Martians want to keep their weeks roughly in sync with Earth. How would they do that?

Question

The Martian Sol is 24 hours and 37 minutes long, so daytime at a fixed point on the planet's surface will drift in and out of sync with a fixed point on Earth's surface, and keeping the tradition of a 7-day week would have similar implications. Roughly every 39 days on Mars, 40 days will have passed on Earth.

Suppose the Martian colonists want to set up their weekly calendar so that their weekends occur roughly at the same time as they do on Earth. Maybe they want to not be bothered on weekends. Maybe there's some other social or religious benefit. The exact reason why is not important here. Also assume this is sometime after basic terraforming so that people live above ground.

They certainly could go by Earth time and avoid the problem entirely, but this quickly and regularly gets them out of sync with the natural biological instinct to go by whatever the sun says. Living your daily life in darkness for 19.5 days on, 19.5 days off doesn't make a lot of sense.

You could do something like leap days to handle this, but those 37 extra minutes do not divide evenly. It's almost a 6 week cycle, so doing something like skipping Wednesday every 5th week will cause Mars weeks to drift ahead slowly. Therefore you would need to create an additional rule of some regular interval of not skipping Wednesday on a fifth week. But then that creates another syncing issue. Layers have to be added until enough precision is achieved, just as we do for leap years.

Are there other alternatives that are mathematically consistent without being too difficult to remember? It would be pretty awful to go to work on a Saturday because you forgot that Friday got skipped this week. Or you could miss work because you thought Friday got skipped, but it wasn't.

If skip days are the only reasonable way of handling this, is there a strategy that could be used to help people remember without it feeling like which day is skipped is arbitrary and unpredictable?

Answer 1

The solution for this is intercalendary days, like you suggested. This is needed any time something doesn't divide neatly. Our day doesn't divide neatly into our year so the rule is:

• February 29th exists when the year is divisible by 4
• Unless the year is divisible by 100
• Unless the year is also divisible by 400.

So 2000 and 1600 are leap years, 1900 wasn't. 2100 also wont be.

Your Wednesday rule will need to be something similar. Skip every 6th Wednesday unless it's the xth Wednesday but not in month y sort of rule.

It could be made as memorable as our full leap year rule. Most people who hear the full rule disagree and google it because they only learnt the rule of 4. I go to work when my smartphone alarm goes off, and would on Mars too.

Note that doing this would anger some religions that want to keep their weekend in sync with the 7 day cycle. Orthodox adherents would have to shift the date of the sabbath by one day every missing Wednesday. Like they would if we adopted the World Calendar

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Addendum:
I did start trying to calculate the exact rule to make this line up, but it's going to be a pain. The martian week is 620494 seconds, the Earth week is 604800 seconds. These form a cycle every 26.8 billion seconds (43,200 martian weeks). A "Martian weekend syncing calendar" is going to need to be this complex.

I wasn't able to calculate it fully due to time constraints, but it will be at least:

• Base clock loses 15694 seconds per week.
• Skip every 6th Wednesday. Now we lose only 5522 seconds every 6 weeks.
• Skip every 97th Tuesday. Now we lose only 649 seconds every 100 weeks.
• Skip every 13641st Thursday. Now we lose only 28ms every 366 weeks.

Answer 2

If it works with your general scenario, they could just have a regular week, but switch the Earth timezone they sync with West every ~2 days. They would drop a day when they cross the date border, but would always have someone on Earth that shares their weekday and roughly time of day.

Of course the would not work if ground control is based in one or few neighboring timezones. But if UN Space or a multinational is doing the groundwork, they could have four+ control stations around the globe that periodically take over main responsibility and are during that time roughly synced with Mars.

The advantage of this scheme is that setting up meetings would work better with your current ground control - you not only have the same weekday (mostly), but also roughly the same time of day.

How would it work in practice? In the following, I will list how the conversion would change. I will always give Raw Mars Time first - this is the time that we don't want to use since it will drift away from Earth. Then I will give timezone and time that Mars syncs with at that time. Times will be in "24-hour format", Raw Mars Time days end at 24:37.

• Monday, 00:00 = Monday, 00:00 UTC
• Tuesday, 00:00 = Tuesday, 23:37 Azores time (UTC-1)
• Wednesday, 00:00 = Wednesday, 00:14 Azores time
• Thursday, 00:00 = Wednesday, 23:51 Mid-Atlantic time (UTC-2)
• Friday, 00:00 = Friday, 00:28 Mid-Atlantic time
• Saturday, 00:00 = Saturday, 00:05 Brazilian majority time (UTC-3)
• Sunday, 00:00 = Saturday, 23:41 Paraguay time (UTC-4)
• Monday, 00:00 = Monday, 00:18 Paraguay time
• Tuesday, 00:00 = Monday, 23:55 ET (UTC-5)
• Wednesday, 00:00 = Tuesday, 23:32 CT (UTC-6)
• Thursday, 00:00 = Thursday, 00:09 CT (UTC-6)

... and so on. You basically move one timezone West when you come too much out of sync. When you cross the date border, you have to skip a day.

Answer 3

Since the lack of a magnetic field would pretty much force any large scale habitation to be done underground and any time spent outside being expensive and needing shielding it wouldn't be at all difficult to use Earth time.

They could use Earth time underground and translate to Martian on the rare occasions they go out which would mostly just be specialists doing tasks. Specialists on Earth do the same thing. Pilots go through timezones, sailors keep track of tides and other cycles etc,.

Answer 4

Frame Challenge: When asked why you responded with this comment.

I think it could reduce surprises for the people who need to interact with Earthlings. Sending an email on a Tuesday on Mars could reasonably take a day for a response, but if you don't realize that's their Saturday at the time, you end up having to wait 2-3 days for a response. Obviously, it's never going to be exactly the same, but if you can rely on an assumption of "Earthlings are within 30 hours of my time and day of week", that would be pretty convenient.

So essentially it sounds like a fundamentally practical problem. You need your Martians to be able to interact with Earthlings in a way that doesn't cause frustration.

I think your Martians would solve this by running two Calendars. The Martian Calendar would fit the local conditions, seasons and social needs. Possibly dropping the seven day week, 12 month year altogether for something more sensible. All their technical gear can also display an Earth clock showing them the time, date and day of whatever part of earth they work most closely with. So they know it's earther weekend just by picking up a phone.

Starting a colony on Mars means everyone taking the same weekend is not going to work. Your environment is trying to kill you, someone is working to stop it every day. Even decades later when life is routine the concept of a shared weekend doesn't catch on again. And having two clocks on a phone is pretty simple. You can probably get a widget showing you 'Martian time and date' from your app store right now.

The biggest problem with this set up is Earthlings don't know if their contact is on xyr weekend when they send xem a message. But given the 'always on duty' outlook of Martian pioneers that has persisted chances are someone will pick the message up quickly in any case.

Answer 5

Spin up Mars! (so it comes to sync with Earth)

As a part of the teraforming process they need to haul large masses of water and other volatile substances. Think about Asimov's martians that bring a kilometers-sized piece of Saturn's rings. To bring them down to the surface, instead of landing them softly, an acretion-like process may be used.

This will transfer angular momentum to Mars.

Few (thousand) quakes later and after a great deal of fireworks they will have denser atmosphere, brand new hydosphere and a planet that rotates properly.

Answer 6

"Layers have to be added until enough precision is achieved."

What's wrong with that? It's not like every schoolchild has to do the math on their own.

Think leap years and leap seconds on Earth. Only one institution with a handful of super-smart, super-knowledgeable time nerds has to do the math. It publishes the results with a very high lead time. The information trickles downs through other institutions, onto regular people who don't need to know anything beyond "month lengths vary and I should check a calendar". So, most Martians only need to know "week lengths vary and I should check a calendar".

Not much would be lost. We have fixed week lengths on Earth, but for many people it's not rare to not know the day of the week before checking their phones.

Answer 7

Frame Challenge: Syncing weekends would not happen

The reason everyone here on Earth likes to sync up their weekends is so that normal people can predict when service businesses will be open or closed. These are things like restaurants, doctor's offices, tech support hotlines, etc. But between Earth and Mars, there can be no exchange of services, because they require real time communication. Mars is 4-24 light minutes away from Earth depending on orbital positions; so, ANY time you communicate with Mars, you have to wait for a response. This means that even those service jobs that can be outsourced between time zones on Earth (like tech support) stop being able to be outsourced between planets. As a result, 99% of the time critical things that apply to international exchange would not apply in an interplanetary environment.

The only things you need to coordinate between worlds in your case is the occasional inter-planetary shipments of goods, but these are huge multi-million dollar transactions handled by a small handful of specialists who would have no problem looking up Earth time in their already specialized tracking software, and those shipments already take the better part of a year to get from point A to point B; so, having to wait an extra 1-2 days for a shipment to be confirmed because you emailed someone on their weekend does not really make much of a difference in the grand scheme of things.

We modern people think everything has to be in real time, but pre-industrial civilizations functioned just fine waiting days, weeks, or even months for communications to happen; so, the evidence is already there that good planning and a bit of flexibility is all you really need here. As for weekends being staggered, many different Ancient civilizations observed different days off. Some only took off Fridays, some only Saturdays, some only Sundays, and they all had their own sets of local holidays meaning a traveler could always be surprised by closed shops because they arrived on some local festival day. So, your 2 planetary calendar system would in most ways already be more predictable than many historical systems.

When you consider that Mars has very little reason to need to sync up with Earth time, you should then ask yourself, how big that minor need is compared to their need to observe their own calendar. Tracking their own days, weeks, and years is something every Martian will need to be able to do. When do they need to go to work, or plant crops, or make a phone call to other Martians. For this, the simplest solution is going to be the best one; so, since observing a consistent local time will be thousands of times more useful to most Martians than worrying about what time it is Earth, it is unlikely that they will make the effort to do anything like this at all.

Answer 8

Only one rule: Every month that is single digits starts a weekday skipped. (The rule does not apply to october, november, december as those are double-digit months, but any mechanism to pick 9 months per year works.)

This will keep martian weekends pretty well aligned with earth weekends for a long time.

Example: August 31 is a Monday -> September 1 is a Wednesday.

Answer 9

Weekly on/off stacking alternating cycle

The problem with Ash's answer is that it's not as simple as it can be. Think about it, you have to deal with a full day one way or another every time you skip for any reason. So you might as well pick nice, round numbers as much as possible. Might give yourself a 10% buffer or so to be more flexible.

Here's my explanation:

• Every 5 weeks, skip Monday or Friday
• Every 40 weeks, don't do this
• Every 480 weeks (approximately 5 Martian years), do this anyways
• Every 27,840 weeks (approximately 250 Martian years), don't

Derivation:

Every 5 weeks skip So you start out ahead 15,694 seconds every week on Mars, so you need to take a day out somewhere at some point. There are 88,643 seconds on each Mars day that we will be skipping. That's roughly a factor of 15,694 / 88,643 = 1 / 5.6, so we need to choose skipping the 5th week or skipping the 6th week. I choose the more frequent one so that we swing the pendulum back the other way, which allows the next correction to restore a day rather than taking a further day off (sorry, no 3 day work weeks). Five week drift minus one Martian day the other way (15,694 * 5) - 88,643 = -10,173 seconds ahead every 5 week cycle on Mars (10,173 seconds behind).

Every 40 weeks don't skip Now we have a factor of 1/8.7. We again want to round down so we skip less often, so the next correction is every 8 5-week cycles we interrupt the skipping. 8 cycle drift plus one Martian day the other way (-10,173 * 8) + 88643 = 7,259 seconds ahead every 40 week cycle on Mars (-7,259 seconds behind).

Every 480 weeks skip Now the factor is 12.2. Round down to 12 40-week cycles, and apply the correction same as the first time. 12 cycle drift minus one Martian day the other way (7,259 * 12) - 88,643 = -1,535 seconds ahead every 480 weeks.

Every 27,840 weeks don't skip Now the factor is 1/57.7. Round to 1/58 (we're stopping here) and apply the correction same as the second time. 58 cycle drift plus one Martian day the other way (-1,535 * 58) + 88,643 = 387 seconds ahead every 27,840 weeks. That seems close enough (factor of 229 which would be one day in ~57,000 years)

Other cycles

Looking at this, I'm sure that the actual Martians will be able to figure out a much more clever arrangement after years of doing business with Earth. For example, if you do a 6 week skip, your factor is then 1/16 (5,521 seconds), which would mean adding another skipped day every 6 * 16 = 96 weeks which is very close to a Martian year. If you do it yearly, you could choose whether to not skip if the yearly lands on the same week as the 6-week cycle, or choose to do it the week before/after. That buys you an optional 6 year cycle that you could choose based on which brings you closer. After that it could all be yearly based.

If you do the year, we have to do the calculations by day. 5,521 seconds per 6 weeks is 131.45 seconds per day. There are 668.5991 Martian days in a Martian year, which means that we would be losing 87,888.94 seconds per year with the 6 week cycle. With the yearly skip, we'd bring that down to gaining 754.06 seconds per year. Every 6 years would be 4,524.34 seconds, so we'd have to double up the days off when they fell during the same week. Every 19.59 years we'd be another day off the other way, so why not every 20 years skip the yearly leap. We're at a cycle greater than 1,000 years after this point.

Answer 10

Running the Maths, I think this is how it works:

A Martian Day is 88,642 seconds. An Earth Day is 86,400 seconds.

Over the course of 365.25 Days, Mars will have an excess of 818,890.5 seconds to lose, which equates to 9.24 Mars Days.

So they can skip 1 day a month for 3 months out of every 4, and then they can mirror Leap Years on Earth for the other 0.24 of a day, except rather than adding a day they'll skip a day.

Answer 11

The solution could perhaps be to work at a lower level and modify the smaller time increments, rather than trying to fit a martion day into an earth one,

If martian timekeeping used a slightly extended length of time for a second (or minute if preferred) then hours and days would stay in sync with their earth counterparts. Devices on mars would need to be configurable for the different time setup, but this should not be an insurmountable issue.

Workers on mars would benefit from slightly extended lunch breaks at the cost of slightly longer working days.

I leave it to others to do the maths for the optimum time adjustment...