People from Earth, living on Mars, would still have many sentimental ties to Earth, and they possibly would also have commercial dealings with Earth as well. While they would need a calendar that related to the days and the seasons on Mars, where they lived, they would have many emotional ties to Earth and its traditions. If the Martian calendar was built of months that matched months on Earth in length, they could celebrate many Earth holidays at about the same time as people on Earth.
As also previously noted, the Gregorian year is 365.2425 days in length, and so the average length of an Earth calendar month is 30.43685 Earth days, or 29.622485 Martian days. And the length of the Martian tropical year is 668.592018 Martian days. So, if one wished to maintain a long-term synchronicity between months on Mars and months on Earth, one could divide the Martian year into 22.570423 months. Approximately, that would lead to having a Martian year with 23 months for four years out of every seven, and with 22 months for the other three years.
If we do decide to synchronize the Martian month with the Earth month, on the basis that the Martian seasons will be of some importance, but a limited one, in Martian daily life, but Mars will remain in constant communication with the Earth, what would the Martian calendar look like as a result?
Twenty-two months of 29.622485 Martian days would be about 651.7 Martian days in length. So, let us fix that part of the Martian year at 652 days. This would amount to fourteen months of 30 days in length, and eight months of 29 days in length.
Seven years would include four intercalary months. If we kept rigidly to that simple scheme of intercalation, to remain synchronized with the Martian tropical year, these months would average 29.036 Martian days in length; to remain synchronized with the Earth calendar month they would average 29.088 Martian days in length.
In practice, it might be expected that the length of the month would be kept rigidly synchronized to the Earth month, and the length of the year would be kept rigidly synchronized to the Martian tropical year, and to do this, a more complicated scheme of intercalation than four extra months in every seven years would be used. For the time being, however, only a first approximation is presented here.
In any case, the above indicates that the intercalary month would usually be 29 days in length, only occasionally being 30 days long.
A cycle of seven years, four of which are 23 months long, and three of which are 22 months long, contains 158 months. So 42 Martian years are very nearly 79 Earth years.
To concretize my calendar proposal, here is a possible arrangement:
A cycle of seven years would consist of three regular years and four leap years, disposed as follows:
L R L R L R L
The two types of years would consist of the following months:
REG LEA REG LEA
Aries 30 30 Libra 30 30
Germinal 29 29 Vendemaire 29 29
Taurus 30 30 Scorpio 30 30
Floreal 29 29 Brumaire -- 29
Gemini 30 30 Saggitarius 30 30
Prairial 30 30 Frimaire 30 30
Cancer 30 30 Capricorn 30 30
Messidor -- 29 Nivose 29 29
Leo 30 30 Aquarius 30 30
Thermidor 29 29 Pluviose 29 29
Virgo 30 30 Pisces 30 30
Fructidor 29 -- Ventose 29 29*
The calendar would begin with the Martian vernal equinox, which would, of course, have even less connection with Aries than the vernal equinox on Earth.
In the last year of the last cycle in a group of seven cycles of seven Martian years, Ventose would have 30 days instead of 29.
Since there are twelve months in the French Revolutionary Calendar, I have chosen, to treat them in a balanced way, to omit two of them in a regular year, and to include them both, but omit a different one, in a leap year. Also, I have chosen to make all the constellation months 30 day months, so in a sense I am treating all the FRC months as if they were intercalary, or at least poor cousins to the other twelve months.
Thus, the cycles would interrelate in a fashion like the following:
1) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2) Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb
3) May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr
4) Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun
5) Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug
6) Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct
Year I
ARI Ger TAU Flo GEM Pra CAN Mes LEO The VIR LIB
Ven SCO Bru SAG Fri CAP Niv AQU Plu PIS Ven
Year II
ARI
Ger TAU Flo GEM Pra CAN LEO The VIR Fru LIB Ven
SCO SAG Fri CAP Niv AQU Plu PIS Ven
Year III
ARI Ger TAU
Flo GEM Pra CAN Mes LEO The VIR LIB Ven SCO Bru
SAG Fri CAP Niv AQU Plu PIS Ven
Year IV
ARI Ger TAU Flo
GEM Pra CAN LEO The VIR Fru LIB Ven SCO SAG Fri
CAP Niv AQU Plu PIS Ven
Year V
ARI Ger TAU Flo GEM Pra
CAN Mes LEO The VIR LIB Ven SCO Bru SAG Fri CAP
Niv AQU Plu PIS Ven
Year VI
ARI Ger TAU Flo GEM Pra CAN
LEO The VIR Fru LIB Ven SCO SAG Fri CAP Niv AQU
Plu PIS Ven
Year VII
ARI Ger TAU Flo GEM Pra CAN Mes LEO
The VIR LIB Ven SCO Bru SAG Fri CAP Niv AQU Plu
PIS Ven
The novel suggestions I advance here are the following, which I admit may well be rejected as impractical:
A Martian minute divided into 57 (or 92, or 43) units is not, I think, too high a price to pay to define the Martian time units very precisely in terms of the second. A Martian calendar with intercalary months, on the other hand, to tie the Martian month to the Earth month is an idea very unlikely to be adopted, but I simply present it to illustrate a possible application of the principles on which calendars are constructed.
Still, people from Earth, living on Mars, would still have many sentimental ties to Earth. While they would need a calendar that related to the days and the seasons on Mars, where they lived, they would have many emotional ties to Earth and its traditions. If the Martian calendar was built of months that matched months on Earth in length, they could celebrate many Earth holidays at the same time as people on Earth.