Lunar calendar

A lunar calendar is a system for tracking time using the Moon. It organizes months based on the cycles of the Moon's phases. These individual cycles are known as lunations or synodic months. A lunar calendar is different from a solar calendar. Solar calendars follow the solar year, which is the time it takes for Earth to orbit the Sun. Because of this difference, a lunar calendar operates on a different schedule than most modern civic calendars.

To understand how these calendars work, we must look at the length of a lunation. One mean synodic month lasts approximately 29.53059 days. This is exactly 29 days, 12 hours, 44 minutes, and 3 seconds. Because months cannot have partial days, lunar calendars often alternate between 29 and 30 days. A full lunar year consists of 12 such lunations. This makes a lunar year 354 days, 8 hours, 48 minutes, and 34 seconds long. This total is about 11 to 12 days shorter than a standard solar year.

Because lunar years are shorter than solar years, they do not stay in the same place in the seasons. Instead, the months cycle through all the seasons of a solar year. This entire rotation through the seasons takes a 33 to 34 lunar-year cycle to complete. Some calendars use a process called intercalation to fix this drift. Intercalation is the act of adding a thirteenth leap month every few years. This helps the lunar months stay in agreement with the solar year. Calendars that use this method are called lunisolar calendars.

There are different ways to decide when a new month actually begins. The rules vary depending on the specific calendar being used. Some systems, like the Hijri calendar used in Islam, rely on the first sighting of the lunar crescent. In Sunni Islam, this sighting is called the Hilal. Other lunisolar calendars, such as the Hebrew and Chinese calendars, use different methods. They mark the first day of the month when an astronomical new moon occurs in a specific time zone. Some Hindu calendars follow a different rule entirely. They begin each month on the day after the full moon.

History shows that humans have observed the Moon for a very long time. Some scholars believe ancient hunters in the Upper Palaeolithic period conducted astronomical observations. The researcher Samuel L. Macey suggests the Moon was used as a time-measuring device as far back as 28,000 to 30,000 years ago. In the 8th century, Muslim astronomers developed a more mathematical approach. They introduced the Tabular Islamic calendar to predict the approximate date of the first crescent moon. This helped determine the start of months more reliably.

The Tabular Islamic calendar uses a specific 30-year cycle to maintain accuracy. Within this cycle, there are 11 leap years that consist of 355 days. The other 19 years consist of 354 days. This mathematical system is incredibly precise over long periods. It is accurate to one day in about 2,500 solar years, or 2,570 lunar years. However, in the short term, it may deviate from actual observations by one or two days. This method was designed to minimize the uncertainty caused by weather or visibility when looking for the Hilal.

Many calendars we think of as lunar are actually lunisolar. This means they use lunar cycles but add months to stay aligned with the Sun. Examples of present-day lunisolar calendars include the Chinese, Korean, Vietnamese, Hindu, Hebrew, and Thai calendars. These systems often add an extra month every second or third year. Some calendars even use natural events to help with calibration. For example, the lunisolar calendar of the Banks Islands tracks the palolo worms. These worms mass on beaches during the last quarter of the lunar month because their reproductive cycle is synchronized with the Moon.