The early Muslims only knew the world and time of Arabia and used the sun to track the day. The world is much bigger today and it's up to modern Muslims to come up with solution(s) that reflect the modern big world not 6th century Arabia.
If Prophet Muhammad (peace and blessings of Allah be upon him) did not tell us and you can't quote a verse in the Quran or a hadith, we're sticking with the rules set by Islam.
Check this hadith:
“Allah has shown me the east and the west and the authority of my Ummah shall reach to whatever was shown to me of it.” [Muslim No.2889, and others Abu Dawud]
Since Allah has shown Prophet Muhammad (peace and blessings of Allah be upon him) every corner on earth, do you think North Pole was not shown to him? Basics guys, basics. If the Prophet (pbbuh) did not tell us to estimate hours, we're not going to accept new heretic innovations that people are coming up now.
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Umar (Allah be pleased with him) reported Allah's Messenger (may peace be upon him) as saying: When the night approaches and the day retreats and the sun sinks down, then the observer of the fast should break it. Ibn Numair made no mention of the word" then". [Muslim No.2421]
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If you obeyed most of those on earth, they would lead you away from the path of Allah. They follow nothing but speculation – they are only guessing. ” (Qur’an 6:115-116)