Praise be to Allah.
Firstly:
The time for Fajr starts with the second dawn (the true dawn) which is the horizontal whiteness that spreads along the horizon right and left, and the time lasts until the sun rises.
In the answer to question no. 26763 we discussed the mistake that many people make by relying on timetables to define the time for Fajr, and that most of these timetables do not give the proper time for the true dawn. This has been stated by more than one of the scholars.
Contemporary scholars differed concerning the extent of this error. Some of them said that it is no more than five minutes, and some said that it is approximately thirty minutes.
We do not know what the situation is in your city, but the people of each city should appoint a group of trustworthy scholars to find out the time for Fajr and inform the people of it, and warn them against following timetables if it is proven that they are wrong.
No one should claim that the prayer is being done before the time begins unless he has proof, especially since finding out the actual time of dawn is very difficult in cities and inhabited areas, because the light of dawn is mixed with the lights of the city.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about a congregation who did not know the time of Fajr and they prayed it based on information from someone whom they trusted, but some of them had doubts.
He replied: So long as they trust him and know that this man has knowledge about the beginning of the time (for prayer), there is no sin on them, because they did not know that they were praying before the time began. If they did not know and they accepted the word of this man whom they trust, then there is no blame on them. But one should take precautions so long as there is some doubt, and not pray until he thinks it most likely or is certain, and he should alert the congregation to that, and suggest to them to wait five minutes or ten minutes, and that will not harm them, because waiting five or ten or fifteen minutes is better than praying even one minute too early. End quote from Fataawa al-Shaykh Ibn ‘Uthaymeen, vol. 12, question no. 146.
Secondly:
You should advise the people in this mosque to delay the prayer until they think it most likely that the time has begun, and if they respond then praise be to Allaah.
But if they insist on what they are doing – and you think that they are praying before the time for prayer begins – then look for another mosque that starts the prayer later, so that your not praying Fajr in the mosque will not make people think badly of you, and think that you are sleeping and missing the prayer, and so that you will not be depriving yourself of the reward for going to the mosque, and so that you will not become lazy about praying later on. Then go back home and repeat the prayer with your family in congregation after the time begins. This is what Shaykh al-Albaani (may Allaah have mercy on him) advised when he was asked: Do you advise me to offer the obligatory prayer of Fajr in the mosque or at home? [Because the people in the mosque offered the Fajr prayer before dawn].
He replied:
I advise him to do two things together: He should go to the mosque and if they offer the obligatory prayer before the proper time, it will be naafil for him. Then he should go back home and offer the obligatory prayer on time, and in particular he should pray with his family. But there is something that is more obligatory, but not everyone can fulfil this obligation, which is alerting the people of the mosque to this serious matter… end quote.
Silsilat al-Huda wa’l-Noor tape no. 767, minute 32.
And Allaah knows best.
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