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Ancient Timekeepers, Part 4: Calendars

All calendars began with people recording time by using natural cycles: days, lunar cycles (months), and solar cycles (years). Ancient peoples have attempted to organize these cycles into calendars to keep track of time and to be able to predict future events of importance to them, such as seasons (e.g. the annual Nile flood in ancient Egypt), eclipses etc. The main problem was that these natural cycles did not divide evenly.

Today, the solar year is 365.242199 days long (or 365 days 5 hours 48 minutes 46 seconds) and the time between full moons is 29.530589 days.

Therefore in 1 year there are 12.37 moon cycles (365.24 / 29.53 = 12.37).

The Moon makes a complete orbit around the Earth with respect to the fixed stars about once every 27.3 days (sidereal period). However, since the Earth is moving in its orbit about the Sun at the same time, it takes slightly longer for the Moon to show the same phase to Earth, which is about 29.5 days (its synodic period).

Moon’s Synodic and Sidereal month. Click to enlarge

Nature’s Nearly Perfect Calendar

The Moon could be “Nature’s perfect clock” if the solar cycle period were exactly divisible by the period of the lunar cycle.

For example if the solar year were exactly 364 days (instead of 365.24 ) and lunar cycle exactly 28 days (instead of 29.53), we would have a “perfect calendar” based on 13 months of 28 days per month, with each month having 4 weeks of 7 days. Such calendar was proposed as “13 Moon Calendar” (discussed later in this article) with the 365th day called the “Day Out of Time”.

Another “perfect calendar” would require solar year to have 360 days and lunar cycle 30 days:

The “perfect” Earth would take 360 days to complete 360 degree circular solar orbit (1 deg per day).

The “perfect” Moon would take 30 days to complete 360 degree circular orbit around the Earth (12 deg per day).

In such case, we could have a year based on 12 months of 30 days. Each month would have 5 weeks of 6 days each.

We can only wonder if these numbers were true for the Earth in the the early period of the solar system…

The Solar and Lunar Cycles

Although the “ideal” periods of the solar and lunar cycle are described by numbers very close to the current values, calendars must reflect the correct numbers in order to properly keep track of time and have seasons in sync.

At present the time for Earth to complete full orbit around the Sun in “Solar Days” is365.242199 days* long (365 days 5 hours 48 minutes 46 seconds). Earth orbits the Sun once every 366.242 times it rotates about its own axis in relation to stars but in relation to the sun it turns only 365.242 times to complete its orbit.

*Earth moves 1 degree on its orbit around the sun in 365.242/360 = 1.0145611 solar days (or 366.242/360=1.0173388 sidereal days).

This is over-rotation by 5.242 degree. How far on the orbit the earth travels during one full solar rotation (in one full day)?

360/365.242 = 0.98565 degree or 59.1389 seconds. During 1 degree orbital travel, earth rotates (in relation to stars) 1 + 0.0173388 times on its axis (360 + 6.242) degrees.

The time between full moons is 29.530589 days.

So a month measured by the moon doesn’t equal an even number of days, and a solar year is not equal to a certain number of moon cycles (months or “moon”ths).

Before we continue with the calendar basics, it is worth to answer this question: What does the orbit of the Moon around the Sun look like? Most people (almost all mathematicians) tend to believe that it will have loops and look something like the picture below:

Pics on link:

http://blog.world-mysteries.com/science/ancient-timekeepers-part4-calendars/