You asked about the Martian calendar. So, here is your first lesson supplement from space. Ha, ha. If you Google ‘Mars Calendar’, you will come up with The CMEX Mars Calendar. This will give you some interesting data about the length of a Martian day and so on. For example: 1 Martian Day = 1.0275 Earth Days or 24 hours, 39 minutes, and 35 seconds, 1 Martian year = 686.98 Earth Days, but only 668.60 Mars days. The CMAX also has a 12-month calendar down the right side of the web page. But, if you add up the number of days in each month, the total is 672. Someone dropped the ball on that, I’m afraid. They also start the Martian calendar in1976, the first year of the Viking probes landing on Mars.
By comparison, Dr. Robert Zubrin, in his book, The Case For Mars based his Mars Zubrinian calendar on Mars’ location within the constellations of the zodiac, as seen from the sun. There are 12 constellations and 12 months, with Gemini being the first. Martian months have a different number of days from Earth months, primarily due to the longer year. The breakdown of the 669 days, by month, is: Gemini 61, Cancer 65, Leo 66, Virgo 65, Libra 60, Scorpio 54, Sagittarius 50, Capricorn 47, Aquarius 46, Pisces 48, Aries 51, and Taurus 56. The reason for such diversity in the number of days per month is due to the elliptical orbit of Mars around the sun. The months are shorter when Mars is close to the sun, and longer when it is further away. Also, as viewed from the sun, not all constellations are created equally.
Dr. Zubrin also dated his calendar years earlier, beginning on January 1, 1961, for the first year of manned space flight. However, he chose to use Sunday through Saturday for the weekdays. If we were to adjust the clock to a Martian day or if a Mars day were 24 hours that would work just fine, but the extra 39 min, 35 sec each day throws a wrench into it. About every 52 days, there is a leap day. That is, you may start out with Sunday on Earth = Sunday on Mars, Monday = Monday, etc. But, after about 52 days, Monday on Earth is still only Sunday on Mars.