I am an amateur astronomer and a member of the West of London Astronomical society ( WOLAS) since 2012. I am a regular attendee of their monthly meetings where well-known astronomers speak on different topics with a half-hour Q&A session afterward. I have attended two sessions dedicated to the Moon. My views on the subject of the new moon are noted below.
The statement in the video about the new moon and sighting of the crescent is mostly correct. Although the date & time of each new moon can be computed exactly; the visibility of the Crescent as the function of the Moon’s age cannot be predicted with certainty and thus it cannot determine that moon would be definitely visible at a given location.
This is because, among other variables, neither the earth’s orbit around the sun nor the moon’s orbit around the earth is perfectly circular, also the moon’s orbital plane (relating to inclination & longitude with reference to earth) is tilted by 5.1° and the moon’s equatorial plane is tilted by 1.5°, therefore the location of the observer earth makes a lot of difference to the actual sighting of the new crescent moon.
Effect of the location is evident by the fact that people living in the northern hemisphere will find that the Moon looks/ appears upside down when looking at it from the southern hemisphere. Moon can also appear as much 14% larger in size on certain occasions.
Without going into too many details which require using the astronomical terms (some of which even I don’t understand completely); IMO, main reasons for the lack of certainty are the moon’s elongation (angular separation between the sun the moon with the earth as the reference point), the width and surface brightness of the crescent; the absorption of moonlight and the scattering of sunlight in the earth's atmosphere and the quality of the eyesight of the person looking at it.
Ramadan & Eid moon sighting is, however, a very important religious matter. Most of the traditional Sunni Islamic scholars follow the Hadith which refers to the physical sighting of the crescent at your location. Actual Hadith is:
“ Abu Hurayrah relates that the Prophet (sall Allāhu ʿalayhi wa sallam) said, ‘Fast when you see it (i.e., the moon) and cease fasting when you see it, and if it is hidden or cloudy, complete the counting of Sha’bān as thirty days.’
The beginning of a Lunar month for the Shia community is also essentially the same as the Sunnis. According to the Shi'a jurisprudence, it can be determined in one of the following ways.
· A person himself sees the crescent of the moon.
· Gaining confidence in the report of others or other rationally acceptable sources.
· Testimony of two just men whose report is not in contradiction to astronomical rules.
· If thirty days have passed since the first of the previous month.
· The verdict of the Sharia ruler (according to the views of some religious authorities)
http://en.wikishia.net/view/Moon_Sighting
Being a Muslim, albeit a sinner, I cannot with clear conscience ignore a very specific Hadith which is accepted as correct by nearly all of the major Islamic sects. However, the Hadith refers to the place where the Muslim is physically located. Since Arabia is too far from Pakistan or the UK where I am residing, I would disregard the option of following the moon sighting in Mecca/Saudi Arabia. Instead, I suggest a duel scientific approach governed by religious principles.
Scientifically speaking; New Moon is born after the completion of the lunar cycle which is 29.530588 earth days. During the first day after New Moon, the nascent crescent Moon appears very low in the western sky after sunset and must be viewed through bright twilight, as it sets very soon after the sunset. The crescent at this time is also quite thin and has a low surface brightness, hence can easily be lost in the twilight glare. This makes the sighting of the lunar crescent within one day of the New Moon, if not impossible; extremely difficult.
Generally, the day old lunar crescent sets about 20 to 30 minutes after the sunset. It would be visible to experienced observers looking in the right direction close to the horizon under good sky conditions. We could use calculations and modern simulations for knowing where and when to look for the crescent moon and when the New Moon is born. There is bound to be a few places in Pakistan with a clear horizon and with help of binoculars/telescope the task would not be too difficult one day after the birth of the new moon.
This method should be employed for the determination of the first day of Sha’ban, Ramadan as well as for first day Shawwaal (Eid). However if for some reason there was no sighting reported as could be the case in the UK; we should celebrate Eid based upon days in the month of Sha’ban as narrated in the Hadith.
One should ignore the reported sightings as lies or hallucinations when it was scientifically determined that crescent moon set before the sun, at the same time as the sun or within a couple of minutes of the sunset; because it would not have been possible to physically sight moon even with a telescope.
no, you didn't 
