Islamic mainstream (madzhab) fiqh in Islam have for a long time state that the only valid way to began Shaum (fasting date) or Iedul Fitriy is by seeing hilal (newmoon), and do not consider hisab (astronomical arithmatics) as the most prefer way. They based their premises, at least to these two hadith:
1. حَدَّثَنَا يَحْيَى بْنُ يَحْيَى قَالَ قَرَأْتُ عَلَى مَالِكٍ عَنْ نَافِعٍ عَنِ ابْنِ عُمَرَ – رضى الله عنهما – عَنِ النَّبِىِّ -صلى الله عليه وسلم- أَنَّهُ ذَكَرَ رَمَضَانَ فَقَالَ « لاَ تَصُومُوا حَتَّى تَرَوُا الْهِلاَلَ وَلاَ تُفْطِرُوا حَتَّى تَرَوْهُ فَإِنْ أُغْمِىَ عَلَيْكُمْ فَاقْدِرُوا لَهُ ». Muslim: 2550
2. حَدَّثَنَا عَبْدُ اللهِ بْنُ مَسْلَمَةَ ، عَنْ مَالِكٍ عَنْ نَافِعٍ ، عَنْ عَبْدِ اللهِ بْنِ عُمَرَ ، رَضِيَ اللَّهُ عَنْهُمَا أَنَّ رَسُولَ اللهِ صلى الله عليه وسلم ذَكَرَ رَمَضَانَ فَقَالَ : لاََ تَصُومُوا حَتَّى تَرَوُا الْهِلاَلَ ، وَلاَ تُفْطِرُوا حَتَّى تَرَوْهُ فَإِنْ غُمَّ عَلَيْكُمْ فَاقْدُرُوا لَهُ. Bukhariy: 1906
But strictly speaking alquran never explisitely ask to see hilal when deciding the beginning and ending of fasting date in ramadhan
3. شَهْرُ رَمَضَانَ الَّذِي أُنْزِلَ فِيهِ الْقُرْآنُ هُدًى لِلنَّاسِ وَبَيِّنَاتٍ مِنَ الْهُدَى وَالْفُرْقَانِ فَمَنْ شَهِدَ مِنْكُمُ الشَّهْرَ فَلْيَصُمْهُ Al-Baqoroh:185
Qoran transcription using “faman SYAHIDA minkum SYAHRU , not TAROWUL HILAL as used in those two hadith
1. The meaning of Al-Baqoroh: 185 is: whoever syahida (testify) from you (its already in) ramadhan then he must fasting. Testifying that something exist not necessarily by seeing the things with eyes directly (in islamic term it’s a rukyah), however can also use the science which validity has been checked. For example, to testify (syahadah) that there is God, is never being required to see Him directly.
2. The question then: what about hadith that required to see hilal before deciding to begin and ending fasting date as had been quoted above? The answer is that the prophet teach his follower (at that time) to certify the beginning of month ramadhan/syawal/dzul hijjah by seeing hilal due to their limitation of ability in astronomical science (at that time). But this by no means never denying astronomical science applications in deciding the months.
3. At the present, seeing hilal to certify the beginning of ramadhan/syawal is a nomore way that more assured than counting it in astronomical way. There are two things that make this happenned: first, the pollution is getting more and more worst from time to time that cause difficulty in seeing hilal (new moon), and the second, modern astronomic science has become more and more accurate in predicting the orbit of planets including the moon.
4. Someone has challenge that the meaning of syahida in albaqoroh:185 is not testify but seeing. This challenge could esaily be argued. In arabic term, syahida is من أَسماء الله عز وجل: الشهيد. قال أَبو إِسحق: الشهيد من أَسماء الله الأَمين في شهادته. قال: وقيل الشهيدُ الذي لا يَغيب عن عِلْمه شيء
Syahida come from the name of Allah As-Syahiid, which mean “can not hiding from His knowledge anything”
Then, interpreting syahida as seeing is by nomeans too narrow and not appropriate since syahid include all things that known by seeing itself or scientifically, as well as His knowledge that already known or haven’t yet known by human being, no doubt in it, whereas the human sight is doubtful.
In ali-Imran:18 : Allah state (syahida) that there is no God but Him, standing firm on justice. The angels (1) and human beings that have knowledge (2) (also state like that).
Allah obviously, state. And (1) The angels state because they already see Allah while (2) human beings state because their knowledge tell them inductively.
If Allah has an intention to mean syahida with seeing what make Him difficult to spell the ayah by : فمن تَرَوُا الْهِلاَلَ فليصمه but He choose the word فَمَنْ شَهِدَ مِنْكُمُ الشَّهْرَ فَلْيَصُمْهُ instead.