Announcement

An Islamic Calendar for Makkah - Page 4

IX.4 Example of Makkah


First of all we calculate ARCL and ARCV. For this we need from MICA LS, the geocentric celestial longitude (or Right Ascension) of the Sun and LM, the geocentric celestial longitude of the Moon. We need DM, the celestial latitude (or declination) of the Moon. We further need DAZ as defined above. Values for Makkah on 17th November 2009 at 14:48 (Best Time).

LS = 235.39°
LM = 245.01°
DM = - 3.76° (the moon is south of the celestial equator)
Azimuth of Sun = 250.62°
Azimuth of Moon = 241.97°
DAZ = 8.65°
RP = Radius vector of the moon (earth – moon geocentric distance = 392 357.996 km = 61.52 (in terms of the equatorial radius of the earth or 6378.1370 km)
Finally, ARCS or AltM (topocentric altitude of moon) = 1.75°

Now:
ARCL = Cos-1 (Cos(LM – LS) * Cos DM)
        = 10.32°
ARCV = Cos-1 (Cos ARCL/Cos DAZ)
        = 5.6484°

We now calculate the semi diameter SD of the Moon in seconds of arc with the following formula:
SD = 56204.92/RP * (1 + Sin AltM/RP)
     = 0.2539°

Yallop gives for the width of the lunar crescent W the following equation:
W = SD * (1 – Cos ARCL)
    = 0.2468’ (minutes of arc)
    = 0.0041°

Finally, with ARCV in degrees and W in minutes of arc,
Q = (ARCV – 11.8371 + 6.3226 W - 0.7319 W2 + 0.1018 W3)/10
   = - 0.467

According to Yallop:

Easily visible or green means                             Q > +0.216
Visible under perfect conditions or blue means     +0.216 ≥ Q > - 0.014
Optical aid probably needed or grey                   - 0.014 ≥ Q > - 0.160
Optical aid certainly needed or red                    - 0.160 ≥ Q > - 0.232
Not visible or black                                         Q < -0.232

So, on 17th November 09 at 14:48, visibility is not there at Makkah (black).

IX.5 Example of intermediate horizon 30°W, 30°S at 21:04


We have:
LS = 235.65°
LM = 248.32°
DM = - 3.55°
Azimuth of Sun = 243.47°
DAZ = 243.47 – 244.69 = 1.22 (always +)
Azimuth of Moon = 244.69°
Zenith distance of Moon = 84.26°
AltM = 90° - 84.26° = 5.74°
Distance earth –moon (geocentric) = 393315 km so RP = 393315/6378 = 61.67
SD according to MICA (illumination of disc) = 15’ 11.14” = 911.14”
ARCL = Cos-1 (Cos(LM – LS) * Cos DM)
       = 13.15°
ARCV = Cos-1 (Cos ARCL/Cos DAZ)
       = 13.10°
SD = 56204.92/RP * (1 + Sin AltM/RP)
       = 0.2536°
W = SD * (1 – Cos ARCL)
   = 0.3986’ (minutes of arc)
   = 0.0066°
Finally, with ARCV in degrees and W in minutes of arc,
Q = (ARCV – 11.8371 + 6.3226 W - 0.7319 W2 + 0.1018 W3)/10
   = + 0.367
According to the Yallop criteria, Q indicates easy visibility in the green.

IX.6 Plotting visibility curves and taking photographs


Once the value of the Q factor is known it is in principle easy – with a good computer programme – to plot visibility curves by calculating this value for a closely knit grid of points on the globe.

It is to be noted that the visibility curves on the world map are not for an instant of time. They are a composite of local sunset time at every point on earth showing the possibility of sighting the moon on one specific day (date of Gregorian calendar) shown on top left. That specific day begins at the International Dateline (IDL) at 180º from the prime meridian of the Greenwich. The day continues towards west of IDL, and ends at the IDL traversing the 24 hour period of a specific day.

Crescent Predictions - 16 March 2010

In March 2010, the new moon was born on the 15th at 12:02 UTC. The visibility curves showed a green belt in Canada on the next day. On our behalf, two photographs were taken of the early crescent on March 16th:

Photo1
Crescent Photograph - 16 March 2010

Above photograph was taken by Roy Bishop at Grand Pre, Nova Scotia at approximately 45°07’ latitude and 64°18’ longitude, the moon being 26 hours past new.

Photo2
Crescent Photograph two - 16 March 2010

Above Photograph was taken by Steve Irvine, also in Canada, at 44.46’ latitude and 80.57’ longitude, the moon being 27 hours and 9 minutes past new.

Both photographs are brilliant and a conclusive proof of the applicability of our calendar. They both are also published on our dedicated Website in Photo Gallery. We have mobilised several observatories and amateur astronomers to provide us early crescent photographs at places determined by the visibility curves and situated within the limiting horizon for Makkah. All these photographs will be published immediately on our Website.