While, as with any civilisation, the Terran people have used any number of calendars and measures of time through their history, there are two that can be specifically thought of as specifically Terran rather than simply one of its cultural or religious groups.
These would be the old, defunct Gregorian system, and the modern Universal Standard system.
Gregorian: Before the Tycho Convention gathered to found the Terran Confederation most nations and planets used, to varying degrees, the Gregorian system. Some worlds did attempt to adapt the clock and/or calendar to their own planet’s orbital and rotational periods, but based these very heavily on this Earth system.
At the smallest common unit was the second. Colloquially it was 1/86400 of the day, but officially was:
the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
Either way 60 of them was the next sized unit, the minute. 60 of those to an hour, and 24 to an Earth day.
The notation for time had two varieties called the 12hour or 24hour clocks.
The 12hour clock used a denotion of AM or PM for morning or evening respectively and noted the hour using 1 through 12. Thus 1:30pm for one and a half hours after midday.
The 24hour clock dropped the AM/PM electing to count the hours as 00 though 23. So 13:30 for the above example. Minutes in either system were 00 through 59, and while either system had a preceding 0 for a single digit hour as optional, minutes and seconds were always 2-digit, and units below seconds were denoted decimally so 1:30:45.123456 might be seen.
The calendar was based on a solar/lunar cycle system and counted the time before or after the estimated birth of the Christian deity Jesus. Events after this event were left merely as a numeric year, or might be specified with A.D. From the Latin Anno Domini, The Year of Our Lord being the common translation. After Christianity fell out of major political influence during the century of the first two world wars C.E. was used instead and meant Common Era. Events preceding the birth were B.C. or B.C.E. for Before Christ or Before the Common Era.
The year, as with the Universal Calendar is based on the Terrestrial orbit of Sol.
This was achieved through estimation, however. The year was measured as 365.2525 days, and was tracked as 3 years of 365 days followed by one of 366, called a Leap Year except on centennial years that weren’t a multiple of 400.
The lunar element was in the subdivision of the year into 12 months as the approximate number of lunar cycles from full moon to full moon in one year. These twelve months had either 30 or 31 days, except the second which had 28 or during leap year 29.
The notation had virtually no standardisation. But the methods involved spelling out or abbreviating the month’s name, and giving the day and year as numerals, or by giving the month a numeral value and listing it all that way using various symbols for seperation. Often the first two digits of the year were omitted, and what order the numerals were placed was very regional.
1 February 2134
Feb. 1, 2134
The system is no longer used for any official purposes but some religious groups do still use it to track holy days.
Universal Standard: Also called simply Standard or decimal it was first proposed some 43 years before the Tycho Convention founded the Confederation by Dr. Otto Smith of Universidad de Amazonis Planitia on Mars as a new calendar system that left behind the religious trappings that had led to the horrible wars that were still ravaging parts of the cradle of Mankind, and as a compliment to the decimal clock that had been gaining momentum for the previous fifty years as a result of the numbers of people who had had to adapt to it for military purposes.
The Universal Clock is, essentially, the same one proposed during the French Revolution centuries before even the first of the Big Three. It proposes the day be divided into tenths, and the accepted form used a division of those tenths by hundredths, then those to be further divided by an hundred. Lacking any proposals for an alternate name, and in the interests of tradition they were called hours, minutes, and seconds.
The length of a day, thanks to modern astrometric capabilities and the creation of the major time servers at each major System Hub means all clocks can adjust themselves to accurately subdivide the Terrestrial rotational period accurately into the required pieces.
The calendar elected to divide the year into ten, again for tradition’s sake the word month was chosen. These were declared to be 37 days on the odd months, and 36 on the even. The exact length of the calendar is automatically adjusted by the System Hubs throughout the year to keep 365 days precisely the span of that years Terrestrial orbital period.
The name Universal Standard is, naturally, because it is intended to be the standard time for all of the Confederation. Due to the exceedingly variable duration of extraterrestrial worlds, as well as spaceships and starships, space stations, etc. it was decided that the Terrestrial orbits and rotations would be the measure of time throughout Mankind and that no timezones need exist. The hour was calculated as 1.0 when The Constitution was ratified as and the date as 1.1.1.
The Universal months were given names for purposes of making saying the date easier, though numerals are to always be used when writing, and were given the Latin for First through Tenth. The clock and calendar were declared to be one and the same so correct notation should always be date, numerically, separated as email@example.com or if greater accuracy is required .seconds or even further.
Colloquially the date is left out of the time in spoken conversations, but this is inappropriate usage when speaking in official or formal capacities.
The single time unit to be absolutely unchanged between either calendar is the week, a unit if 7 days. The week held more importance in the Gregorian eras, but even under modern circumstances a middle measure between day and month is useful and while it has been suggested that six might be a better choice the proposal always lacks support so the old measure remains.