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How Many Days Are in a Month

# How Many Days Are in a Month

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How many days are in a month is a mathematical question that first-year software engineering students across the globe are asked to know in the first week of classes.

### Day

A month is a unit of time, used with calendars, that is approximately as long as a natural orbital period of the Moon; the words month and Moon are cognates. The traditional concept arose with the cycle of Moon phases; such lunar months ("lunations") are synodic months and last approximately 29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon's phases as early as the Paleolithic age. Synodic months, based on the Moon's orbital period with respect to the Earth–Sun line, are still the basis of many calendars today, and are used to divide the year.

A synodic month is the most familiar lunar cycle, defined as the time interval between two consecutive occurrences of a particular phase (such as new moon or full moon) as seen by an observer on Earth. The mean length of the synodic month is 29.53059 days (29 days, 12 hours, 44 minutes, 2.8 seconds). Due to the eccentricity of the lunar orbit around Earth (and to a lesser degree, the Earth's elliptical orbit around the Sun), the length of a synodic month can vary by up to seven hours. (Source: en.wikipedia.org)

### Month

A synodic month is longer than a sidereal month because the Earth-Moon system is orbiting the Sun in the same direction as the Moon is orbiting the Earth. The Sun moves eastward with respect to the stars (as does the Moon) and it takes about 2.2 days longer for the Moon to return to the same apparent position with respect to the Sun.

At the simplest level, most well-known lunar calendars are based on the initial approximation that 2 lunations last 59 solar days: a 30-day full month followed by a 29-day hollow month—but this is only roughly accurate and eventually needs intercalation (correction). Additionally, the synodic month does not fit easily into the solar (or 'tropical') year, which makes accurate, rule-based 'lunisolar' calendars complicated. The most common solution to this problem is the Metonic cycle, which takes advantage of the fact that 235 lunations are approximately 19 tropical years (which add up to not quite 6,940 days). However, a Metonic calendar will drift against the seasons by about one day every 200 years. Metonic calendars include the calendar used in the Antikythera Mechanism about 2,000 years ago, and the Hebrew calendar. (Source: en.wikipedia.org)

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