For all calculations, the coordinates of sun for the given date is calculated.The distance of the sun to the earth is long enough that the geocentric coordinates of sun gives good results.
Dhuhr (Noon): Dhuhr or zawal is the time that the sun reaches its highest altitude. This time is a little bit different from the time that the sun passes the meridian. At this time any vertical object may have a shadow. The length of shadow also should be calculate for finding Asr time.
Asr: Is the time that the length of the object’s shadow is equal to the length of the object plus specific amount that for majority of schools, this amount is equal to the object’s shadow length at Dhuhr and for Hanafi school is equal to twice of the object’s shadow length at Dhuhr.
Sunrise and Sunset: The astronomical definition of sunrise and sunset is the time that the upper limb of the sun (apparent sun) is at the horizon. Because of the refraction of the atmosphere the sun can be seen when its center is about 0.866 degrees below horizon. Since the atmospheric refraction depends on air temperature and air pressure, we cannot predict these times very accurately and the predicted time can be within the couple of minutes of the actual sunrise or sunset. Also in many calculation the effect of the elevation of the place is ignored. In reality we should take into account this effect but currently the effect of elevation is not included in the calculations.
Fajr, Maghrib and Isha: These time is related to the astronomical term of “twilight”.In astronomy twilight is the time that the center of the sun is some specific value under the horizon. This value is 6 degrees for civil twilight, 12 degrees for nautical twilight and 18 degrees for astronomical twilight. For calculation of Fajr this angle is something between 19.5 degrees to 15 degrees according to the different schools. For all schools except Shia schoold, Aaghrib is the same as sunset. And for Shia school it is about 4.3 degrees. Again for Isha, according to different schools this angle may be 14 to 18 degrees. For Umm al-Qura University, the time between Isha and sunset is fixed and is 2 hours in Ramadhan and is 1.5 hours for the other months.