A Martian day would be 1.027491443588 times as long as an Earth day, if the Earth were still spinning on its axis as fast as it did on December 31st of the year 1899. The current length of a day on the Earth is roughly 86,400.002 seconds, leading to a leap second in about three of every four years. With this factor taken into consideration, a Martian day is 1.02749142 times as long as an Earth day.
If one wanted to make every day on Mars correspond to the current day on Earth, one would have to skip a day roughly every 36.375 days.
As far as I am aware, there is no church on Earth that takes observance of the Sabbath quite so seriously as to have decided that the Prime Meridian ought to run through Jerusalem instead of Greenwich, and which has therefore enjoined its communicants within a span of roughly 35 degrees of longitude (which would include the entire state of Hawaii, among other places), unlike its communicants everywhere else, to attend services on the day called Saturday (or Friday) by the surrounding secular community, while its communicants elsewhere in the world go to church on Sunday (or Saturday).
Some of what I am going to be discussing below may seem to require taking this matter with a similar level of seriousness.
Some years ago, two papers with an unusual proposal for calendar reform appeared in the Journal of the Royal Astronomical Society of Canada. Their author was, apparently, a Muslim, and it may be that what he was proposing may have more closely accorded with the Islamic view of how time should be measured than our current civil calendar. In any event, the idea was quite novel, and differs considerably from our conventional ideas of how a calendar is supposed to work.
One of the two papers dealt with a lunar calendar, the other with a solar calendar, based on his new principle. The Islamic calendar, is, of course, a lunar calendar, and the traditional way of determining the beginning of the month in Islam is through local observations of the New Moon.
I will, however, only discuss the application of this novel principle to a solar calendar, for ease of understanding.
The length of the tropical year on Earth is about 365.2422 days. This is why about every fourth year is a leap year.
If you look in an almanac, you will find that the vernal equinox, which conventionally marks the first day of Spring, although it might be argued that it should fall in the middle of that season rather than its beginning, is not merely given a date, but also a time.
Let us suppose that every location on Earth marked New Year's Day on the day of the vernal equinox. This is roughly March 23 by our present calendar, and, indeed, at one point, March 25 was celebrated as New Year's Day (just as we celebrate Christmas on December 25, and not December 22, the day of the winter solstice).
And furthermore suppose that the day of the vernal equinox were the day, from midnight to midnight, using local mean solar time instead of Standard Time, within which the actual instant of the vernal equinox falls. What's the difference between local mean solar time and Standard Time? That means none of those wimpy time zones. Instead of setting your clock ahead one hour after traveling 15 degrees of longitude eastwards, you set it ahead one minute after every one-quarter of a degree of travel eastwards. Every city, town, or village might have its own central meridian, and the time in each location, therefore, would not be constrained to differ from that in other locations only in units of whole hours, half-hours, or even whole minutes or whole seconds.
And the New Year is determined by the date during which a specific astronomical event, the vernal equinox, whose exact time is known, takes place according to such local time.
Under such a system, every year would be a leap year, but only for the people living within an expanse of about 87.2 degrees of longitude. And that means that the International Date Line would only stay in one place for one year at a time. After leap year's day was over for the people who were enjoying it on a given year, the International Date Line, which had heretofore been located to the east of the expanse of 87.2 degrees that was there abode, would take up its new location to their west.
As I have noted, this is a system that would seem bizarre to most of us. Just as the Islamic lunar calendar of twelve lunar months of about 29 1/2 days every year seems strange to those of us whose heritage belongs to a northern temperate climate, for whom a calendar is an instrument meant to tell us when it is time to plant crops, and when it is time to harvest them, so does this proposal seem strange to those of us who see a calendar as something that should be stable, fixed, and predictable, so as to make a convenient backdrop for scheduling the payment of rents and salaries and setting appointments, including, in this modern age, appointments for teleconferences the locations of participants in which might well span the globe. An International Date Line that never fell in the same place twice would not work well with that. Even if Standard Time were retained, so that the International Date Line advanced by 90 degrees most years, but by only 75 degrees once every five (or, about a third of the time, six) years, the potential for confusion is obviously immense.
The proposal discussed above for Earthly calendar reform is clearly one that would never be adopted by a society with the priorities of our present civilization. And, furthermore, this page is discussing schemes for timekeeping on Mars. Given this, why was space devoted to a discussion of this scheme here? As you no doubt have guessed, it is because it illustrates, in a relatively simple form, the operation of a principle which would also be required to make the day of the week on Mars, at any location, correspond as closely as possible to the day of the week on Earth.
Presumably, Mars would have an International Date Line that occupies a fixed location on Mars. As on Earth, if you cross that line going westward, it might suddenly change from being the 2nd of the month to being the 3rd of the month in the middle of the day.
Let us say that, for any given location on Mars, the day of the week were to be determined by the following rule: when it is noon, local time, at that location, then, somewhere on Earth, it is also noon. The day of the week at that time, at that place on Earth, will also be the day of the week for that day in that place on Mars.
Then, while the International Date Line would remain fixed on Mars, the International Day Line, crossing which in a westward direction would make Wednesday suddenly become Thursday, would creep across the Martian surface at a rate of about 9.632 degrees of longitude each Martian day, in this case in an eastwards direction, since days are being occasionally omitted.
Of course, there is one additional factor. Given that 36 Martian days roughly correspond to 37 Earth days, this means that any scheme of making days on Mars correspond to days on Earth leads to a day being skipped once in a while. Those who take their churchgoing seriously enough to wish to ensure they go to church on the day that actually is Sunday (or Saturday) on Earth, where they believe God established the seven-day week, rather than simply on every seventh Martian day, obviously aren't going to stay home from church one week because their holy day is missing from that week.
Fortunately, a simple enough rule can be devised to deal with this. When it is noon on Mars in a given location, the place where it is noon on Earth, thus determining the day of the week for that Martian location, is either in the Eastern hemisphere or the Western hemisphere. More to the point, each time this happens, once a Martian day, it is 39 minutes and 35 seconds later by Earth time, and thus the Earthly location where it is noon when it is noon at that Martian location has moved 9.897 degrees of longitude to the west.
When a day is skipped, then, the corresponding Earth location has jumped across the International Date Line. Thus, if one Martian day is a Saturday, and the next one is a Monday, by the rules outlined so far, the one for which the corresponding Earth location that determined the day of the week lies closest to the International Date Line on Earth can be considered to be the one that is disfavored, and therefore the one that will serve as the Sunday for that week.
It is, of course, possible to apply these rules only to a location on the Martian prime meridian, and keep the same day of the week for all of Mars as well.
Generally speaking, though, most people on Mars will have no interest in resorting to such an elaborate scheme to keep the days of the week on Mars in harmony with the days of the week on Earth. Instead, if the seven-day week is used on Mars, doubtless the seven days of the week will just follow, one from another, in fixed succession, as they do on Earth. If so, which Martian day is which would be entirely arbitrary, and would likely be determined either from the first manned landing on Mars, or the initial establishment of a colony on Mars.
Since a voyage to Mars would normally take nine months, and there is a difference in length between the Martian day and the Earth day, however, by judiciously choosing when to change from Earth time to Mars time during the voyage, the passengers could experience no sudden jumps in the succession of days of the week. Since the ratio between the lengths of the Earth day and the Martian day is as 36 to 37, however, the time taken for a journey to Mars is just barely long enough to pull off this particular trick.
Also, it has been proposed that Earth convert to the World Calendar, where one day a year belongs to none of the seven days of the week, and in addition, the extra day for leap year is outside the week. I feel that this particular proposal is unlikely to ever be adopted, because of its obviously controversial nature.
But would it be possible to keep the Martian week somewhat more roughly in step with the week on Earth through a similar scheme?
As previously noted, there are 668.592 Martian days in a Martian tropical year. If we divide 668 by 36, we find that during a Martian year, we will need to skip over 18 or 19 days. Neither 649 nor 650 is a multiple of seven, so a calendar as constant as the World Calendar will not result from such a scheme.
However, one certainly could imagine a Martian calendar with 20 months, where one skips a day of the week when going from the last day of 18 of those months to the first day of the next month in a normal year, and in a leap year, one skips a day of the week at the end of every month. This is the reverse of using the leap year day to replace one of the days skipped, though, which might seem more sensible. Also, of course, the number of days to be skipped will sometimes have to be varied, and whether or not to skip a day after the last day of the year will be the easiest thing to change
Giving priority to the days of the week, we could imagine a Martian calendar consisting of a first 648 days belonging to 18 months of 36 days, followed by an additional 20 or 21 days belonging to a short 19th month.
Thus, if we also adopt the rule that neither Friday, Saturday, or Sunday, the three days of the week of interest to major religions to which the seven-day week is significant, are to be skipped, the Martian calendar for one year might look like this:
Pop Uo Zip
S M T W T F S S M T W T F S S M T W T F S
1 2 3 4 5 6 7 1 2 3 4 5 1 2 3
8 9 10 11 12 13 14 6 7 8 9 10 11 12 4 5 6 7 8 9 10
15 16 17 18 19 20 21 13 14 15 16 17 18 19 11 12 13 14 15 16 17
22 23 24 25 26 27 28 20 21 22 23 24 25 26 18 19 20 21 22 23 24
29 30 31 32 33 34 35 27 28 29 30 31 32 33 25 26 27 28 29 30 31
36 34 35 36 32 33 34 35 36
Zotz Tzec Xul
S M T W T F S S M T W T F S S M T W T F S
1 1 2 3 4 5 6 1 2 3 4
2 3 4 5 6 7 8 7 8 9 10 11 12 13 5 6 7 8 9 10 11
9 10 11 12 13 14 15 14 15 16 17 18 19 20 12 13 14 15 16 17 18
16 17 18 19 20 21 22 21 22 23 24 25 26 27 19 20 21 22 23 24 25
23 24 25 26 27 28 29 28 29 30 31 32 33 34 26 27 28 29 30 31 32
30 31 32 33 34 35 36 35 36 33 34 35 36
Yaxkin Mol Chen
S M T W T F S S M T W T F S S M T W T F S
1 2 1 2 3 4 5 6 7 1 2 3 4 5
3 4 5 6 7 8 9 8 9 10 11 12 13 14 6 7 8 9 10 11 12
10 11 12 13 14 15 16 15 16 17 18 19 20 21 13 14 15 16 17 18 19
17 18 19 20 21 22 23 22 23 24 25 26 27 28 20 21 22 23 24 25 26
24 25 26 27 28 29 30 29 30 31 32 33 34 35 27 28 29 30 31 32 33
31 32 33 34 35 36 36 34 35 36
Yax Sac Ceh
S M T W T F S S M T W T F S S M T W T F S
1 2 3 1 1 2 3 4 5 6
4 5 6 7 8 9 10 2 3 4 5 6 7 8 7 8 9 10 11 12 13
11 12 13 14 15 16 17 9 10 11 12 13 14 15 14 15 16 17 18 19 20
18 19 20 21 22 23 24 16 17 18 19 20 21 22 21 22 23 24 25 26 27
25 26 27 28 29 30 31 23 24 25 26 27 28 29 28 29 30 31 32 33 34
32 33 34 35 36 30 31 32 33 34 35 36 35 36
Mac Kankin Muan
S M T W T F S S M T W T F S S M T W T F S
1 2 3 4 1 2 1 2 3 4 5 6 7
5 6 7 8 9 10 11 3 4 5 6 7 8 9 8 9 10 11 12 13 14
12 13 14 15 16 17 18 10 11 12 13 14 15 16 15 16 17 18 19 20 21
19 20 21 22 23 24 25 17 18 19 20 21 22 23 22 23 24 25 26 27 28
26 27 28 29 30 31 32 24 25 26 27 28 29 30 29 30 31 32 33 34 35
33 34 35 36 31 32 33 34 35 36 36
Pax Kayab Cumhu
S M T W T F S S M T W T F S S M T W T F S
1 2 3 4 5 1 2 3 1
6 7 8 9 10 11 12 4 5 6 7 8 9 10 2 3 4 5 6 7 8
13 14 15 16 17 18 19 11 12 13 14 15 16 17 9 10 11 12 13 14 15
20 21 22 23 24 25 26 18 19 20 21 22 23 24 16 17 18 19 20 21 22
27 28 29 30 31 32 33 25 26 27 28 29 30 31 23 24 25 26 27 28 29
34 35 36 32 33 34 35 36 30 31 32 33 34 35 36
Uayeb
S M T W T F S
1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
Initially, I had declined to suggest possible names for the months for this calendar. However, it seems likely that people on Mars concerned with maintaining a connection to the day of the week on Earth would also wish to maintain a connection with at least some of the holidays tied to the seasons on Earth. The thought occurred to me that this might mean that this calendar would be used in conjunction with a calendar like that described in the preceding section. The use of two calendars in conjunction immediately suggested the set of month names shown here. On further reflection, however, since this calendar assigns a day of the week to each Martian day by putting it into correspondence with an Earth day, one could deal not only with the days of the Earthly week, but with dates on Earth as well, by using that correspondence.
Also, since Uayeb may have either 20 or 21 years, in order to keep the calendar strictly in step with the Martian seasons, this is not a "vague year" like the Mayans had. Instead, the fundamental structure of this calendar, with the small, epagomenal, month including the leap-year day, is closer to that of the calendar shared by the Coptic and Ethiopic Christian churches.
In this calendar, the first 18 months of the year go through seven possible forms in regular succession, but in successive years, the form used for each month would differ, although the order of the succession would remain the same. There are some further details, however, which will be dealt with in the next section, which proposes a specific epoch for this calendar.
Of course, the fact that the calendar is conventionalized, ending in 20 or 21 odd days, instead of allowing the relationship between Earth and Mars days to take priority over the Martian year means that the closest possible fit to the nearest Earth day is not obtained. One could instead have a cycle of 16 months, 10 of which are 36 days long, and 6 of which are 37 days long, and a Martian year which consisted of either 18 months or 19 months.