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Last week, the 9th of November 2011, marked the end of Eid al-Adha, the Muslim festival to commemorate Abraham’s willingness to sacrifice his only son Isaac to God. Eid al-Adha started on Sunday the 6th of November (or Monday the 7th, depending on where you are) and ended on the 9th (or 10th) of November in 2011. But, next year it will start on Friday the 26th of October, and last year (2010) it started on the 16th of November. Why does it move?

It all has to do with the Moon. For the Muslim calendar, which is based on the Moon, Eid al-Adha is celebrated on the 10th day of the 12th month, so on the 10th day of the month of Dhu al-Hijja. There are 12 months in the Muslim calendar, and each month lasts from one new Moon to the next new Moon.

A Waning gibbous Moon

A waning gibbous Moon

I got this quote from here

Regional customs or moon sightings may cause a variation of the date for Islamic holidays, which begin at sundown the day before the date specified for the holiday. The Islamic calendar is lunar and the days begin at sunset, so there may be one-day error depending on when the New Moon is first seen.

Most societies initially created calendars based on the Moon. If you think about it, there are only three natural cycles, apart from the daily one of day and night. These are

  • the waxing and waning of the Moon
  • the time it takes for the stars to appear in the same part of the sky at e.g. sunrise.
  • the solar cycle, e.g. the time between successive longest days of the year.

Of these 3, the cycle of the Moon is by far the most obvious and easiest to observe, and it is why most early civilisations based their calendars on the Moon. Today, most calendars are either Solar (based on what the Sun is doing), or Lunisolar, a combination of Lunar and Solar calendars. Examples of lunisolar calendars are the Jewish calendar, the Chinese calendar, the Hindu calendar and even parts of the Christian calendar, such as the date of Easter [which is determined by a combination of what the Sun and the Moon are doing]. Any festivals which are based on a Lunisolar calendar will move from year to year, but back and forth rather than just getting earlier each year.

The Moon actually takes 27.32 days to complete a 360 ^{\circ} passage around the Earth. This is known as the sidereal period of the Moon, the word sidereal deriving from the Latin word “sidus” meaning “star“. So the sidereal month is the completion of an orbit with relation to the “fixed” stars [so, if you were in a space ship looking down on the Moon moving around the Earth, with the distant stars in the background to provide a reference, you would see the Moon move 360^{\circ} in a sidereal month].

However, this is not the time between one new Moon and the next, or one full Moon and the next. For a second new Moon to occur, the Moon has to travel a little further than 360^{\circ} in its orbit. This is because, in the time between the previous new Moon and this one, the Earth has moved around the Sun, and so the Moon has to travel a little further than 360^{\circ} to produce a 2nd new Moon.

A sidereal and synodic month

The difference between a sidereal Month and a synodic Month

This takes 29.53 days, and is called the Synodic period of the Moon. [Note: due to variations in the Earth-Moon system, and the fact that the Earth varies its speed of orbit about the Sun during the course of the year, the synodic period varies between 29.18 and 29.93 days. 29.53 is the average.]

There are nearly exactly 365.25 days in a year [I will come back to discuss the measurement of what a “year” is in a future blog], so if you divide \frac{365.25}{29.53} you get 12.37, which is not exactly 12, so a 12-month calendar based on the Moon will not fit into a year without some days being left over. The civil calendar in all(?) countries is the Gregorian calendar, which keeps the Sun doing the same thing on the same day each year (i.e. it is a solar calendar). The number of extra days between a 12-month Lunar calendar and a year is 0.37 \times 29.53 = 10.89, so nearly 11 days. In a 12-month Lunar calendar, the same day in the same month will be approximately 10-11 days earlier each year.

This is why Eid al-Adha started 10 days later in 2010 than it did this year, 2011, and why Easter will not be on the same day in 2012 and it was in 2011, and why the Chinese new year will not be on the same date in 2012 as it was in 2011, or Diwali, or Hanukkah.

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