Vinicio Coletti Web Site

A Calendar for Mars

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Download my Mars Calendar Windows program (v0.91)

I read on a Nasa note by Michael Allison and Robert Schmunk that a Mars mean solar day (sol) lasts 24 hours 39 minutes 35.244 seconds and that a Mars tropic year lasts 668.5921 sol.

Time of the day – watches

Of course it’s better not to change the definition of the second, which is the standard reference time. In the first version of my calendar I did not change the concepts of minute and hour, so that Mars watches would have the same clock of terrestrial ones, but they should have an internal millisecond computing and should reset to 00:00:00.000 after indicating 24:39:35.243.

This is practical for science and events, but peculiar times such as midnight and noon would have rather strange values. Thus, in v0.91 of my program I let the user decide among three different ways of telling time on Mars:

1. Second, minute and hour are the same as on Earth; the sol lasts 24:39:35.244; noon is at 12:19:47.622
2. Second and minute are the same as on Earth, but the sol is divided into 20 hours of 74 minutes each, with the last minute of the day being a leap-minute of 35.244 seconds; noon is at 10:00:00
3. The last method is the same used by Mars24 program, that is watches are identical to ours, but the second lasts a bit more (about 1.0275 earth seconds); of course noon is at 12:00:00

Calendars

The purpose of all calendars is to define a year made of an integral number of days, although the revolution of a planet around the sun lasts usually a fractional number of days. All that without shifting astronomical references (equinoxes etc.) for very long periods. In Earth calendar we add a day every 4 years, but not every 100 years, unless the year is a multiple of 400. This gives a mean duration of the year very close to the real, fractional one.

A calendar for Mars

About Mars, we must deal with the tropical year duration of 668.5921 sol. Since this number is not close to an integral number but almost halfway, the first decision about this calendar is:

• Odd Martian years shall last 668 sol
• Even Martian years shall last 669 sol

Of course this will give a mean duration of 668.5 sol, already quite close to the real duration.

To come more close, we introduce leap years lasting one more sol and happening every eleven years. This actually defines a 22 year cycle, because:

• Leap year 11 shall last 669 sol (instead of the 668 of a normal odd year)
• Leap year 22 shall last 670 sol (instead of the 669 of a normal even year)

In a 22 year cycle the mean duration of the Martian year will be 668.5909 sol, short by only about 0.21%.

To reach a greater precision we will simply add a long term leap year every 850 Martian years ⁽¹⁾. This will give a mean duration of 668,5921 sol, with an error less than 0,01% or a shift of 1 sol in more than 10,000 Martian years (more than 18,000 Earth years). This is as good, or even better, than the Gregorian calendar we currently use on our planet.

Years will last at most 670 sol, except every 9350 years ⁽¹⁾, when both leap years will coincide and the year will last 671 sol. The year will be divided in 12 months and every month will last either 55 or 56 sol. To avoid months longer than 56 sol, the three additions regarding even years, leap years and long term leap years will happen on three different 55-sol months.

Each month will be divided in weeks, each formed by 7 sol. Thus the 56-sol months will be formed by exactly 8 weeks. Months could be named as usual but to avoid confusion with the terrestrial calendar, they could also have different names. I propose to call them with the Latin terms for First, Second, Third, etc. The table below summarize these concepts.

Duration of Martian months (sol)

Martian month	Odd year	Even year	Leap-odd year	Leap-even year	Long term leap year (always even)
Primus	56	56	56	56	56
Secundus	55	55	56	56	55
Tertius	56	56	56	56	56
Quartus	56	56	56	56	56
Quintus	56	56	56	56	56
Sextus	55	55	55	55	56
Septimus	56	56	56	56	56
Octavus	56	56	56	56	56
Nonus	55	56	55	56	56
Decimus	56	56	56	56	56
Undecimus	55	55	55	55	55
Duodecimus	56	56	56	56	56

That is:

• All months are short or long as in Gregorian calendar, except Quartus, which is long.
• On even years Nonus becomes long (every 2 years)
• On leap years Secundus becomes long (every 11 years)
• On long term leap years Sextus becomes long (every 850 years ⁽¹⁾)

Mean year duration quickly converges very close to the actual value

The Martian week

About weeks, we could use the current weekday names or use new ones. I propose the following names. Weeks start with the equivalent of our Monday and finish with the two weekend sol.

The Martian week

Week-sol	Sol name
1	Phobosol
2	Deimosol
3	Earthsol
4	Moonsol
5	Venusol
6	Mercusol
7	Sunsol

The names are given thinking to an imaginary trip from Mars to the Sun, starting from Mars moons, through Earth and its moon, Venus and Mercury.

The starting date

Every calendar needs also a starting date, so we must establish what earth date and time (UTC) is equivalent to 00:00:00.000 of Phobosol Primus 1th, of the Martian year 1.
Symbolic dates could be that of the first arrival of a probe around Mars or that of the first landing of a probe, but I agree with the Allison and Schmunk proposal to select a date well before any detailed observation of the planet. This way all past scientific observations of Mars could be expressed in terms of the Mars calendar.
Thus, I adopt for this calendar the starting date proposed by Allison and Schmunk: December 29, 1873 at 00:00 UTC, corresponding to Julian day 2405522.0

(1) Note: on first version of this calendar (March 25, 2004) I proposed a long term leap year every 840 Martian years, but, since it's only important that a day be added in the 22 year cycle ending with year 858, I changed the long term leap year to year 850, because this number looks more round.

This Mars Calendar is proposed by
Vinicio Coletti
Rome, Italy
E-mail mailto:vcoletti@libero.it

First published on March 25, 2004 in my site: http://digilander.libero.it/vcoletti/ideas/marscalendar.html
Last updated on April 2, 2004