Moon’s Earliest Visibility
Adopted from Monzur Ahmed
computation of the appearance of the new crescent is a very long and difficult
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
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, 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]
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
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]
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
RGO 67............ [Alt, Elong]
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
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:
Shaukat........... [Alt, Crescent width]
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:
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.
the current lunar month will last 30 days.
Yallop ........... [Rel Alt, Crescent Width]
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.
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:
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
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.)