Moslems Must Observe the apparent movement of the sun across the sky in order to performs prayers.

There is no consensus on the times of the prayers among different Moslem factions and developing an algorithm was affected by this fact.

For example, Sun depression angle considered to calculate Fajr and Isha prayers are not agreed upon.

In the following table we can see these differences:

Any how, these calculations depend on the latitude and the declination. Before we are able to calculate these values, we have to calculate a number of things including the Julian day ,hour angle and equation of time.

Hour Angle =1/15 x cos^-1((sin(elevation angle-sin(declination)sin(latitude))/cos(declination)x cos(latitude))

The Equation Of Time can be calculated by this formula:

EoT = 9.873 x sin(4PI*day/375 + 3.588) – 7.665 x (2PI *day / 365)

Zohr Time Can be calculated by the follwoing formula:

Zohr = 12 + TimeZome – longitude/15 – EoT/60 + delta.

delta is the time needed for the Sun to cross the meridian and is about 4-5 minutes.

Asr Prayer can be calculated by the following formula:

Asr = Zohr + Hour Angle/15

Maghreb time equation is as follows:

Maghreb = Zohr + (1/15) x arcsin( (sin(-0.833 °) – sin(declination)sin(latitude))/(cos(declination) cos(latitude)) )

For Fajr prayer it is :

Fajr = Zohr – (1/15) x arcsin((sin(-18 °)-sin(declination)sin(latitude)) / (cos(declination)cos(latitude)) )

Isha prayer :

Isha = Zohr + (1/15) x arcsin((sin(-18 °)-sin(declination)sin(latitude)) / (cos(declination)cos(latitude)) )

Prayer Times according to Moslem World League is already available in a previous post.

Following is the prayer times according to Shia Ithna-asharia , Leva Research Institute, Qum:

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Islamic Prayers Times

Day Month Year

Hour Minute Second

TimeZone

Latitude Longitude

Prayer	Time	Notes
Fajr		If values are not valid ,use astronomical twilight time
Zohr
Asr
Maghreb		+(8-10 minutes).For Shia Muslims Use Civil Twilight-night Time
Isha		If values are not valid, use astronomical twilight time
AstroTwilight-morning		In Extreme latitudes, values can be nonvalid or appear negative.
NautiTwilight-morning		In Extreme latitudes, values can be nonvalid or appear negative.
CivilTwilight-morning		In Extreme latitudes, values can be nonvalid or appear negative.
CivilTwilight-night		In Extreme latitudes, values can be nonvalid or appear negative.
NautiTwilight-night		In Extreme latitudes, values can be nonvalid or appear negative.
AstroTwilight-night		In Extreme latitudes, values can be nonvalid or appear negative.

In latitudes above 66° N or below 66° S , it could be light all day or dark all day. Calculations then are not possible

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