The Moon and its Phases

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The Moon must have made an incredible impression on the first members of the human race. Apart from being the brightest object in the night sky, its constantly and regularly changing shape may have led to the invention of the first calendars.

Lunar Facts
Diameter	3 476 km
Mean distance from Earth	384 400 km
Moon:Earth mass ratio	1:81.3015
Synodic Month	29.530588 days
Sidereal Month	27.321661 days
Orbit’s eccentricity	0.0549
Orbit’s inclination to ecliptic	5° 8' 43"
Orbit’s inclination to Earth's equator	18.5° to 28.5°
Mean magnitude of full Moon	-12.7
Optical libation in latitude/longitude	±6.7°/±7.6°
Temperature	-153°C to +134°C
Surface gravity	1.622 m/sec²
Escape velocity	2.38 km/sec

What could be more natural than to say: ‘Let’s meet again at the next full Moon.’ The Moon’s phases were there for everyone to see and their use would avoid the counting and recording of the number of days since the last meeting. It was thus inevitable that the month would become an inseparable part of our calendar — along with the day, marked by the movement of the Sun, and the year which was marked by the passing of the seasons.

A natural next step would have been to link the lunar month with the year — and this is where the difficulties began. Initially, twelve lunar months with four seasons of three lunar months would have seemed a good approximation to the year. Unfortunately, the lunar month is just over 29½ days long which means that twelve lunar months falls short of a year by about eleven days.

Starting a year eleven days early might not seem much, but after only three years the lunar year would be a calendar month out of step with the seasons which would certainly cause problems with the sowing of crops if you live in an agricultural community.

So, how about a year of 13 lunar months? Unfortunately, this would lead to a year that would be over 18 days too long.

In 433 B.C. Meton discovered that 19 years (6939.689 days) is almost exactly the same length as 235 lunar months (6939.602 days). This would produce a year that would be that a 19-year cycle consisting of 12 years that were 12 lunar months long and 7 years that were 13 lunar months long would keep the lunar months in step with the seasons. These dates were inscribed in gold lettering on public monuments and, for this reason, the number of a year in a Metonic cycle is called the Golden Number.

The first year of a cycle can be chosen arbitrarily but the cycles now in use can be traced back to 1 BC where the cycle begins at 1 when the New Moon occurs on 1 January (1995, 2014, 2033). You can also see whether a year is the beginning of a cycle by dividing it by 19 and checking whether the remainder is 0.

Predicting the phases of the Moon

Calculating the date of many religious festivals, including Easter, requires you to be able to predict the dates of the full Moon. As the mean time between the Moon’s phases is just over 29½ days, you could roughly predict the next few occurrences of the same phase by alternating gaps of 29 and 30 days. Unfortunately, this method will become inaccurate after a few months because the Moon is subject to over 1500 influences which can affect the date of the full Moon from month to month.

You could also use a more accurate figure for the mean lunar month. In the following program I have used a value which holds good for the year 2009 and the start of 2010 but becomes inaccurate after that. Click the button, and click again to show the following years. Please note that this program will only work with browsers that recognise four-figure years, e.g. 2009 not 09.

The Metonic cycle described above is more accurate and the table shown below give you the dates of the full Moon for 2014–2051 and the Golden Number for each of those years.

2014-2051

		#	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
2014	2033	1	16	15	17	15	14	13	12	10	9	8	7	7
2015	2034	2	5	4	5	4	3	1	1,30	28	27	26	25	24
2016	2035	3	23	22	24	22	22	20	20	18	16	16	14	14
2017	2036	4	12	11	13	11	11	10	9	8	6	5	4	3
2018	2037	5	2,31	2	31	30	30	28	28	26	25	24	23	22
2019	2038	6	21	19	20	18	18	16	16	15	13	13	11	11
2020	2039	7	9	8	9	8	7	6	5	4	2	2	1,30	30
2021	2040	8	28	27	28	27	26	24	24	22	21	21	20	19
2022	2041	9	18	16	18	16	16	14	13	12	10	10	9	8
2023	2042	10	7	6	6	5	4	3	2,31	30	28	28	26	26
2024	2043	11	25	24	25	24	23	22	21	19	18	17	16	15
2025	2044	12	14	13	14	13	13	11	11	9	7	7	5	5
2026	2045	13	3	2	3	2	2	1,30	30	28	26	26	24	24
2027	2046	14	22	21	21	20	20	18	18	16	15	14	13	12
2028	2047	15	11	9	11	9	9	7	7	6	4	4	2	2,31
2029	2048	16	30	28	30	28	27	26	26	24	23	23	21	21
2030	2049	17	19	18	19	18	17	15	15	13	12	12	10	10
2031	2050	18	9	7	8	6	6	4	3	2,31	30	29	28	28
2032	2051	19	27	25	27	25	25	23	22	21	19	18	17	17
		#	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec

Muslim Calendar

The Muslim calendar continues to use a system based on lunar months with alternating months of 29 and 30 days. This means that all the months including the ninth month Ramadan — the month of fasting — continually cycle through the seasons.

To keep the months in step with the Moon’s phases, a further correction is made by varying the length of the twelfth month over a 30 year cycle: 29 days long for 19 of the years, and 30 days long for the remaining 11 years.

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