Source : Google Earth Software
Understanding of the direction of Qiblah is very simple, because the problem of the direction of Qibla is only a directional problem, is the direction of the Ka'ba which is in Mecca and each place must have different direction in facing Qibla.
In simple terms it can be seen that the area in the South Kabah facing to the North, the area located in the North Kabah facing to the South, the area in the East Kabah facing to the West, the area in the West Kabah facing East,
If further clarified then the area located in the North East Kabah facing to the South West, the area located in the South East of the Kabah facing to the North West, the area located in the South West Kabah facing the North East and the area located in the North West Kabah facing South East.
It can be a bit complicated if we further see that the earth is round, then there must be a special calculation for it, but if in a state of urgency can use the logic above.
The meaning of Qiblah in language is derived from the word قبل- يقبل - قبلة, which means facing, whereas in term, the islamic astronomers define with the Direction closest to the Ka'ba, The direction in which Muslims confront their faces during the prayer.
So why should we face qibla ???
The scientist of the fiqh agree that facing the Qiblah in the prayer is a requirement of the validity of the prayer, as the syar'I proposition exists:
Allah has commanded this three times, namely in Al-Baqarah: 144,149 and 150:
قد نرى تقلب وجهك في السماء فلنولينك قبلة ترضاها فول وجهك شطر المسجد الحرام وحيث ما كنتم فولوا وجوهكم شطره وإن الذين أوتوا الكتاب ليعلمون أنه الحق من ربهم وما الله بغافل عما يعملون
and in the hadith :
قال أبو هريرة رضي الله عنه: قال رسول الله صلى الله عليه وسلم: اذا قمت الي الصلاة فاسبغ الوضوء ثم استقبل القبلة وكبر. رواه البخارى ومسلم
For people around the holy mosque overlooking the Ka'ba is not a problem because they easily do that. Then what about the people who are far away with the Grand Mosque even outside the city of Mecca. Are we still required to face the true Ka'ba? Or just with an estimate only?
The opinion of the scholars:
Imam As Syafi'i & Shi'a Imamiyah:
Obligatory to the Ka'ba itself, both for the near and far.
If you can know the direction of the Ka'ba itself (exact), then it must face in that direction. If not, then just with an estimate only. (az-Zuhaily, Tafsir Al-Munir, p. 234)
Imam Hambali, Maliki, Hanafi & some scholars of Shi'a Imamiyah:
The direction of qibla is the direction in which the Ka'ba is located, not the Ka'ba itself. (As Suyuthiy, Al Asybah Wa An Nazair, p. 116)
The clerical agreement
All scholars agree that the Ka'ba is a qibla for those who are close and can see it. But they differ on the qibla for the distant and can not see it. (as-Sya'rani, Al-Miizaan Al-Kubra p. 116)
Based on the strongness of prejudice, there are 3 methods in determining the direction of Qibla
1. Overlooking Qibla Sure
A person who is inside the Grand Mosque (Masjidil Haram) and sees the Ka'ba directly, must face himself to Qibla with confidence. This is also referred to as "Ain al-Ka'ba".
2. Overlooking Qibla Estimates
Someone who is outside the Grand Mosque so that they can not see the Ka'ba building, they are obliged to face the Grand Mosque as the intent of facing Qibla in a dzan or approximation is called "Jihat al-Ka'ba"
3. Facing Qibla with
Ijtihad
Ijtihad can be used to determine the direction of Qibla from a place far from the Holy Mosque, such as someone outside the holy land of Mecca or even outside Saudi Arabia, the method used is "Jihat al-Qiblah"
Why should a mathematical approach in determining the direction of Qibla?
As long as there is a more accurate way why choose another less accurate way, In a qaidah ushul fiqh
لا عبرة بالظن البين خطؤه
"The theory or practice that is based on the zan (allegation) that is clearly wrong is not considered"