trees is still a matter of debate (e.g. short Gamma-Ray Burst or solar super-flare), we have searched in Arabic chronicles for reports about unusual transient celestial events. In the {\em History of al-Tabari we found two (almost identical) reports about such an event. The group around caliph al-Mansur observed a transient event while on the way from Baghdad to Mecca on AD 775 Aug 29 - Sep 1 (Julian calendar), most probably during the morning twilight of AD 775 Aug 29. A celestial object kawkab was seen to fall or set inqadda, and its trace atharuhu was seen for at least tens of minutes (up to 70-90 min) during morning twilight. The reports use the Arabic words kawkab and athar(uhu), which were also used in the known Arabic reports about supernovae SN 1006 and 1054, so that one might consider an interpretation as a nova-like event. The kawkab (celestial object) was observed only during the morning twilight at a brightness of probably between about -3 and 0 mag. Such a brightness and time-scale would be expected for optical kilonovae (at 3 to 9 kpc) in the context of short Gamma-Ray Bursts. There are no similar reports from eastern Asia for this time. However, the short reports are fully consistent with a bolide: The word kawkab can be used for meteor, the verb inqadda normally means "falling down", the word atharuhu can mean "its trace". We therefore prefer the interpretation as bolide. We discuss in detail how to convert the Muslim calendar date to a date in the Julian calendar using first the calculated Islamic calendar and then considering the time when the crescent new moon could be visible at the given location.
Article
Since its popular resurgence in the 1960s, the interdisciplinary field of archaeoastronomy, which seeks evidence from the written as well as the unwritten record to shed light on the nature and practice of astronomy and timekeeping in ancient civilizations, has made ever-increasing significant use of the archaeological record. This essay briefly touches on the origin and history of these developments, discusses the methodology of archaeoastronomy, and assesses its contributions via the discussion of selected case studies at sites in North, South, and Mesoamerica. Specifically, archaeology contributes significantly to clarifying the role of sky events in site planning. The rigorous repetition of axial alignments of sites and individual oddly shaped and/or oriented structures can be related to alterations in the calendar often initiated by cross-cultural contact.Together with evidence acquired from other forms of the ancient record, archaeology also helps clarify the relationship between functional and symbolic astronomical knowledge. In state-level societies, it offers graphic evidence that structures that served as chronographic markers also functioned as performative stages for seasonally timed rituals mandated by cosmic connections claimed by the rulership.
Article
Celestial visibility is the study of the limits of observability of objects in the sky, with application to deducing the truth about historical events or to the derivation of astronomical information of modern utility. This study is based on what is seen by ordinary humans, either in their everyday lives or at times of historical events. The results of such studies have more relevance to non-scientists than does any other area of astronomy. Celestial visibility is a young discipline in the sense that the number of interesting applications with simple solutions outnumber the solved problems; it is a broad interdisciplinary field that involves work with astronomy, meteorology, optics, physics, physiology, history, and archeology. Each of these disciplines contribute specialized mathematical formulations which quantify the many processes that affect light as it leaves a source, traverses the atmosphere, and is detected by the human eye. These formulas can then be combined as appropriate to create mathematical models for the visibility of the source under the conditions of interest. These model results can then be applied a wide variety of problems arising in history, astronomy, archeology, meteorological optics, and archeoastronomy. This review also presents a dozen suggestions for observing projects, many of which can be directly taken for individual study, for classroom projects, or for professional research.
Article
Full-text available
We outline the priority of high quality data of astronomical content as our strategy for the analysis of the ancient astronomical records in the search of the absolute chronology of the Near East in II millennium BC. The correspondingly defined set of data for two lunar eclipses of EAE 20 and 21 tablets linked to Ur III period enables us the choice of eclipses of 27 June 1954 BC and 17 March 1912 BC; here the information on the exit position of the darkening of the lunar disk acts as a crucial informator survived in the records. We then discuss why the 56/64 year Venus cycle cannot be traced in the Venus Tablet and therefore cannot serve as an anchor for the search of chronologies. The month length method is discussed as well. In sum the available data support the Ultra-Low Chronology proposed in the book by H.Gasche, J.A.Armstrong, S.W.Cole and V.G.Gurzadyan, "Dating the Fall of Babylon" (1998) and, particularly, leave no astronomical background for the High Chronology. Ultra-Low Chronology is supported also by archaeological, dendrochronological, Assyrian king lists and other data as summarized at the Intern. Colloquium on Ancient Near Eastern Chronology (Ghent, July, 2000).
Article
Full-text available
A mathematically rigorous formalism is derived by which an arbitrary photometric function for the bidirectional reflectance of a smooth surface may be corrected to include effects of general macroscopic roughness. The correction involves only one arbitrary parameter, the mean slope angle , and is applicable to surfaces of any albedo. Using physically reasonable assumptions and mathematical approximations the correction expressions are evaluated analytically to second order in . The correction is applied to the bidirectional reflectance function of B. Hapke (1981, J. Geophys. Res.86, 3039–3054). Expressions for both the differential and integral brightnesses are obtained. Photometric profiles on hypothetical smooth and rough planets of low and high albedo are shown to illustrate the effects of macroscopic roughness. The theory is applied to observations of Mercury and predicts the integral phase function, the apparent polar darkening, and the lack of limb brightness surge on the planet. The roughness-corrected bidirectional reflectance function is sufficiently simple that it can be conveniently evaluated on a programmable hand-held calculator.
Article
The photometric parameters of B. W. Hapke's (1986, Icarus 67, 264–280) equation are fit to the lunar disk-integrated visual lightcurve and to disk-resolved data of R. W. Shorthill, J. M. Saari, F. E. Baird, and J. R. LeCompte (1969, Photometric Properties of Selected Lunar Features, NASA Contractor Report CR-1429) for dark, average, and bright lunar terrains. The lunar nearside geometric albedo and phase integral computed from the disk-integrated results are consistent with those of earlier investigators. The single scattering albedos of disk-resolved average and bright lunar terrains are systematically larger than that of lunar mare. Average particles in dark terrain regoliths are more backscattering than those in average and bright lunar terrains. The angular width of the opposition surge is greatest in dark terrains and is found to be best explained by modest differences in regolith particle-size distributions which might accompany the normal regolith maturation process. The total amplitude of the opposition surge for dark terrains is larger than for average and bright terrains. This result appears to be a consequence of the fact that in opaque particles, a larger fraction of singly scattered light at zero phase comes from first-surface reflection. The average subcentimeter macroscopic roughness of dark terrains is significantly lower than that of average and bright terrains. The relative magnitude of this difference is consistent with that obtained from radar measurements at decimeter scales.