When calculating moon phases and prayer times found acceptance among the scholars?

Question

After posting the question Are questions on the historical inauguration of some "utilities" or "methods" on topic? on meta I finally decided to ask ask it here:

I'm pretty sure that calendars or methods to calculate the moon phases have been developed in the golden ages of islamic caliphates, as there have been lots of scientists such al-Biruni (even Imam Malik has been said to have written a book about that) and many others. But what I'd like to know is:

When and where scholars or clerics introduced or accepted them as a utility for declaring or calculating important dates like 1st day of Ramadan?

Any details on this historical inauguration would be fine!

I think of information like: how was the general acceptance at the time, who was the cleric, who was the person or scientists whom's caclulation methods or calendar was accepted ...

Answer 1

i have found some information in wikipedia: https://en.wikipedia.org/wiki/Tabular_Islamic_calendar :

The Tabular Islamic calendar (an example is the Fatimid or Misri calendar) is a rule-based variation of the Islamic calendar. It has the same numbering of years and months, but the months are determined by arithmetical rules rather than by observation or astronomical calculations. It was developed by early Muslim astronomers of the second hijra century (the 8th century of the Common Era) to provide a predictable time base for calculating the positions of the moon, sun, and planets. ...

but i do not know anything other than that.

Answer 2

it is quite hard and as i know a good algorithm was invented only in 20th century: http://www.staff.science.uu.nl/~gent0113/islam/islam_lunvis.htm . and it seems to me it is not very good, because it is written there that new moon visible only after sunset, but i saw in stellarium that it is visible before sunrise in southern hemisphere.

and it is not muslim scientist invented that, as i see.