Unexact years

As on Earth, the average year on Mars has not an integer for the numbers of sols (days of Mars). Therefore, in the same way that gregorian calendar uses years with an additional day every four years, except when the first year of a century is not divisible by four, there's a way to correct this error. For Mars, the trick is to add a sol when the year is divisible by 10, except when it is divisible by 100 but not by 500. For the months, I decided to use the same length for all (4 months of 167 soles).

For this story, the martian calendar starts its count on september 3rd, 2038, date of the establishment of the first human colony on the planet.

References

• Calendar Converter
• Timekeeping on Mars
• Julian year

Longer days

On Earth, a solar day (the time it takes from a miday to another) is 24 hours. In Mars, it takes 24 hours 39 minutes and 35.244 seconds. This means each day is 2.7% longer than the one on Earth. If you travel to Mars, it will be strange to ask for the time and recieve an answer like 24:30 hours, and asking again 10 minutes later, 0:01 hours. I read about some ways to solve the problem thinking about the possibilities of living in such exotic landscape. Some solutions are to create a new metrical system, or make martian seconds 2.7% longer, or using the same time system that we use in our tiny green rock (with the incomplete hour at the end of every day).

I decided to use the 2.7% longer seconds solution, allowing to use the same kind of clock as on Earth. This because it's easier for a human to be used to a 24 hours clock, but it makes harder to make a conversion for dates between Mars and Earth. The 24:39:35.244 hours of a martian day is called Sol. The timezones in Mars are the same than the ones in Earth. Each timezone is a strip of 15º longitude, taken from meridian zero. This has been defined as the center of the Airy-0 crater.

Martian Date

Calendars introduce some complications in time calculations. These were created to track seasons and organize the activities along the year. However, making calculations like the number of days between two dates is more complex. To do this, astronomers use a counting system of progressive days called Julian Day. It counts the number of days since the miday of a start date called epoch. The julian day uses 24 hours day as units, but as we have seen, Mars days have a different length.

The first step to transform a julian day date to a martian solar date, is using this formula:

Martian Solar Date = (Julian Date - 5 - 51549.0 + k)/1.02749125 + 44796.0

When k is a small correction of 12 seconds (0.00014 days) for an issue with the coordinates of Airy-0 crater. This way we get the number of sols occurred since the epoch for a martian solar date. To these dates, both julian day and martian solar date, we must apply other formulas to get their equivalences for the gregorian calendar (the one we use in this side of the world) and a calendar for Mars.

References

• Timekeeping on Mars (Wikipedia)
• Julian Day