Moon’s Earliest Visibility Adopted from Monzur Ahmed
“The computation of the appearance of the new crescent is a very long and difficult procedure.”
Al-Biruni (973-1048 CE)
Since ancient times, astronomers have tried to predict the likelihood of seeing the new moon by defining minimum visibility criteria. Monzur’s MoonCalc currently supports 13 such criteria. The user can choose the moon visibility criterion to be used. The following options exist:
* Babylonian……… Age at sunset>24hrs & Lag>48 mins
The Babylonians moon sighting criterion was >48mins (ie the difference in RA of sun and RA of moon at sunset was >12 degrees) and moon’s age at sunset was >24 hours.
Ibn Tariq…….. [Alt, Lag]
Muslim astronomers extensively investigated the problems of moon sighting in the 8th-10th century AD. They developed visibility criteria and created tables for calculations. MoonCalc supports Ibn Tariq’s criterion which depends on moon altitude at sunset and moonset lag. Future versions will support the criteria of Al-Kwarizmi, Al-Batani, Habash, etc.
* Fotheringham…… [Alt, Rel Azi] (1910)
In 1910 Fotheringham developed a moon visibility criterion based on Schmidt’s documented sightability or unsightability of moons in Athens over a period of 20 years. Using Schmidt’s data, Fotheringham plotted a scatter diagram of moon’s altitude at geometric sunset versus the difference in azimuth (relative azimuth) between the sun and the moon at sunset. A curve was drawn separating the ‘visible’ moons from the ‘unsighted’ moons. This curve was then used to predict the likelihood of sighting young moons – if a new moon’s alt/rel azi. falls above the curve than it should be sightable, if it falls below the curve it should not be sightable.
* Maunder……….. [Alt, Rel Azi] (1911)
In 1911, Maunder again used Schmidt’s data together with a few more observations and drew the curve lower than Fotheringham.
* Indian/Schoch…… [Alt, Rel Azi]
The Indian Astronomical Ephemeris used a slightly modified version of the above two criteria, drawing the line slightly lower than Maunder (ref 8). The Indian criterion was initially developed by Carl Schoch.
* Bruin ………. [Alt, Crescent width] (1977)
In 1977 F. Bruin published details of his theoretical moon sighting criterion based on crescent width and sun/moon altitude (ref 10). Bruin used 0.5 minutes as the limiting crescent width. The criterion was criticized for making erroneous assumptions. MoonCalc uses a slightly modified version of the Bruin criterion with limiting crescent width=0.25 minutes as suggested by Ilyas (1984).
* Ilyas_A……… [Alt, Elong]
MoonCalc supports three of Ilyas’ best known sighting criteria. The first criterion depends on the ‘moon’s relative altitude at sunset’ and the angular separation between the sun and the moon.
* Ilyas B…… [Lag, Alt.] (Modified Babylonian)
Ilyas’ second criterion is a modification of the ancient Babylonian system of moonset lag times. Ilyas compensates for latitude (eg at latitude 0 deg: lag 41 min; 30 deg:46 mins, 40 deg:49 mins, 50 deg: 55mins).
* Ilyas_C…………. [Alt, Rel Azi] (1988)
Ilyas’ third criterion is a slight modification of Ilyas A and depends on the moon’s relative altitude at sunset and the difference in azimuth between the sun and moon at sunset. This is the default criterion used in MoonCalc.
* RGO 67………… [Alt, Elong] (1980s)
The Royal Greenwich Observatory UK predicted that the best time and place for earliest sightings on the globe are when the moon is vertically above the sun at sunset so that their azimuths are equal (ie relative azimuth at sunset=0) and where the apparent altitude of the moon at sunset is 10 degrees. If the sky is clear and the horizon is flat, sighting should be possible just before the sun reaches a geocentric altitude of -5 degrees. The criterion as implemented in MoonCalc is useful for finding the earliest location where the new moon is likely to be sighted. On a global scan, the criterion does *not* show all areas west of the ‘earliest point’ where the crescent will be seen.
* S. African Astro. Observatory (SAAO)…. [Alt, Rel Azi]
Drs. John Caldwell and David Laney of the South African Astronomical Observatory criterion was based on published crescent sightings together with a few local sightings from Signal Hill. The criterion depends on ‘topocentric moon altitude (to lower limb) at apparent sunset’ and ‘difference in azimuth at sunset’. Two lines are drawn on a graph of altitude versus relative azimuth. The sightability of a crescent is ‘possible’ if above upper line, ‘improbable’ if between the two lines and ‘impossible’ if below the lower line.
* CFCO (Alt, Elong, Lag) (1979)
This criterion, proposed by Dr. Abdali of the Committee for Crescent Observation Intl. is stated separately on CFCO’s web: www.islamicmoon.com
* Shaukat……….. [Alt, Crescent width] (1995?)
Khalid Shaukat’s criterion depends on the ‘topocentric altitude of the moon (to the lower limb) at sunset’ and the ‘calculated crescent width at sunset’. The altitude must be >3.4 degrees at sunset and (alt/12.7) + (crescent width in arcmin /1.2)>1. The crescent width is calculated in a slightly non-standard way.
* Saudi Ummal-Qura calendar
From 1423 AH (15 March 2002) onwards, the Saudi Institute of Astronomical & Geophysical Research has modified its rules as follows:
If on the 29th day the following conditions are satisfied, then the next day is the first day of the new lunar month:
1. The geocentric conjunction occurs before sunset.
2. The Moon sets after the Sun.
Otherwise, the current lunar month will last 30 days.
* Yallop ……….. [Rel Alt, Crescent Width] (1997/1998)
Bernard Yallop (Royal Greenwich Observatory, UK) took into account 295 published moon sightings / non-sightings compiled by Schaefer and Doggett in late 1980s and early 1990s. A parameter ‘q’ is derived from the relative geocentric altitude of the moon (ARCV) and topocentric crescent width.
In the original technical note by Yallop ‘q’ was derived at ‘best time’ (i.e. sunset + (4/9)* moonset lag). However, it is not always practical to apply the criterion at ‘best time’. MoonCalc allows the criterion to be applied at sunset or when the sun is at -5 degrees as well as at ‘best time’. The value of ‘q’ is stratified to give 6 types of predictions:
Criterion q Range Remarks
A q > +0.216 Crescent easily visible
B +0.216 >= q > -0.014 Crescent visible under perfect conditions
C -0.014 >= q > -0.016 May need optical aid to find crescent
D -0.016 >= q > -0.232 Will need optical aid to find crescent
E -0.232 >= q > -0.293 Crescent not visible with telescope
F -0.293 >= q Crescent not visible, below the Danjon limit
Note: Applying the criterion at sunset makes the visibility predictions slightly more pessimistic compared to ‘best time’, and global visibility zones are west shifted by about 5 degrees of longitude.
(CFCO note: Moon watchers have criticized Yallop’s curves as too liberal at their eastern most points. None of them predicts that a Hilal will always be visible to a person with normal vision if the criterion is met.)