A Mars Calendar
A variety of calendar systems have served human civilization to organize time according to the needs of society and religion. A calendar of sorts even exists for another planet...
It is the end of the year 2009 and you probably have a calendar or two for the new year ready to hang on the wall or put on your desk. To be more precise it will be the New Year 2010 of the Gregorian Calendar. This is the international standard calendar and is also the official calendar for many of the world's countries.
But in addition to the Gregorian Calendar about 40 different calendar systems are in use today. Most of them serve to fix religious and cultural activities but some are also used as official calendars in certain countries. The majority of calendars are based on the periodic motions of the Sun and the Moon and thus astronomy gets into the act.
The principal astronomical bases of calendars are the mean length of the tropical year (365.2421897 days) and the mean synodic month (29.530588853 days). These numbers change slightly over the centuries but for the purpose of calendars we don't have to worry about that.
The Gregorian Calendar is a purely solar calendar with the months being fixed according to convention and not with regard to the phase of the Moon. To approximate the tropical year with an integral number of days the well known leap year rule is used which states that years have 365 days with every fourth being a leap year of 366 days (except years which can be divided by 100 but not by 400).
By contrast the Islamic Calendar is a purely lunar calendar. One year has 12 months with the beginning of each month defined by the New Moon or rather by the first sighting of the lunar crescent after New Moon. But as 12 synodic months fall short of the tropical year by about 11 days this means that Islamic New Year and all the other holidays will shift throughout the seasons.
To avoid this shift lunisolar calendars use months of 29 or 30 days beginning with New Moon but add an extra month every two or three years to adjust for the position of the Sun. An additional day may be added or subtracted for fine-tuning. The Hebrew Calendar and the Chinese Calendar are examples of this. They have ordinary years of 353, 354 or 355 days and leap years of 383, 384 or 385 days.
While the Hebrew Calendar uses an adopted period for the synodic month and fixed rules about leap years the Chinese Calendar is based on modern calculations of the actual positions of the Sun and the Moon and those positons are used to define leap years.
The Indian Civil Calendar synchronizes with the Gregorian Calendar but the beginning and the lengths of months are defined to approximate the Indian Religious Calendar. This in turn uses actual positions of the Sun and the Moon in some way similar to the Chinese Calendar.
All these calendars served us well here on Earth. But a new situation arose with interplanetary spaceflights. When spacecraft landed on Mars mission controllers were faced with the problem to synchronize operations according to the day/night cycle on Mars.
One Mars day is 24 hours, 39 minutes and 35 seconds long. Mission controllers called this a sol and scheduled operations according to the number of sols elapses since the day of landing. Thus the first extra-terrestial calendar of sorts was improvised.
Looking way ahead into the future there might be human colonies on Mars some day. They might find it useful to synchronize their activities not just with the Martian day but also with the Martian year. One Mars year has 668.6 Mars days. This number is close to 660 so you could define a Mars calendar with 22 months of 30 or 31 Mars days (and about every other year a leap year).
Alternatively you might find it useful to keep close connections with the Earth. As one Earth year is 355.48 Mars days you could have a Mars/Earth calendar with 12 months of mostly 30 (and a few 29) Mars days.
But I guess I will leave this problem to future generations and rather wish all of you on our beloved home planet a
HAPPY NEW YEAR
January 1 Gregorian year 2010
February 14 Chinese year of the Tiger
March 22 Indian year 1932
September 9 Jewish year 5771
December 8 Islamic year 1432
On Mars, the solar longitude is a useful measure of the planet's progress along its orbit. The solar longitude is in essence the same as the true anomaly, so it goes from 0 to 360 degrees over the course of one Martian year.
It is defined as zero on the vernal equinox, the start of spring on the Northern hemisphere. An ideal date to start the Martian year, an opportunity we have unfortunately missed on Earth. In fact, the scientists who study the Martian climate and atmosphere do exactly that.
Alternatively, making use of the marked eccentricity of the Martian orbit, one might start the year at the perihelion pass, i.e., around a solar longitude of 255 degrees - late winter on the northern hemisphere, late summer on the southern.
That would be not to dissimilar to the Gregorian new year on Earth, which is close to (but not exactly at) the perihelion of the Earth orbit.