One of the important issues Muslims face which needs to be addressed scholarly and juristically is the issue of whether the start and end of the lunar months through Astronomical Calculations is valid in Islamic Jurisprudence, or is physical moon sighting the only valid opinion. Scholars on the two sides of the divide present arguments and support their views by citing the same sources. In Nigeria, moon sighting has been a serious problem for many years. The Islamic calendar is lunar. Lunar calendars follow the phases of the moon, beginning with the crescent moon and ending with the conjunction of the moon. The foundation of legal ruling in Islam is the Qur’an and the Sunnah. It is in the absence of decisively authentic and unequivocal texts that, scholars may resort to ijtihad. There are several positions on moon sighting. The most prominent are regional sighting, physical sighting globally, Mecca time-point for reference, and Astronomical Calculation. The popular view among Muslim jurists is the actual sighting of the crescent. The paper, therefore, concludes that all the aforementioned trends are acceptable. Eid al-Adha is independent of Arafah because both are observed on different days, therefore the observance of Eid al-Adha on Arafah day in any part of the world is allowed and acceptable. However, the evidence compels Muslims to follow the opinion of the majority of Muslims in any country. The paper, therefore, recommended the establishment of a Federal Ministry of Islamic Affairs to be in charge of moon sighting and Eids.