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Calendars and clocks are used to keep track of time. Unlike simple timepiece such as an hourglass, which just measures elapsed time, the function of the calendar is to keep track of periodic events. Most common periodic events are the cycles of day and night, the waxing and waning of the Moon, seasons of the year.
The solar day is the period of time in which the Earth completes the rotation on its axis. As the day progresses it manifests itself in apparent movement of the Sun, stars and planets. The period of darkness - night is followed by the period of light -- day. Since the Sun rises and sets each day and man's life revolves around this cycle, this basic calendar unit was accepted by all men as the solar day.
The daily cycle of the Sun is most obvious, but to measure longer periods of time and to commemorate events we need longer calendar units. What shall be the standard used to mark a longer period? In nature we have only two other obvious cyclical occurrences - the monthly lunar cycle and the yearly solar cycle.
The concept of the month is based on the lunar cycle and indeed, the word "month" is derived from the word "Moon", while its Hebrew equivalent Chodesh / *** is from Chadash / *** - new, which points to renewal of the Moon.
Lunar month is the period of time in which the Moon completes its rotation around the Earth and lines up between the Sun and the Earth. It manifests itself in apparent waxing and waning of the Moon - from new Moon (Molad / *** in Hebrew) to full Moon and to next new Moon. The actual time between two new Moons may vary by several hours due to a number of factors, including changes in the gravitational force from the Sun, and the Moon's orbital inclination.
The average lunar month is called in astronomy the mean lunation period or a synodic month. Latest astronomical research measures its current length as 29.5305889 days. However, the length of average lunar month changes over very long period of times. Around 1900 it was 29.5305886 days, and around 2100 it is believed to be 29.5305891 days.
The solar year is the period of time in which the Earth completes its rotation around the Sun. As the year progresses it manifests itself in apparent changes of the Sun's height above the horizon, changes in daylight length and the cycle of seasons. The actual length of a particular year will vary by several minutes from the next due to the changing influence of the gravitational force from other planets.
The average solar year, which is the time measured from one fixed point, such as a solstice or equinox, to the next is called in astronomy tropical year. Its length is currently measured as 365.242190 days, but, again, around 1900 the year was 365.242196 days, and around 2100 it will be 365.242184 days. The reason for this variance is that the Earth's orbital position shifts slightly each year. Together with the fact that the Earth's orbit is not perfectly circular, it causes changes in the length the solar years.
In the rest of this article we shall refer to synodic month and tropical year as simply lunar month and solar year.