I have a suggestion of the timekeeping on Mars:
Divide the year into 23 months of 29 sols each (with a few exceptions). One benefit is that 12 months on Mars will be almost the same as 12 months on Earth.
One day on Earth is 24 hours = 86,400 seconds.
One year on Earth is 12 month. The months length differs between 28 and 31 days.
One Julian year is 365.25 days.
One day on mars is 24 hours, 39 minutes and 35 seconds = 88,775 seconds.
(Give it or take some parts of a second).
One Martian year is around 687 Earth days = 668.5991 Martian days.
2. Proposal for a Martian chronology
We keep the earth seconds as a base measurement for time. This has a
lot of advantages, especially then many SI units and most technique that
handling time in some way use seconds.
2.1.1 The day
The Martian day is 88.775 seconds, witch is divisible with 25.
Therefore it is wise to dividing it in 25 Martian hours that is
3,551 seconds long.
The Martian hours can be divided by 67 × 53 (67 minutes by 53 seconds,
or 53 minutes by 67 seconds)
Leap seconds are frequently needed in Mars with a timekeeping in Mars, hence 67 minutes of 53 seconds are a better choice
2.2.1 The year
The Martians will be dependent on Earth for a very long time. Therefore it is wise to keep units to be close to the one on Earth.
The length of the year is very close to 668.6 Martian days, which means that 60% of all years needs to be leap year. My suggestion is that years 0, 2, 4, 5, 7 and 9 of every decade have to have 669 days, and the rest of years to have 668 days.
2.2.2 The months
22.214.171.124 The length of months
The Martian year should be divided in 23 Martian months with most Martian month to be 29 Martian days long. Let's take a look of the months sorted by lengths by seconds:
28 Earth days : 2,419,200 seconds
29 Earth days : 2,505,600 seconds
29 Martian days: 25,74,475 seconds
30 Earth days : 2,592,000 seconds
30 Martian days: 2,663,250 seconds
31 Earth days: : 2,678,400 seconds
Almost all months should be 29 Martian days long. Only month 11 should be 30 days long.
The last month on the year has the leap day.
Month 1: 29 Martian days
Month 2: 29 Martian days
Month 3: 29 Martian days
Month 4: 29 Martian days
Month 5: 29 Martian days
Month 6: 29 Martian days
Month 7: 29 Martian days
Month 8: 29 Martian days
Month 9: 29 Martian days
Month 10: 29 Martian days
Month 11: 29 or 30 Martian days
Month 12: 29 Martian days
Month 13: 29 Martian days
Month 14: 29 Martian days
Month 15: 29 Martian days
Month 16: 29 Martian days
Month 17: 29 Martian days
Month 18: 29 Martian days
Month 19: 29 Martian days
Month 20: 29 Martian days
Month 21: 29 Martian days
Month 22: 29 Martian days
Month 23: 30 Martian days ** 30 Days on the last month on the year.
This calendar has several benefits. The best argument is that the length
of 12 Martian months is quite close to 12 months on Earth, which will make it easier to do rough calculations and cross referring calendars:
1 earth year, no leap year : 31,536,000 seconds
1 Julian year (365,25 days): 31,557,600 seconds
1 earth year, leap year : 31,622,400 seconds
12 Martian months, long : 30,982,475 seconds
12 Martian months, short : 30,893,700 seconds
The difference between 12 Martian months and 1 Julian year is ~2%
(around 1 Earth week).
The Earth Calendar (Western calendar) has a lot of bigger differences built in. The earth months is usually a bit longer, but not always:
February to April is 89 Earth Days = 7,689,600 seconds.
Three Martian Months i usually 7,723,425 seconds.
126.96.36.199 The months names
The original Julian calender on Earth had Mars as it's first month. Therefore has the months "September", "October" "November" and "December" the meaning in Latin 7, 8, 9 and 10. Unfortunately this changed. so the start of the year became January. That made the months quite a bit
With starting a new Martian calendar, we have a unique chance to repair that mistake. Therefore I suggest the Martian year to start with Mars, which also is the name of the planet!
After the Martian month the rest of the Earth months names follow, and then one can use different celestial bodies or the Latin name of the numbers:
Earth name Latin number Celestial Proposal
Month 1: 29 Martian days Mars Unuber Mars Mars
Month 2: 29 Martian days April Duober April
Month 3: 29 Martian days May Triaber May
Month 4: 29 Martian days June Kvartober June
Month 5: 29 Martian days July Kvinkober July
Month 6: 29 Martian days August Sexber August
Month 7: 29 Martian days September September September
Month 8: 29 Martian days October October October
Month 9: 29 Martian days November November November
Month 10: 29 Martian days December December December
Month 11: 29 Martian days January January
Month 12: 29 or 30 Martian days February February
Month 13: 29 Martian days Triadecimber Jupiter Jupiter
Month 14: 29 Martian days Qvartdecimber Saturn Saturn
Month 15: 29 Martian days Qvincdecimber Uranus Uranus
Month 16: 29 Martian days Sexdecimber Neptune Neptune
Month 17: 29 Martian days Septemdecimber Pluto Pluto
Month 18: 29 Martian days Octodecimber Sol Sol
Month 19: 29 Martian days Novemdecimber Mercury Mercury
Month 20: 29 Martian days Vigintiber Venus Venus
Month 21: 29 Martian days Unvigintiber Terra Terra
Month 22: 29 Martian days Duovigintiber Phobos Phobos
Month 23: 30 Martian days Tresvigintiber Deimos Deimos
2.3 The weeks
The weeks can be the same as on Earth:
Possibly, if you want to make the calendar simple, you can have double or triple Sundays in the end of the month to make every month begin with a Monday.
2.4 Then should the new year be?
Most ancient earth calendars have there new years in the spring equinox and that is also a good idea for the Mars calendar. The first day after the equinox should be the first day on the year. The hemisphere the first settled landing is on decides what hemispheres spring equinox should be calculated from.
2.5 Which year should be year 0?
It would be properly to start counting the years after the first
permanent (or at least planned to be permanent) settler set his foot
on the surface of Mars. That should be the year 0. Unlike the Earth calendar—the Western calendar does not have any year 0 in the calendar—
the Martian should have a year 0 in its calendar. It makes it more easy to calculate years before the setting of mars. It will also have the consequence that some day in the year 50, it will be 50 years after the settling, and not 49 years.
2.5. How about the clock? When should be midnight be?
The midnight 00:00:00 should be like on the Earth, when the Sun has its lowest position on the night. Because of Mars will have 25 hours per day, the Sun will have its highest position at 12:33:27.