A Martian calendar should be for Martians, obviously. But who are the Martians? At first, they will be settlers from Earth, and for a long time the population will grow almost solely from immigration. Therefore, a calendar should not be completely unfamiliar to ex-Earthlings.
For the Vophick Calendar, I've used the Gregorian names because they are already in common usage. The words no longer refer to the god of doorways or an ancient purification festival, but to a particular time of year. Not many people on Earth know or care about the month names' origins, so why should people on Mars be bothered to learn them either? And anyway, if Martians are not going to teach Earth history, they won't have *any* history. Martians will still be humans, after all.
As for the length of a week, I choose nine sols. A seven-sol week fits too well into a Darian or Vophick month. For me, living by a perpetual calendar would just get boring after a while. Believe you me, I've tried it. There just ain't no flavor to that kinda calendar. Imagine: there wouldn't be a point in naming holidays as "the last Monday in May" since the last Monday in May would always be the 23rd! Talk about taking all the fun out of life!
So, you say, why would a traditionalist argue for a nine-sol week? Well, because seven divides evenly into 21 and 42, of course (28, too, if you want that length of month). Each month would start on the same sol of the week until the calendar got to a short month, and then it would only change by one day. I believe that a week should never fit evenly into a month. We need some variety in our calendars! So in order to keep the status quo, we need to change the length of a Martian week.
I arrived at nine sols per week by considering how our current seven days received their names. Sun, Moon, Tiu (Mars), Woden (Mercury), Thor (Jupiter), Frigg (Venus), Saturn -- all were originally named after the seven known planets 4000 years ago (Babylonians, was it? And apparently the seven day cycle has never been broken!). They named the 24 hours of the days after the seven planets (sun and moon included). They started with Saturn, then Jupiter, then Mars, then the Sun (geocentric in those days), then Venus, Mercury, and the Moon. So the first hour of the first day was Saturn's hour, followed by Jupiter's hour. Due to the fact that seven doesn't fit into 24 very well, the next day began with the Sun's hour. The day after that began with the Moon's hour. Mars's, Mercury's, Jupiter's, Venus's, and back to Saturn's. ...Different religions have changed the starting day of the week, but we've kept the same cycle going for millenia.
So, as you can see, it is mere chance that the big ol' sun and the big ol' moon are the first two days of our week. If we were to list all objects visible from Mars, they would be Sun, Mercury, Venus, Earth, Luna, Phobos, Deimos, (any asteriods visible?), Jupiter, (could you see the Galilean moons without a telescope?), Saturn, Uranus. This would be at least a ten-day week! But then again, what self-respecting astronomer does not have a telescope? *All* of the planets and moons and asteroids and comets are visible nowadays! How many of those are there? This is why I suggest sticking with the nine traditional planets plus the sun. Throw out Mars 'cause you're standing on it, and you're left with a nine-day week: Sunisol, Wensol, Frisol, Earsol, Thursol, Satursol, Urasol, Neptasol, Plutisol. Or, if you love Latin: Solisol (ick!), Mercasol, Vensol, Terrasol, Jupisol, Satursol, Urasol, Neptasol, Plutisol.
Another option that I have worked with is the largest N bodies in the solar system. Just count down from the Sun and Jupiter until you get the number of days you want in your week. Sunisol, Jupisol, Satursol, Urasol, Neptasol, Earsol, Vensol, Marsol, Ganysol, Tatnsol, Mercasol, Callisol, Iosol, Monsol, Ropasol, Trisol, Plutisol, ....
But I have changed my mind. I now favor a twenty-month calendar.
If any of you are wondering where I picked the name "Vophick" from, read on.
42 sols in a month still seemed too long to me, so I cut them each in half! Instead of 16 months, there would be 32 months of 20 and 21 sols in length. The original sixteen names could still be used to refer to the entire 42 sols with the new month names only referring to a subset of those 42 sols (the second half).
Thusly, January 22 is also Atnough 1, January 42 is Atnough 21, and January 1 is only January 1.
"Atnough?" I hear you ask. "Where did Atnough come from?"
Well, if I gotta make new months, they gotta have new names. They will be known as Atnough, Bithogin, Kupf, Gysle, Ghizzam, Natten, Hibtho, Jivv, Ognate, Phaichu, Rilwha, Thogna, Vophick, Xurl, Islif, and Zhimga. (Yes, they were once in alphabetical order, but I had to change the spellings to make them *look* right.)
January 1 - January 21
January 22 - January 42 = Atnough 1 - Atnough 21
February 1 - February 21
February 22 - 41 = Bithogin 1 - Bithogin 20
March 1 - March 21
March 22 - March 42 = Kupf 1 - Kupf 21
Geldof 1 - Geldof 21
Geldof 22 - Geldof 42 = Gysle 1 - Gysle 21
April 1 - April 21
April 22 - April 42 = Ghizzam 1 - Ghizzam 21
May 1 - May 21
May 22 - May 42 = Natten 1 - Natten 21
June 1 - June 21
June 22 - June 41 = Hibtho 1 - Hibtho 20
Yorte 1 - Yorte 21
Yorte 22 - Yorte 42 = Jivv 1 - Jivv 21
July 1 - July 21
July 22 - July 42 = Ognate 1 - Ognate 21
August 1 - August 21
August 22 - August 42 = Phaichu 1 - Phaichu 21
September 1 - September 21
September 22 - September 42/41 = Rilwha 1 - Rilwha 21/20
Herjber 1 - Herjber 21
Herjber 22 - Herjber 42 = Thogna 1 - Thogna 21
October 1 - October 21
October 22 - October 42 = Vophick 1 - Vophick 21
November 1 - November 21
November 22 - November 41 = Xurl 1 - Xurl 21
December 1 - December 21
December 22 - December 42 = Islif 1 - Islif 21
Vidman 1 - Vidman 21
Vidman 22 - Vidman 42 = Zhimga 1 - Zhimga 21
As simple as that!
...Since I wonder about the month names in the Thothian Wheel, I suppose I should explain my own:
Yorte is named after Pyotr Ilyich Tchaikovsky (Pyotr -> Yotre -> Yorte
(Yotre sounded too French!))
Vidman is named after David Letterman (52 weeks, 52 cards in a deck, day left over is Joker)
Geldof was used in "Better Than Life" episode of _Red Dwarf_ ("Here is the news on this Friday, the 27th of Geldof.")
Herjber is named after Herge (Belgian creator of Tintin comic strip) (-ber added since it's a autumn month)
Atnough through Zhimga are named after animals. Well, sort of. I designed a calendar in which the month names rotated on a 35-animal cycle, but the year was only 26 months long (14-day months). The 35 month animals each began with a different letter (plus Ch, Gh, Gn, Ll, Ph, Ps, Sh, Th, and Wh. (Know any animals beginning with Ps?)). Each year was named after the first month of the year plus an adjective. (This is the year of the Flying Zebra.) The first month of the year began as Alligator, but next it was Toad, then Narwhal, then Ghost. To create a difference between year names and month names, I took the first letter of each of the first four animals for each month:
A T N Gh
B Th O Gn
C U P H
Ch V Ph I
D W Ps J
E Wh Q K
F X R L
G Y S Ll
Gh Z Sh M
Gn A T N
H B Th O
I C U P
J Ch V Ph
K D W Ps
L E Wh Q
Ll F X R
M G Y S
N Gh Z Sh
O Gn A T
P H B Th
Ph I C U
Ps J Ch V
Q K D W
R L E Wh
S Ll F X
Sh M G Y
T N Gh Z
Th O Gn A
U P H B
V Ph I C
W Ps J Ch
Wh Q K D
X R L E
Y S Ll F
Z Sh M G
...and then I tried to pronounce them. I'm only giving you the best sixteen out of 35, so feel lucky! (Whaqked or Doopsadge, anyone?)