Helios calendar
Time on Earth has little meaning to someone who spends their life on another planet. While Martian calendars and clocks have existed since the 20th century, coordinating calendars for every last rock is untenable. As the years progress, precession, tidal dragging, and other factors adjust the time it takes for a body to rotate and orbit - already responsible for a day of error since Egyptian times. Even relativity causes problems. Compared to a stationary observer outside of the solar gravitational well, a second on Earth is, in actuality, only about 0.999999984345 of a second.
The Helios calendar was devised as a solution, at least in the context of the Solar System, and is sometimes referred to as 'the Solar calendar' (note capitalization). When corrected properly for the nearest major, singular masses, it is fairly accurate, even outside the solar system.
See the Arean calendar for timekeeping on Mars, and Gregorian calendar for the (slightly) modified Earth calendar.
Mechanics
At its core, the Helios calendar has a lot in common with the Julian Date, though the intent is to have a reference completely independent of Earth. Specifically, it measures the number of true hours since the beginning of the epoch (as in, groups of 3,600 seconds or 216,000 thirds). Officially, it is also grouped into 'solar months' of a thousand hours and 'solar cycles' of a thousand months. People often add an additional unit, with a 'solar day' being 25 hours long and having 40 days to the month.
The epoch of the Helios Calendar begins with the legendary June 15th, 763 B.C.E solar eclipse during its maximum at 08:23 UT ('GMT') on the Julian Calendar (Julian Date 1,442,902). According to Roman legend, Remus was conceived during this eclipse, and it is mentioned in an Assyrian tablet known as the Eponym Canon. It is perhaps the most familiar as the eclipse referred to in Amos 8: "And it shall come to pass in that day, saith the Lord GOD, that I will cause the sun to go down at noon, and I will darken the earth in the clear day." (KJV)
Common Usage
A date is typically written as 24.277.522:17:17 (Midnight, January 1st, 2008, UTC), when fully written out. Terms like 'cycle 24', or 'the 24th cycle', are common, as are phrases like 'month two-seventy-seven' when the cycle is obviously known, or 'hour five-twenty-two' when the month is.
Since the basic subunit is the hour, outside of Earth, Luna, and Mars, a day is frequently considered to be 25 hours long, with 40 days to the month. A week is usually considered to be ten days long, referred to as quarters - "first week/quarter, second week/quarter", etc.
While it was not, originally, intended as a social calendar, it has quickly gained acceptance as such, even on Earth, due to communication between planets through satmets requiring a more universal timescheme.
After the Purge, it has slowly become the dominant galactic calendar. When corrected for local masses, it is exceedingly accurate within the nominal band drawn by Sol as it orbits the Milky Way. Moving closer to or further from the galactic center, or off the galactic plane, results in another slight difference usually termed drift. The same drift is also found when moving to another Galaxy. Even still, it remains a fairly standard measurement of time, with tachyonic measurements used to measure the 'true' rate of time for a specific region (at least, with respect to another region).
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