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Year

A year is the amount of time it takes for a planet to orbit its sun. If the planet has an axial tilt, this results in seasons (winter, spring, summer, autumn).

Vulcan year: In Gene Roddenberry’s novelization of The Motion Picture he indicated that 9 Vulcan seasons were equal to 2.8 Earth years. This would make Vulcan’s year 456 ± 33 Earth days long.

Earth year

One Earth year is equal to 365.2425 Earth days in the Gregorian calendar. To compensate for the fraction of a day, a leap day is added to every year whose number is divisible by four, unless it is a century, unless it is divisible by 400. These leap years consist of adding an extra day to the month of February. Instead of the usual 28 days, there would be 29.

Scientists usually use a Julian year of 365.25 days for measurements and scientific comparisons.

The mean solar year was 365.242190419 days in 2000 AD, and will be shorter still by the 23rd century.

Month

A month is usually the amount of time it takes for a moon to orbit its planet. This is usually a portion of a year, and a large number of days (in which case it may be broken down into weeks).

On planets without moons, a month could either A) not exist, B) be equal to a season, or C) be a fractional division of a season. For example, Vulcan "has no moon", so it is unknown what portion of a year is represented by the "month" of Tasmeen. The novelization of The Motion Picture could be read to imply that Vulcan's "months" are whole seasons.

On Earth a month was originally the length of the lunar cycle (29.53 days). Most calendars at some point made the month one twelfth of a solar year (30.44 days). In Earth's most common calendar, the months are either 30 or 31 days long, with one shorter month (February) having 28 or 29 days depending on the year.

Week

A week is small number days grouped together as part of a calendar system. It could be a portion of a month or an unrelated grouping.

On Earth a week is seven days.

Seven days was a close approximation to one fourth of a lunar month. When months became one twelfth of a solar year the connection was broken, and one month is now about 4.35 weeks long.

Day

A day is the amount of time it takes for a planet to spin once on it own axis. This results in a day/night cycle (with day in this second case meaning the sunlit portion of the full day).

On Earth a full day is divided up into 24 hours.

Hour

An hour is a portion of a day, this could be a decimal tenth of a day, or some other fractional portion of a day.

On Earth an hour is 1/24 of a day, and is divided up into 60 minutes.

Minute

A minute is a portion of an hour, this could be a decimal hundredth of an hour, or some other fractional portion of an hour.

On Earth a minute is 1/60 of an hour, and is divided up into 60 seconds.

In colloquial speech, a minute can also mean an undefined short amount of time, as in "I'll be just a minute".

Second

A second is a portion of a minute, this could be a decimal hundredth of a minute, or some other fractional portion of a minute.

On Earth a second 1/60 of a minute, and is usually divided up decimally.

The second is now precisely defined based on the atomic behavior of caesium, and the lengths of minutes, hours, and days are now defined in these seconds. This means that these other times are no longer exactly the same as there solar equivalents based on actual planetary motion.

See also second at Wikipedia.

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