Length of The Lunar Month
The length of a month orbit/cycle is difficult to predict and varies from its average value. Because observations are subject to uncertainty and weather conditions, and astronomical methods are highly complex, there have been attempts to create fixed arithmetical rules.
The average length of the synodic month is 29.530589 days. This requires the length of a month to be alternately 29 and 30 days (termed respectively hollow and full). The distribution of hollow and full months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day. In the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed:
- 29 / 1 (error: 1 day after about 2 months)
- 30 / 1 (error: 1 day after about 2 months)
- 59 / 2 (error: 1 day after about 33 months)
- 443 / 15 (error: 1 day after about 30 years)
- 502 / 17 (error: 1 day after about 70 years)
- 1447 / 49 (error: 1 day after about 3 millennia)
- 25101 / 850 (error: dependent on change of synodic month value)
These fractions can be used in the construction of lunar calendars, or in combination with a solar calendar to produce a lunisolar calendar. The 49-month cycle was proposed as the basis of an alternative Easter computation by Isaac Newton around 1700. The tabular Islamic calendar's 360-month cycle is equivalent to 24×15 months minus a correction of one day.
Read more about this topic: Lunar Calendar
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