The Moon was New on Saturday October 1, very early on that date, and therefore conceivably becomes visible as a very thin crescent at the sunset of October 2.
The figures “+48” etc. represent the “age” of the Moon, in hours from its New moment.
The instant of New Moon was 0h 11m by Universal (Greenwich) Time, which means that in America it was back in Sep. 30 (8:11 PM in the eastern and 4:11 PM in the Pacific zones). One of those fairly rare instances of a Moon phase that may be put in one month by a certain printed calendar and a different month by another.
This New Moon was the one that was closest to the September 22 equinox. The result is that both the Jewish and the Muslim years begin on October 2.
A thing that has to be borne in mind, with some difficulty, is that, in both these calendars, days begin at sunset – not at midnight as in our familiar calendar. So we can say that the Jewish and Muslim years began at sunset on Oct. 2, but Oct. 3 is the “first day” of each calendar.
The Jewish rule is that the year begins at the first sighting of the young Moon, after the New Moon nearest to the autumn equinox. There is a tradition that the slender Moon was looked for when the sky becomes dark enough for three stars to be seen. However, the date is calculated with tables and formulae drawn up by Hillel II, great Nasi or “prince” of Judaism, in 363 AD, based on the Moon’s mean motion, and is occasionally one day too early, as in 2002. The calculation provides (I’m not sure why) that if the new year Day should be a Sunday, Wednesday, or Friday, it is moved one day later. (Day 1 of the Jewish week begins at Saturday sunset.) That apparently didn’t apply this time.
The Muslim calendar is more thoroughly lunar, so it is not tied to the autumn equinox. Its months, too, begin at the first visibility of the Moon. This may be based on actual local sightings of the Moon, so that if it is not seen as expected the beginning of the month, and year, can be delayed, even by two days. But now in most Muslim countries the date is based on calculations, which have been revised not long ago. There are twelve months, and since they are lunar (averaging about 29.5 days as against solar months of about 30.4) the year is shorter, and its beginning slides progressively earlier.
. Jewish Muslim
2007 Sep 12/13 Jan 19/20
2008 Sep 29/30 Jan 9/10 AND Dec 28/29
2009 Sep 18/19 Dec 17/18
2010 Sep 8/ 9 Dec 7/8
2011 Sep 28/29 Nov 26/27
2012 Sep 16/17 Nov 14/15
2013 Sep 4/ 5 Nov 4/5
2014 Sep 24/25 Oct 24/25
2015 Sep 13/14 Oct 14/15
2016 Oct 2/ 3 Oct 2/3
2017 Sep 20/21 Sep 21/22
In my list, “12/13” for example means that the day begins at sunset on the 12th and ends at sunset on the next day. I haven’t given the calendars’ own year-numbers. Jewish year 5777, and Muslim year 1438, begin today.
Notice that the starts of two Muslim years fell within Gregorian year 2008.
So there is a cycle, of around 32 years, though irregular, since the Jewish year-beginnings, though not varying so widely, do vary from early September into (as now) the beginning of October.
The Jewish and Muslim new-year days last coincided in 1984 and 1985. And now they come around to coinciding again.
And they will almost do so next year, when New Moon will be less than 3 days after the equinox; but not quite. Unless the capricious Moon, who chooses whether to show herself in those early evenings of her life, makes a one-day difference.
The Muslim new-year day is called the 1st of Muharram, being the beginning of that month; also Ra’s al-Sanah, “head of the year.” The Jewish new-year day is the 1st of the month Tishri, and is Rosh ha-Shanah, with the same meaning as its Arabic cognate. And here is the new-year greeting, Shanah Tovah, “Good year!,” copied from the copious blog of my friend by occasional correspondence Aharon Eviatar, emeritus professor of geophysics and planetary science at Tel Aviv University, and indefatigable campaigner for the human rights of Arabs and everyone else.