What is a Hilal?
Hilal, an Arabic term, refers to the bright waxing crescent when it becomes visible to a normal observer by naked-eye.

What is a New Moon?
The New Moon is a modern astronomical term. It refers to the completely invisible moon at the start of a synodic cycle (29 days 12 hours, 42 minutes and 2.8 seconds).
Often Muslim and non-Muslim experts alike confuse astronomical “New Moon” (completely invisible at conjunction) for “Hilal”. During the time of the Messenger (S) Arabic language had only “Qamar” (Moon), and Hilal (Visible crescent moon) terms. It had no word for the astronomical New Moon (now translated as al-Qamar al-Mawlid (Born moon)) although the Jews in Medina used the Hebrew Calendar based on the “Conjunction at Jerusalem” criterion with some modifications.

Why the Islamic month cannot start from the New Moon?
Since the time of the Messenger (SAW) Islamic lunar month began from the sunset after a moon was clearly visible to observers with normal vision.
Please keep in mind that there was no printed calendar, not even a set calendar in early Islam. The Messenger (SAW) could easily adopt the Jewish lunar calendar in Medina, as he did for many other traditions like the fast on the tenth day of Muharram. Instead the Quran instructed the Muslims to fix the time by the ‘visible’ moon.
The Messenger (SAW) established the tradition of visual moon watch on the 29th day. If it was not seen then asked Muslim to complete the lunar month to 30 days. It was an established fact that a moon would always be visible on 30th evening. If it was seen on 28 the or not seen on the 30th evening then the start of the lunar month was wrong.
Muslim start their month from the sunset after a waxing crescent moon is clearly visible on the 29th or 30th day. It is not the black disk, a few shining dots, or broken crescent that experienced moon-watchers track through powerful telescopes and binoculars. In other words, a moon visible only through telescope and binoculars, but not to the casual observers by naked-eye IS NOT the Hilal that signals the beginning of the month

Visibility Criteria
The Islamic calendar has retained an observational definition of the new moon, marking the new month when the first crescent moon is actually seen, and making it impossible to be certain in advance of when a specific month will begin (in particular, the exact date on which Ramadan will begin is not known in advance). In Saudi Arabia, the new King Abdullah Centre for Crescent Observations and Astronomy in Makkah has a clock for addressing this as an international scientific project. In Pakistan, there is a "Central Ruet-e-Hilal Committee" whose head is Mufti Muneeb-ur-Rehman, assisted by 150 observatories of the Pakistan Meteorological Department, which announces the sighting of the new moon. Since its creation in 1974, the status of the Central Ruet-e-Hilal Committee has been controversial as it refused the "Witnesses" (Shahadats) from other sects. In Iran a special committee receives observations of every new moon to determine the beginning of each month. This committee uses one hundred groups of observers.
An attempt to unify Muslims on a scientifically calculated worldwide calendar was adopted by both the Fiqh Council of North America and the European Council for Fatwa and Research in 2007. The new calculation requires that conjunction occur before sunset in Mecca, Saudi Arabia and that moonset on the following day must take place after sunset. These can be precisely calculated and therefore a unified calendar is imminent if it becomes adopted worldwide

Hilal Sighting in Saudi Arabia: A First Hand Report (Salman Zafar Shaikh)
I met the brothers at KACST who were calculating the Umm-ul-Qura Calendar for Hijri dates. The brothers were very warm and welcoming. I was able to find out first hand, the details behind the Umm-ul-Qura Calendar. I found that there has been a major change in the computation criteria starting 1420 AH. Before that year, the Umm-ul-Qura calendar was based on Greenwich and not Makkah. Also it was based on the dark invisible Astronomical new moon being born. Thus it was totally different from the actual Hilal observation. Starting about 1420 AH, the new criterion is that the Moonset be after Sunset in Makkah (even by one second). Starting 1423 AH Insha’Allah, it will again change slightly to directly take the astronomical new moon (conjunction) into account. But the main input I got was that the Umm-ul-Qura calendar was for civil use only, and not for predicting the Hilal for religious dates. The author of the calendar is well aware that the moonset needs to be after sunset by a long time, and not just one second (along with other factors) for the Hilal to be visible. But the point was that the Umm-ul-Qura calendar neither attempts nor claims to predict the Hilal. It is merely used for the official dates in the Ministries, schools, Saudia Airlines, and indeed all over the country.
I was a bit hesitant to introduce the issue of errors in the Saudi announced dates for fear of offending my hosts. But Alhamdulillah they themselves expressed that they knew there were a lot of errors.

Official Saudi Hilal Sighting Committees
I was told that after the Saudi Government became aware of the complaints of errors in the announced dates, around 1419H, the ruling council ordered the formation of Hilal sighting committees. Each such committee includes:
one member of Qada (Islamic Scholar/Justice department),
one member of KACST/Astronomer,
one member of Imarah (ruling council of the city), and
volunteers.
Currently there are six such committees in Saudi Arabia - near Makkah, Riyadh, Qassim, Hail, Tabuk and Asir. While they may carry a telescope with them, the official sighting of the committee is with naked eye only. (Saudi scholars like Sheikh Al-Othaimeen are against use of telescopes. Sheikh Al-Othaimeen for example indicates that using telescopes increases the "Takalluf" (Burden) on Muslims, which Allah does not want.).
While the establishment of the committees is an excellent idea, these committees have not been given exclusive jurisdiction over the issue of moon sighting, thereby reducing their usefulness. The Justice department still accepts the witness of "any" Muslim. Thus, often the new month is declared while none of these six official Hilal sighting committees saw the Hilal. In fact, most people, including scholars are unaware of the existence of these official committees…..
……I also learned that apparently it is the same few people at certain locations, reporting on those occasions when the claims are extraordinarily early in Saudi Arabia, year after year. WAllahu A’alam! THIS COULD BE VERY POSSIBLE IN NIGERIA TOO (WaAllahu A’lam)

Moon sighting versus Moon fighting
Syed Khalid Shaukat, national coordinator, and moon sighting consultant to ISNA, expressing his disappointment over the issue, says: “In the present era of scientific and technological advancement, three decades after man landed on the moon, some Muslims are still avoiding the use of scientific knowledge for making an Islamic calendar and get over with the feuds and having to wait till midnight for a confirmation of moon sighting.”
Shaukat stresses, “Today, Muslims have expertise and access to technology to understand the calculations of when and where the sighting occurs. Recorded data shows how the science of moon sighting is compared with the actual observations. The results show that calculations of sighting and observations have matched every month since 1993. Calculations of moon sighting and actual sighting are not two different things for an Islamic Calendar when it was found that they both match.”
He stresses that the results show that with today’s technology, calculations are far more accurate than the claims of sighting, which we all have experienced, that often people mistake other objects for the crescent moon.
Shaukat points out that calculations for sighting are surety (haqqul-yaqeen), while claims of sighting may be suspicion (zann) or mistake. He says that Allah (swt) has given us the knowledge about the motions of earth and moon, and an Islamic calendar based on calculations that has proven to match with actual sighting would enable us to plan ahead of time, while actual sighting will prove to be confirmatory. This, he says, only meets the intent of Qur‘an and Sunnah and its benefits greatly surpass the consequences faced by false claims of sighting and waiting for a decision until midnight.
The most misunderstood question is whether the sighting is a means or a requirement of ascertaining the beginning of an Islamic month. Shaukat says that the answer to this question is better understood by people in the Caribbean (Caribbean Islands, Trinidad, and Guyana) where they have a 6-month long rainy season and sighting is not possible because of clouds. If they count 30 days for 3 or 4 months in a row, the moon is then sighted on the 28th or 27th day. This, he says, is a clear indication that the Sharia did not intend the sighting as an only requirement but simply as a facility, that was the sole method available to the Muslims of that era.
The opponents of scientific calculations also cite Bukhari, Vol. 3:130, and maintain that the people at the time of the Prophet (pbuh) were illiterate and thus physical sighting was the method prescribed by Allah (swt) and thus cannot be changed. Among this group, there are differences on the number of witnesses needed for confirming such a sighting.
The Fiqh Council’s view that physical sighting must go hand in hand with scientific calculations finds numerous grounds in the Hadith. ISNA, which serves as coordinator of the ISCNA moon sighting program, has set up a system where people who claim sighting the moon call the headquarters. The scientists then examine this information and discuss the various nuances with the reporter to establish the veracity of his sighting.
The need for such dual sighting is only strengthened by the fact that in contemporary times when the skies are also inhabited by numerous man made objects that may befool the viewer.
Use Astronomy to Negate Erroneous Sighting, Not to Replace Sighting
As a Muslim, we believe that all knowledge is from Allah, who is the ultimate source. Thus we find that the Qur’an has no contradiction with established facts of science. In fact the description of the embryo in the womb of the mother, the stability provided by the mountains, the hydrology / water cycle, composition of living matter mostly with water, origin of the universe and the movement of both the sun and the moon are among the amazing examples of how accurately the Qur’an revealed about 1400 years ago describes scientific facts discovered recently. The Qur’an states in Sura Ar-Rahman #55,Verse 5: (Yusuf Ali translation): The sun and the moon follow courses (exactly) computed
Thus we see that Astronomy supports Ikhtilaf Al-Matale (Local sighting) since areas outside the "Lunar Date Line" curve see the Hilal on the next day (Cross International Solar Date Line). Hence we should aim towards Eid-ul-Fitr and Eid-ul-Adha celebration around much of the world in about 24 hours (But two "solar dates" because of the artificial International solar date line). We should not force an effort to artificially make the worldwide lunar date coincide with a solar date. Also, note that at any one given moment of time, one part of the world has one solar day/date while another part of the earth has the next solar day /date! For example, at the exact time of my writing this sentence, it is Wednesday evening in USA, but Thursday morning in China / Japan! So we should focus on Eid prayer around the globe in about 24 hours rather than one solar date. Local sighting for Eid is as natural as local timings for prayer. After all, New York does not pray Fajr by Tokyo time!

All said and done I have a gut feeling some people will report to the Sultan that they saw the moon even despite all empirical possibilities.

See evidence below of when the NEW MOON will be borne in Nigeria (Lagos).
Its amazing how we get to see the Hilal when the moon just started a new course

Muslims have a long way to go.

and the KSA Kingdom of Saudi Arabia is not helping matters in any way to say the least

KSA announced that tomorrow is eid.
http://www.arabnews.com/featured/news/777491

We await to hear if Sultan will follow suit.

the visibility curves below says otherwise sha. except if they employ instruments such as telescopes for the session

As Sultan has now announced tomorrow as eid.
This is to wish all muslims happy eid celebrations.
But I wish things could be better

We muslims have a looooooong way to go.

how we sight a moon that is yet to be born is amazing.

Its a global problem that the Sheikhs needs to sit and resolve