Some Islamic rituals are performed using the parameters obtained from various astronomical phenomena. Traditionally, they are determined from manual, self-performed, visual observations. Science allows them to be instead determined from calculations that use the spherical Earth model. The fact that the results of the calculations corroborate with centuries of visual observation proves the Earth is a sphere. Full disclosure, I'm a Muslim myself. These astronomical observations are something that can be done by everyone, not just Muslims, and the results will be consistent only with the spherical Earth model. Muslims simply provide the results of observation, over several centuries, from plenty of locations on Earth. 1. The direction of the Qibla Muslims perform prayers by facing the Qibla, or the direction to the Kaaba in Mecca, Saudi Arabia. Traditionally, the Qibla is determined from the direction to the Sun when the Sun is directly overhead the Kaaba. This occurs every year on May 27-28 at 9:18 GMT and July 15-16 at 9:27 GMT. If the sun is visible from a location at one of those times, then the direction to the Sun will be the same as the direction of Qibla. Using the knowledge of the correct shape of the Earth, the Qibla can also be determined from spherical trigonometry. This is the same problem as finding the initial bearing of a great-circle route, only with Mecca as the destination. Comparison of flat & spherical Earth model, using Perth as an example: During the sunset in Perth, on May 27-28 and July 15-16, the direction to the Sun is the same as the Qibla. Spherical trigonometry will give us the correct direction, while the result from the flat Earth model is about 32° off. If the sun is below the horizon when it is directly above Mecca, it is not possible to do the observation above. It will be necessary to do the reverse: when the sun is above Mecca's antipode (in the Southern Pacific Ocean, close to Tematagi Island, French Polynesia), the direction away from the sun is the same as the direction of the Qibla. In other words, the shadow of an object will point to the Qibla. This occurs on January 12-13 at 21:29 GMT and on November 28 at 21:09 GMT. I created an online tool for comparing the Qibla in the flat vs globe Earth model here: kiblat.bumidatar.id. It is in Indonesian, but usable in English using Google Translate. 2. Salah/Praying Times There are five compulsory prayers every day, each with a specific time range to do it. Fajr: from the beginning of twilight until sunrise. Zuhr: from the culmination of the sun, until the start of asr below. Asr: starts when the shadow of an object is the same length as the object itself, plus the shadow length at zuhr. Maghrib: from sunset until the start of isha below. Isha: starts when the twilight disappears, until the beginning of fajr above. Traditionally, praying times are determined from visual observation, but practically nobody does that anymore. Most Muslims today are using tables, apps, or online calculators to determine praying times. All which are the results from calculations using the spherical Earth model. There are some slight variations of the criteria between different denominations, and many different algorithms to calculate them. Wikipedia has an explanation of how to do the calculation here: https://en.wikipedia.org/wiki/Salah_times; I've seen more sophisticated algorithms that account for altitude, atmospheric refraction, and adjustment for the result to cover an entire city. It is evident that whatever the algorithm, it only applies to the spherical Earth model, and does not make any sense on the flat Earth model. Case in point, the criteria for Fajr and Isha is defined as the time when the altitude of the sun is 19° and 17° below the horizon (Indonesian criteria, might be different elsewhere). However, in the flat model, the sun never set below the horizon. 3. The Beginning of Month in the Hijri Calendar A lot of Islamic rituals depends on the determination of the beginning of the month in the Hijri calendar. The Hijri calendar is a lunar calendar that starts on the new moon. The observance of the new moon just after sunset —Muslims call it 'hilal'— marks the beginning of the month. Some denominations regard the visual observation of the hilal is part of the ritual. Others think it is OK to determine it solely from calculations. The Hilal is determined from the ephemeris, and obviously, only make sense on the spherical Earth model. There are many different convoluted algorithms to calculate hilal, with parameters unclear where they are coming from. For educational purposes, I find it easier to explain it using brute force: The fact that the results of calculations corroborate with centuries of observation proves spherical Earth. It is not possible to perform the calculation using the flat Earth model and still gives us the correct results. The results of visual observation sometimes lag a day from the results of calculations due to weather and atmospheric conditions, etc., not because the calculations are wrong. For the denominations that insist on visual observation, they usually still include how to do the calculations in their 'guide books,' because it is still useful as an aid for the visual observation. 4. Determining the Occurrences of an Eclipse Salat al-Khusuf & Salat al-Kusuf are optional prayers during a lunar & solar eclipse. Traditionally these rituals are performed when it is observed that an eclipse is happening. Today, science allows an eclipse to be predicted far before it occurs. This allows the prayer to be scheduled far in advance. Predicting eclipses can only be done with the knowledge that the Earth is spherical, especially solar eclipses, where it does not happen everywhere on Earth. All the usual arguments involving eclipses also apply here. Before anyone asks... Yes, there are Muslim flat-Earthers despite all of these. The calculations are usually done by a religious body, and regular Muslims simply use the results without knowing how they were calculated. No, once they think the Earth is flat, it is hard to convince them otherwise, despite all of these. Telling these facts to Muslim flat-Earthers that never heard of them before will sometimes yield a very explosive cognitive dissonance. Sometimes they start with the usual, technical, flat-Earth arguments, but when they feel cornered, they will unleash the religious arguments, thinking it would 'save' them. Muslim flat-Earthers also like to quote scripture to support flat-Earth, just as it occurs with other religions; despite they do their prayers every day using the results from spherical Earth calculations, and it is a fact that requires no interpretation. It appears that the more 'religious' the environment, the more susceptible a Muslim to become a flat-Earther. A lot of Muslim flat-Earthers here in Indonesia came from Islamic high schools and universities. The Aceh Province implements the sharia law, and they lead the country on the belief in a flat Earth, by quite a margin. Islamic extremists have killed people because of their belief in a flat Earth.