Visibility Window of the First Lunar Crescent (original) (raw)

Predicting the First Visibility of the Lunar Crescent

Academia Letters, 2021

We observe the first visibility of the lunar crescent on the western horizon shortly after sunset, and it is the beginning of the month in the Islamic calendar. There are numerous techniques for predicting the day of the first sight of the Moon, but our interest is in the physical method, which began with the investigations of Samaha, Assad, and Mikhail (1969) and Bruin (1977). To predict when we will observe the first crescent Moon, we need: 1. The topocentric altitude of the Moon; azimuth difference between the centers of the Sun and the Moon (DZ); Sun depression (d); Earth-Moon distance and topocentric phase angle (or selenocentric angle between the observer's position and the center of the Sun). 2. The luminance of the Moon without atmospheric absorption for the phase angle; (we understand luminance as the luminous flux per unit of the luminous area perpendicular to the observation direction and per unit of solid angle). 3. The atmospheric extinction coefficient for the place of observation, which determines the luminance of the Moon Bm at the surface of the Earth. 4. The twilight sky luminance Bs, as a function of d and DZ. 5. The threshold contrast or the threshold illuminance for viewing the Moon in the twilight sky; (we define the contrast by C = Bm/Bs, and the illuminance is the luminous flux that reaches the observer per unit area normal to the observation direction). Photometric measurements of the Moon at large phase angle are difficult since its observation has to be made at a low altitude above the horizon and therefore, is highly affected by atmospheric attenuation; also, the observation has to be done with twilight light, therefore the Moon's own illumination is added to the illumination of the sky, and finally, it must be added

ANALYSIS OF OBSERVATIONS OF EARLIEST VISIBILITY OF THE LUNAR CRESCENT

The Observatory, 2018

Predicting the visibility of thin lunar-crescents following the new moon is difficult and challenging for several technical reasons. The visibility of the earliest new moon has long been used to determine the lunar-crescent calendar and is still used today. Many criteria exist for the first visibility of the lunar crescent. Here, we test the most-commonly-used criteria for thin-lunar-crescent visibility.We used 545 observations, including both positive and negative sightings, made by professional and highly-trained astronomers over duration of 27 years 1988 2015) and from different locations at latitudes between 20° N and 29° N (within Saudi Arabia). We developed new criterion for lunar-crescent visibility using lunar-crescent width W ) and the arc of vision (ARCV).This new model can be used to predict the visibility of the lunar crescent by naked eye or aided eye, which is fundamental for the lunar-crescent calendar followed by several cultures and religions.

Time of the first sight of the lunar crescent

We calculate, as a function of latitude, the universal time when the visibility of the first lunar crescent begins. We verified that for the same meridian, the time of the first visibility of the crescent depends on the latitude and that the atmospheric absorption that attenuates the moonlight has little influence.

The Extended Crescent Visibility Criterion

2017

Crescent visibility has been a concern for determining the start of any lunar month. Various criteria have been offered by the astronomers since the Babylonians. The indigenous criterion proposed in this paper uses the two reliable parameters, altitude and crescent width, and makes it possible to estimate the visibility for any phase of the Moon, not just limited to thin crescents. Though very simple, the algorithm presented here produces rather consistent results. Various visibility graphs are included. In addition is introduced a tool for demonstration.

Fotheringham's graphs of visibility of the first lunar crescent

We call Fotheringham curves of visibility of the first lunar crescent graphs of the altitude of the center of the Moon and its difference in azimuth with the center of the Sun (represented at the moment when the center of the true Sun is on the horizon), which separates the zones lunar visibility and invisibility. These are multiparameter curves, which are dependent on astronomical and atmospheric parameters. In this investigation, we find the Fotheringham graphs deriving them from the Segura (2022b) lunar visibility theory and check their dependence on astronomical and atmospheric parameters.

Multi-functional lunar visibility criteria

Among the bi-parametric empirical criteria designed to determine when we will see the lunar crescent for the first time are multi-functional criteria, characterized by using several functions or visibility curves, which provide information about the difficulty of seeing the crescent. We show in detail six of these criteria and compare them with the criterion deduced from the Crescent Moon Visibility (from now on CMV) software, based on physical principles, which defines several visibility functions characterized by the probability of vision of the crescent. We analyze the proposals to determine the best time to view the crescent. We conclude that the best known of them, the one presented by Yallop, has an erroneous deduction. All six empirical criteria considered are compatible with CMV, and the various visibility curves of these criteria are crescent vision probability curves. From these empirical criteria, we deduce that the probability of 20% is the lowest to see the crescent. The empirical criteria analyzed are simplifications of the complex problem of visibility of the crescent of the Moon, in particular, because they do not consider the variable atmospheric attenuation.

Software to calculate the best time for the visibility of the Moon's crescent

In the evening when we see the crescent of the Moon for the first time, sometime after its conjunction with the Sun, there is a time when we see the crescent more easily, which we call the best time for visibility of the crescent of the Moon. We present software that determines this best time, knowing the date, the geographic coordinates, and the atmospheric conditions. * If the object is large, the background luminance could be different in its surroundings, which is what happens with the luminance of the twilight sky. ** It only sometimes happens that way. If the altitude of the Moon at sunset is large enough and/or the atmospheric absorption is small, then it is possible to see the crescent until moonset. *** The visibility window can be set depending on the depression (drawing 1) or depending on the altitude of the Moon.

Computational Astronomy and the Earliest Visibility of Lunar Crescent

Citeseer

Basic techniques of Computational Astronomy are reviewed and presented as the essential tools for simulation of Lunar phenomena. The importance of accurate determination of Julian Date and the Local Sidereal Time is discussed that are essential to determine the local time of sunset and the local coordinates of any object at that time. During the 20 th century, a number of authors have contributed towards the understanding of the problem of earliest sighting of crescent Moon. The work of Maunder, Schoch, Bruin and Schaefer has been crucial in the development of this understanding. More recently, the work of Yallop, Ilyas, Ahmed and Shaukat has received great recognition. The work of Ahmed and Shaukat has been based mostly on the Yallop's Criterion. However almost all the modesl are based on the observational data of Schmidt who made observations from Athens for over 20 years during the late 19 th century. In this work, a model of q-values developed by Yallop is analyzed in view of Maunders and the Indian Criteria along with the actual semi-diameter of the crescent Moon. The basic criterion is modified on the basis of data more recently collected.

Apex of the zone of first visibility of the Moon

The month of the Islamic calendar begins with the first observation of the crescent of the Moon. This phenomenon is highly dependent on the geographical position of the observation site. We expose the dependency of the first sighting of the Moon on latitude and longitude. We define the concepts: terrestrial terminator, Month Change Line, zone of first lunar visibility, apex, point of the first vision of the crescent, and isochrones. We check the dependence of these concepts on the equatorial coordinates of the Sun and the Moon.

Optimal latitude to see the lunar crescent

The latitude of optimum viewing of the lunar crescent is the latitude for a specific meridian where it is easiest to see the lunar crescent. We show an algorithm to determine the optimum latitude, which depends on the meridian and the depression of the Sun. We draw the line of optimum viewing or line that joins the places of optimum viewing of each meridian, which is different for each lunation and depends on the depression of the Sun.