Submitted by mossy2100 on Tue, 04/25/2017 - 00:36

There are many questions about how a mir should be divided into months:

  • Should a Mars calendar have months?
  • If so, how many should each mir contain? (and thus, how long will they be?)
  • Should they be related to lunar cycles? How about the cycles of the Martian moons?
  • Should the months be synchronised with mirs? (i.e. should every mir have the same number of months?)
  • What should the months be called?

Should the calendar include months?

“Month” means “Moon”, and months on Earth were originally defined by the cycle of lunar phases. A “new moon” (when Luna is between the Sun and Earth, and Luna is therefore barely visible) means, literally, “new month”, and in lunar calendars such as the Islamic, Hebrew, Chinese, and Hindu calendars, months do indeed begin with the new moon.

Mars has two moons. Phobos, the larger, inner moon, has an orbital period of about 7.65 hours, or 0.31 sols. Deimos, the smaller, outer moon, has an orbital period of about 30.3 hours, or 1.23 sols. Neither of these periods seem especially useful for incorporating into the Martian calendar.

Months in solar calendars, such as the Gregorian, are not synchronised with the lunar cycle. Rather, the year is divided into 12 approximately-equal periods, which are slightly longer than lunar months. This tends to suggest that the month is a useful calendrical time period, irrespective of whether it coincides with an astronomical cycle. Calendar months are commonly used for purposes such as defining when bills and salaries are paid, scheduling monthly or quarterly meetings or reports, and for dividing the year into approximately halves, thirds, or quarters.

It’s reasonable to imagine that the Martians will also want the calendar mir divided into months, with approximately the same duration and purpose as months in Terran calendars.

Months in Terran calendars

On Earth we have lunar, lunisolar, and solar calendars. Lunar and lunisolar calendars are defined by the cycle of Luna’s phases as it orbits Earth, a period called a “synodic month” or “lunation”. The average lunation duration is 29.53 days, although a lunation can vary from this average by up to 7 hours.

Lunar calendars such as the Islamic Calendar have 12 months per year, aligned with the lunar cycles. This gives an average calendar year length of about 354.36 days, which means the calendar year is not synchronised with the tropical year.

Lunisolar calendars such as the Hebrew and Traditional Chinese calendars also have months synchronised with the lunar cycles, but each calendar year contains 12 or 13 months per year, in order to also synchronise the year with the seasons. This results in short years of 354 or 355 days or long years of 383 or 384 days, a variation of up to 30 days. Neither short nor long years are close in length to the tropical year, but the overall average is.

Solar calendars such as the Gregorian Calendar have exactly 12 months per year, and these are synchronised with the seasons and not with lunar phases. The average month length is 365.2425 / 12 = 30.44 days.

On Earth, solar calendars are more popular and useful than lunar or lunisolar calendars because the calendar year length, whether a normal 365-day year or a leap year of 366 days, is always very close to the tropical year length, therefore seasonal markers (equinoxes and solstices) always occur around the same dates. Seasons are more important to the lives of modern humans than lunar cycles, being strongly associated with weather, and therefore also agriculture, holidays, etc.

Another benefit of a solar calendar is highlighted by the “leap baby” problem. People born on February 29 are called “leap babies”, because this date only occurs in leap years. In short years, when the date February 29 does not appear in the calendar, leap babies celebrate their birthdays on either February 28 or March 1. Since February 29 occurs only 97 times in 400 years, this only affects 664 people out of every million.

In a lunisolar calendar, however, the intercalary 13th month is included approximately every second year, which means about 3% (about 29775 per million) of all people are born during this month. In years with only 12 months these birthdates don’t appear, which means many more people are affected by this problem. These leap babies move their birthday to some other date, usually the same day of the month in an adjacent month. Apart from the fact that a far greater number of people are affected, this date adjustment is much greater, i.e. 29 or 30 days. Two people, one a leap baby and one not, may celebrate their birthdays in a different sequence in different years.

Advantages of a solar calendar can thus be summarised:

  • Dates are closely synchronised with seasons.
  • It’s easy to divide the year into 2, 3, 4, 6, or 12 approximately equal parts.
  • The leap baby problem is minimised.

How many months per mir?

Many options for the number of months in a Martian year have been proposed, including 10, 12, 16, 20, 24, and 32. The Darian and Utopian Calendars use 24 months per mir, which is the best choice for several reasons:

  • It will be familiar to users of the Gregorian Calendar, since 24 is the same number of months as in two years.
  • This choice enables a mir to be easily divided into 2, 3, 4, 6, 8, 12, or 24 approximately equal parts.
  • A Martian month then becomes about the same length as in a Terran calendar. The average length of a Utopian Calendar month becomes 668.591 / 24 = 27.858 sols (28.6 days). Months in the Gregorian Calendar range in length from 28-31 days, with an average duration of 30.44 days. The average length of a lunar month is 29.53 days. Thus, while Utopian months are slightly shorter, on average, than Terran or lunar months, they fit within the familiar range of 28-31 days. In future interplanetary conversations, when referring a number of months, for most practical purposes it will not be necessary to specify whether speaking about Terran, lunar, or Martian months.

How many sols per month?

From the number of months per mir we can determine the the average month length is 27.858 sols. However, we wish to define calendar months as whole numbers of days, so that each month has either 27 or 28 sols. We therefore need to define rules, similar to those for short and long mirs, to determine when a month is a short month of 27 sols, or a long month of 28 sols.

  1. By default, a month is long.
  2. By default, every 6th month (i.e. the last month in each quarter) is short.
  3. The exception is that, in a long mir, the last month of the mir is long.

Thus, a short mir has equal quarters, with 28 * 5 + 27 = 167 sols per quarter, which is 668 sols per mir. A long mir has an extra sol tacked on the end, making 669 sols. (This pattern is easier to visualise when viewing calendar pages.)