Martian Calendar

by Anton Sherwood

It would be convenient for human settlers on Mars to divide the Martian year into 24 months. But how many days should each month have? If the year is divided equally by time, obviously each month has 27 or 28 days (the year is 668.5994 Martian days). An alternative is to define a month as 15 degrees of motion around the sun, so that the periods between equinox and solstice are each exactly six months.

Using Kepler's Second Law, I have computed the following lengths for such months. Orbital eccentricity is 0.093 and my year begins at northern spring equinox, LS=0 (110 degrees after perihelion). I've done no error analysis yet; I would like to know how sensitive these months are to an error in the last digit of the eccentricity or the phase angle.

month#  days    A       B       C       D
  0     30.01   30      30      28      30
  1     31.30   31      31      28      31
  2     32.37   32      32      28      32
  3     33.10   33      33      28      33
  4     33.41   33      33      28      34
  5     33.25   33      33      28      33
  6     32.66   33      32      28      32
  7     31.69   32      31      28      31
  8     30.46   31      30      28      30
  9     29.10   29      29      28      29
 10     27.73   28      27      28      28
 11     26.43   26.6    26      28      27
 12     25.28   25      25.6    28      26
 13     24.35   24      25      28      25
 14     23.65   24      24      28      24
 15     23.20   23      24      27      23
 16     23.03   23      24      27      23
 17     23.11   23      24      27      23
 18     23.47   24      24      27.6    24
 19     24.09   24      25      28      24
 20     24.95   25      25      28      25
 21     26.03   26      26      28      26
 22     27.28   27      27      28      27
 23     28.64   29      28      28      28.6
 

I hope I haven't blundered somewhere!

In column A, I've rounded according to the rule of largest remainder: those months with a fraction larger than .43 are rounded up, those with a smaller fraction are rounded down, and month 11 is leap-month, with an extra day in three years out of five.

In column B, to make the months slightly more equal in length, the longer months are rounded down, the shorter months rounded up.

Column C takes the idea of B to the logical end: the shorter months get 27 days, the longer months 28. In column D, the rule is that each month be assigned its "true" number of days, rounded either up or down (as in A and B), but with the further rule that wherever possible adjacent months differ in length by no more than one day. Unfortunately months 21-23 are pulled both ways; so I've put leap-day there, so that at least the two-day step is not in the same place every year.

Comments?

I'd like to name each month for the brightest star (weighted by cosine of celestial latitude) to cross the midnight line in that month; that might be an interesting exercise for someone with access to an appropriate stellar database.