# Martian calendar

Anton Sherwood (dasher@netcom.com)
Sun, 4 Jan 1998 17:22:37 -0800 (PST)

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

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.

In column C, I took B a step further: the shorter months get 27 days,
the longer months 28.