Determining the beginning and the end of a new month through astronomical calculations is unfounded in the Qur'an and Sunnah. The standard in the shari'ah for discerning the beginning of a new month and the end of the last month is based on actual moonsighting. Which means that if the moon is not sighted, the month will be completed with thirty days. In the ahadith, the Blessed Prophet incessantly put emphasis on this:
Do not fast unless you see the moon, do not break your fast until you see the moon. (Bukhari H.1773, Muslim H.1795, Nasai H.2093, Abu-Dawood H.1976, Muatta Malik H.557)
Meaning that if you do not see the moon, then do not begin the month of Ramadan and likewise, do not celebrate the Eid until you sight the moon. In another hadith the Blessed Prophet clearly prohibited the use of calculations. He said:
We are an illiterate nation. We do not write or calculate months. He said it is like this, this, or this. So saying, the Blessed Prophet lifted his hands three times with all fingers spread the first two times and the thumb hidden the third time to indicate 29 days. Then he said the month is like this, this, and this and again lifted his hands three times, this time all fingers spread out each time to indicate 30 days. (Muslim H.1806, Bukhari H.1780, Nasai H.2111, Abu-Dawood H.1975)
In this hadith, The Blessed Prophet certainly doesn't mean to say that this is an ummah of illiterates, but rather he is emphasising their simplicity of not being educated in the subject which we are discussing. The purpose behind this is to declare that we do not know calculations nor are we going to use this method to figure our months. This is a universal religion. Anyone from anywhere can follow it wherever he may be. If the system was based on calculations, the decision of millions of people would be in the hands of the few who would decide when the month begins and when it ends. Instead, Islam based the lunar calendar on moonsighting so that even bedouins, who are out of touch with most modern sciences and technologies, could sight the moon and know when the month begins and ends.
This may raise a question in the mind of many that if Islam is all about simplicity, then why do we use time tables for salah and depend on the calculations which produce those time tables. This is an important question because the answer to it will prove how Islam is indeed a universal religion and will also reveal the most fascinating miracle of the Blessed Prophet . To understand this we need to remember that in Islam, the beginning and end of the month rely on the sighting of the moon while the salah timings are based on the movement of the sun.
Calculations to this day have not been able to inform us of when the moon can first be sighted; the only thing known to us from the calculations is when the moon is born. And we as humans cannot see the moon immediately after its birth. How many hours does it take before the moon can be seen? Sometimes it can be seen after 14 hours and at other times it cannot be sighted even after 20 hours. This is because there are many different factors which contribute to the sighting of the moon.
The sun is different. During the day, the sun is very easily seen every day except for when the skies are overcast. This is one difference between the sun and moon. Another big difference between the two is that the sun runs on a set path that is the same each and every year. For example, if one measures the time of the rising and setting of the sun on the first of January, 2005 he will find that is no different from the time of the rising and setting of the sun on the same date, one year before or after. And if one measures the time of the rising and setting of the sun on the same date ten years later it will still be no different from the time the sun rose and set on January 1, 2005. So if one person notes the movement of the sun one whole year and makes a time table out of his observations he could continue using that time table for the rest of his life. And in reality this is exactly how the time table for the salawat was made. Once this time table was produced, there was no need to repeat the process of observing of the sun.
The moon in this aspect is a very different case. If Ramadan was 30 days this year, it won't necessarily be 30 days the next year or the year after that. And this highlights the miracle of the Blessed Prophet that he prohibited the use of calculations and formulas to determine the birth of the moon (nor do we write nor do we make calculations), but didn't include under this order the movement of the sun. How was the Blessed Prophet to know 1,400 years ago of the consistency that was in the movement of the sun and that, despite the latest breakthroughs in astronomical data and calculations, no one would ever be able to read the exact time of the sighting of the new moon.
In summary, it is not possible nor has the Shari'ah allowed the Islamic lunar calendar to be based on calculations. This has never been permitted and has been the consensus of the Ummah. Though, this much can be said that Islam does allow using astronomical calculations to aid in moonsighting. For example, it can be helpful in providing us the approximate timings to when the moon will be most likely visible, or the age of the moon at the time of the setting of the sun, or at what time the moon will set.