The Moon and its Phases

© 2000–2006 Mike Wills Learning Services

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) and 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.

 

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 2009and 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. Fortunately, in 433 B.C. Meton discovered that after a 19-year cycle the phases of the Moon start to reoccur, within about 2 hours, on the same days of the same months of the year. If the dates of the full Moon are recorded during one 19-year cyle, we can work them out for all the years of the following cycles. 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 B.C. so, the golden number of a year is the remainder after the year has been divided by 19. If the remainder is 0, the golden number is taken as 19. The tables shown below give you the dates of the full Moon for 1995–2032 and 1957–1994 as well as for all 19 years of the Metonic cycle. Lunar Links Daily Moon Phases - astronomical data from the US Navy Phases of the Moon - astronomy site with moon pictures Lunar Book List Science and Technology Messageboard 1995–2032   # Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1995 2014 1 16 14 16 15 14 13 12 10 9 8 6 6 1996 2015 2 5 3 5 4 4 2 2,31 29 28 27 25 25 1997 2016 3 23 22 24 22 22 20 20 18 16 16 14 14 1998 2017 4 12 11 13 11 11 10 9 8 6 5 4 3 1999 2018 5 2,31 2 31 30 30 28 28 26 25 24 23 22 2000 2019 6 21 19 20 18 18 16 16 15 13 13 11 11 2001 2020 7 9 8 9 8 7 6 5 4 2 2 1,30 30 2002 2021 8 28 27 28 27 26 24 24 22 21 21 20 19 2003 2022 9 18 16 18 16 16 14 13 12 10 10 9 8 2004 2023 10 7 6 6 5 4 3 2,31 30 28 28 26 26 2005 2024 11 25 24 25 24 23 22 21 19 18 17 16 15 2006 2025 12 14 13 14 13 13 11 11 9 7 7 5 5 2007 2026 13 3 2 3 2 2 1,30 30 28 26 26 24 24 2008 2027 14 22 21 21 20 20 18 18 16 15 14 13 12 2009 2028 15 11 9 11 9 9 7 7 6 4 4 2 2,31 2010 2029 16 30 28 30 28 27 26 26 24 23 23 21 21 2011 2030 17 19 18 19 18 17 15 15 13 12 12 10 10 2012 2031 18 9 7 8 6 6 4 3 2,31 30 29 28 28 2013 2032 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 1957–1994   # Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1957 1976 1 16 14 16 15 14 13 12 10 9 8 6 6 1958 1977 2 5 3 5 4 4 2 2,31 29 28 27 25 25 1959 1978 3 23 22 24 22 22 20 20 18 16 16 14 14 1960 1979 4 12 11 13 11 11 10 9 8 6 5 4 3 1961 1980 5 2,31 2 31 30 30 28 28 26 25 24 23 22 1962 1981 6 21 19 20 18 18 16 16 15 13 13 11 11 1963 1982 7 9 8 9 8 7 6 5 4 2 2 1,30 30 1964 1983 8 28 27 28 27 26 24 24 22 21 21 20 19 1965 1984 9 18 16 18 16 16 14 13 12 10 10 9 8 1966 1985 10 7 6 6 5 4 3 2,31 30 28 28 26 26 1967 1986 11 25 24 25 24 23 22 21 19 18 17 16 15 1968 1987 12 14 13 14 13 13 11 11 9 7 7 5 5 1969 1988 13 3 2 3 2 2 1,30 30 28 26 26 24 24 1970 1989 14 22 21 21 20 20 18 18 16 15 14 13 12 1971 1990 15 11 9 11 9 9 7 7 6 4 4 2 2,31 1972 1991 16 30 28 30 28 27 26 26 24 23 23 21 21 1973 1992 17 19 18 19 18 17 15 15 13 12 12 10 10 1974 1993 18 9 7 8 6 6 4 3 2,31 30 29 28 28 1975 1994 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. Subscribe to Gold Membership Your own Learning Page plus access our online 'Icebreaker Manual' 'Resource Collection' and other exclusive areas Free Newsletter Learning Resource Collection Icebreaker Manual

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