Darian calendar

The Darian calendar is a proposed system of timekeeping designed to serve the needs of any possible future human settlers on the planet Mars. It was created by aerospace engineer, political scientist, and space jurist Thomas Gangale in 1985 and named by him after his son Darius. It was first published in June 1986. In 1998 at the founding convention of the Mars Society the calendar was presented as one of two calendar options to be considered along with eighteen other factors to consider for the colonization of Mars.

Year length and intercalation

The basic time periods from which the calendar is constructed are the Martian solar day (sometimes called a sol) and the Martian vernal equinox year. The sol is 39 minutes 35.244 seconds longer than the Terrestrial solar day, and the Martian vernal equinox year is 668.5907 sols in length (which corresponds to 686.9711 days on Earth).

The basic intercalation formula therefore allocates six 669-sol years and four 668-sol years to each Martian decade. The former are still called leap years, even though they are more common than non-leap years, and are years that are either odd (not evenly divisible by 2) or are evenly divisible by 10: this produces 6,686 sols per ten years, giving an average year of 668.6 sols.

A 1998 iteration of the Darian calendar had leap years cancelled if the year was divisible by 100, unless the year was also divisible by 500; adding these rules produces an average year of 668.592 sols, a more reasonable approximation.

However, these static intercalation schemes did not take into account the slowly increasing length of the Martian vernal equinox year. Thus, in 2006, Gangale devised a series of intercalation formulas, all of which have in common the basic decennial cycle, as shown in the following table:

Range of years Formula Mean length of calendar year
0–2000 (Y − 1)\2 + Y\10 − Y\100 + Y\1000 668.5910 sols
2001–4800 (Y − 1)\2 + Y\10 − Y\150 668.5933 sols
4801–6800 (Y − 1)\2 + Y\10 − Y\200 668.5950 sols
6801–8400 (Y − 1)\2 + Y\10 − Y\300 668.5967 sols
8401–10000 (Y − 1)\2 + Y\10 − Y\600 668.5983 sols

This extended intercalation scheme gives an average year of 668.59453 days over the 10000 years: this results in an error of only about one sol at the end of 12,000 Martian years, or the year 24,180 of the Common Era.

Calendar layout

The year is divided into 24 months. The first 5 months in each quarter have 28 sols, while the final month has 27 sols unless it is the final month of a leap year, when it contains the leap sol as its final sol.

The calendar maintains a seven-sol week, but the week is restarted from its first sol at the start of each month. If a month has 27 sols, this causes the final sol of the week to be omitted.

This is partly for tidiness and can also be rationalised as making the average length of the Martian week close to the average length of the Terrestrial week; 28 Earth days is very close to 27+14 Martian sols, whereas a month is an average length of 27+56 Martian sols.

In the table, the sols of the week are Sol Solis, Sol Lunae, Sol Martis, Sol Mercurii, Sol Jovis, Sol Veneris, Sol Saturni.

Sagittarius Dhanus Capricornus Makara Aquarius Kumbha Pisces Mina Aries Mesha Taurus Rishabha Gemini Mithuna Cancer Karka Leo Simha Virgo Kanya Libra So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 8 9 10 11 12 13 14 8 9 10 11 12 13 14 15 16 17 18 19 20 21 15 16 17 18 19 20 21 15 16 17 18 19 20 21 22 23 24 25 26 27 28 22 23 24 25 26 27 28 22 23 24 25 26 27 28 So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 8 9 10 11 12 13 14 8 9 10 11 12 13 14 15 16 17 18 19 20 21 15 16 17 18 19 20 21 15 16 17 18 19 20 21 22 23 24 25 26 27 28 22 23 24 25 26 27 28 22 23 24 25 26 27 So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 8 9 10 11 12 13 14 8 9 10 11 12 13 14 15 16 17 18 19 20 21 15 16 17 18 19 20 21 15 16 17 18 19 20 21 22 23 24 25 26 27 28 22 23 24 25 26 27 28 22 23 24 25 26 27 28 So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 8 9 10 11 12 13 14 8 9 10 11 12 13 14 15 16 17 18 19 20 21 15 16 17 18 19 20 21 15 16 17 18 19 20 21 22 23 24 25 26 27 28 22 23 24 25 26 27 28 22 23 24 25 26 27 So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 8 9 10 11 12 13 14 8 9 10 11 12 13 14 15 16 17 18 19 20 21 15 16 17 18 19 20 21 15 16 17 18 19 20 21 22 23 24 25 26 27 28 22 23 24 25 26 27 28 22 23 24 25 26 27 28 So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 8 9 10 11 12 13 14 8 9 10 11 12 13 14 15 16 17 18 19 20 21 15 16 17 18 19 20 21 15 16 17 18 19 20 21 22 23 24 25 26 27 28 22 23 24 25 26 27 28 22 23 24 25 26 27 So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 8 9 10 11 12 13 14 8 9 10 11 12 13 14 15 16 17 18 19 20 21 15 16 17 18 19 20 21 15 16 17 18 19 20 21 22 23 24 25 26 27 28 22 23 24 25 26 27 28 22 23 24 25 26 27 28 So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa So Lu Ma Me Jo Ve Sa 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 8 9 10 11 12 13 14 8 9 10 11 12 13 14 15 16 17 18 19 20 21 15 16 17 18 19 20 21 15 16 17 18 19 20 21 22 23 24 25 26 27 28 22 23 24 25 26 27 28 22 23 24 25 26 27 28

The last sol of Vrishika is an intercalary sol that only occurs on leap years, as per February 29 in the Gregorian calendar.

Start of year

The Martian year is treated as beginning near the equinox marking spring in the northern hemisphere of the planet. Mars currently has an axial inclination similar to that of the Earth, so the Martian seasons are perceptible, though the greater eccentricity of Mars' orbit about the Sun compared with that of the Earth means that their significance is strongly amplified in the southern hemisphere and masked in the northern hemisphere.

Epoch

Gangale originally chose late 1975 as the epoch of the calendar in recognition of the American Viking program as the first fully successful (American) soft landing mission to Mars (the earlier 1971 Soviet Mars 3 Landing having delivered only 15 seconds of data from the planet's surface). In 2002 he adopted the Telescopic Epoch, first suggested by Peter Kokh in 1999 and adopted by Shaun Moss in 2001 for his Utopian Calendar, which is in 1609 in recognition of Johannes Kepler's use of Tycho Brahe's observations of Mars to elucidate the laws of planetary motion, and also Galileo Galilei's first observations of Mars with a telescope. Selection of the Telescopic Epoch thus unified the structures of the Darian and Utopian calendars, their remaining differences being nomenclatural. It also avoids the problem of the many telescopic observations of Mars over the past 400 years being relegated to negative dates.

Nomenclature

The Darian calendar has been widely imitated. Suggested variations abound on the internet that use different nomenclature schemata for the days of the week and the months of the year. In the original Darian calendar, the names of the 24 months were provisionally chosen by Gangale as the Latin names of constellations of the zodiac and their Sanskrit equivalents in alternation. The 7 sols of the week, similarly, were provisionally named after the Sun, the largest Martian moon Phobos (Sol Phobotis) and the 5 brightest planets as seen from Mars including Earth (Sol Terrae). These were later modified to follow the familiar convention of the Romance languages, replacing Sol Phobotis with Sol Lunae and Sol Terrae with Sol Martis. The Darian Defrost Calendar, however, uses the Rotterdam System to create new names for the Martian months out of patterns relating letter choice and name length to month order and season. The Utopian Calendar, devised by the Mars Time Group in 2001, also has additional suggestions for nomenclature modification.

Comparison of month names by system
Darian Rotterdam Utopian
2 Dhanus Bora Cetus
4 Makara Deti Lepus
5 Aquarius Edal Columbia
6 Khumba Flo Monoceros
7 Pisces Geor Volans
8 Mina Helimba Lynx
9 Aries Idanon Camelopardalis
10 Mesha Jowani Chamaeleon
11 Taurus Kireal Hydra
12 Rishabha Larno Corvus
13 Gemini Medior Centaurus
14 Mithuna Neturima Draco
15 Cancer Ozulikan Lupus
16 Karka Pasurabi Apus
17 Leo Rudiakel Pavo
18 Simha Safundo Aquila
19 Virgo Tiunor Vulpecula
20 Kanya Ulasja Cygnus
22 Tula Wakumi Grus
23 Scorpius Xetual Pegasus
24 Vrishika Zungo Tucana

Mars Julian sol

The Mars Julian sol count is analogous to the Julian Day count on Earth, in that it is a continuous numerical counting of days from an epoch. The Mars Julian sol epoch is the same as for the Darian calendar, thus Mars Julian sol 0 is 1 Sagittarius 0.

Comparison with timekeeping systems in planetary science

Since the Darian calendar is designed as a civil calendar for human communities on Mars, it has no precise analog in the scientific community, which has no need to mark Martian time in terms of weeks or months. Two unrelated epochs that have gained some traction in the scientific community are the Mars sol date and the Mars year. In 1998 Michael Allison proposed the Mars sol date epoch of 29 December 1873 (Julian Day 2405521.502). In 2000 R. T. Clancy et al. proposed the Mars year 1 set to the epoch 11 April 1955 (Julian Day 2435208.456). The Clancy Mars year is reckoned from one Martian northward equinox to the next (Ls = 0°), and specific dates within a given year are expressed in Ls. The Clancy Mars year count is approximately equal to the Darian year count minus 183. The Allison Mars sol date epoch equates to Ls = 276.6° in a year that is undefined in the Clancy Mars year count. It converts to 25 Virgo 140 on the Darian calendar and Mars Julian sol 94128.511.

Martiana calendar

In 2002 Gangale devised a variant of the Darian calendar that reconciles the months and the sols of the week in a repeating pattern and removes the need to omit days of the week. In the Martiana variant, all the months in a given quarter begin on the same sol of the week, but the sol that begins each month shifts from one quarter to the next, based on the scheme devised by the astronomer Robert G. Aitken in 1936.

The following table shows the sol of the week on which each month in the quarter begins. The first quarter corresponds to spring in the Martian northern hemisphere and autumn in the Martian southern hemisphere.

First quarter Second quarter Third quarter Last quarter
Even-numbered years Sol Solis Sol Saturni Sol Veneris Sol Jovis
Odd-numbered years Sol Mercurii Sol Martis Sol Lunae Sol Solis

The leap sol occurs at the end of odd-numbered years as in the original Darian calendar. Since the last month of odd-numbered years contains 28 sols, the following year also begins on Sol Solis, resulting in a two-year cycle over which the relationship of the sols of the week to the months repeats. The sol that is added every tenth year is epagomenal (not counted as part of the week), thus the two-year rotation of the sols of the week is not disrupted. The Martiana scheme avoids the Darian calendar's need to shorten the week to six sols three to four times per year. The disadvantage is that the scheme results in a two-year cycle for reconciling the sols of the week and the months, whereas the Darian calendar is repeatable from month to month.

Other Darian calendars

In 1998 Gangale adapted the Darian calendar for use on the four Galilean moons of Jupiter discovered by Galileo in 1610: Io, Europa, Ganymede, and Callisto. In 2003 he created a variant of the calendar for Titan.

Important dates in Martian history

Event Earth timekeeping (UTC SCET) Mars timekeeping (Airy Mean Time)
Gregorian date Time Darian date Mars Julian Sol Mars Sol Date Time
Mariner 4 flyby 15 July 1965 1:00:57 26 Taurus 189 126668 32539 23:25
Mariner 6 flyby 31 July 1969 5:19:07 15 Cancer 191 128106 33977 15:10
Mariner 7 flyby 5 August 1969 5:00:49 20 Cancer 191 128111 33982 11:29
Mariner 9 entered orbit 13 November 1971 18:00 20 Kanya 192 128919 34790 19:19
Mars 2 entered orbit 27 November 1971 6 Libra 192* 128933* 34804*
Mars 3 contact lost 15 seconds after landing 2 December 1971 13:52 11 Libra 192 128938 34809 3:06
Mars 2 contact lost 22 August 1972 16 Kumbha 193* 129194* 35065*
Mariner 9 contact lost 27 October 1972 26 Mina 193* 129259* 35130*
Mars 4 failed to enter orbit 10 February 1974 10 Sagittarius 194* 129717* 35588*
Mars 5 entered orbit 12 February 1974 15:45 12 Sagittarius 194 129719 35590 17:18
Mars 5 contact lost 7 March 1974 6 Dhanus 194* 129741* 35612*
Mars 7 lander missed Mars 9 March 1974 8 Dhanus 194* 129743* 35614*
Mars 6 landing, contact lost after 224 seconds 12 March 1974 9:11:05 11 Dhanus 194 129746 35617 16:56
Viking 1 entered orbit 19 June 1976 12 Pisces 195* 13055420* 36425*
Viking 1 landing 20 July 1976 11:53 14 Mina 195 130584 36455 18:40
Viking 2 entered orbit 7 August 1976 4 Aries 195* 130602* 36473*
Viking 2 landing 3 September 1976 22:58 3 Mesha 195 130629 36500 0:34
Viking 2 Orbiter contact lost 25 July 1978 5 Mesha 196* 131300* 37171*
Viking 2 Lander contact lost 11 April 1980 2 Mina 197* 131909* 37780*
Viking 1 Orbiter contact lost 17 August 1980 14 Rishabha 197* 132033* 37904*
Viking 1 Lander contact lost 11 November 1982 1 Leo 198* 132828* 38699*
Phobos 2 entered orbit 29 January 1989 11 Vrishika 201* 135038* 40909*
Phobos 2 contact lost 27 March 1989 10 Dhanus 202* 135093* 40964*
Mars Pathfinder landing 4 July 1997 16:57 26 Taurus 206 138034 43905 4:41
Mars Pathfinder rover Sojourner contact lost 27 September 1997 10:23 25 Mithuna 206 138116 43987 15:43
Mars Global Surveyor entered orbit 11 September 1997 1:17:00 9 Mithuna 206 138100 43971 17:08
Mars Climate Orbiter destroyed entering atmosphere 23 September 1999 9:05 8 Karka 207 138823 44694 4:16
Mars Polar Lander impact 3 December 1999 20:15 21 Simha 207 138892 44763 17:32
2001 Mars Odyssey entered orbit 24 October 2001 2:18:00 24 Simha 208 139564 45435 12:21
Nozomi failed to enter orbit 14 December 2003 6 Tula 209* 140325* 46196*
Mars Express entered orbit 25 December 2003 3:00 16 Tula 209 140335 46206 8:27
Beagle 2 lander impact 25 December 2003 3:54:00 16 Tula 209 140335 46206 9:20
MER-A Spirit landing 4 January 2004 4:35 26 Tula 209 140345 46216 3:35
MER-B Opportunity landing 25 January 2004 5:05 18 Scorpius 209 140365 46236 14:35
Mars Reconnaissance Orbiter entered orbit 10 March 2006 21:24 20 Dhanus 211 141120 46991 12:48
Phoenix landing 25 May 2008 23:54 25 Kumbha 212 141906 47777 1:02
Phoenix contact lost 28 October 2008 9 Rishabha 212* 142057* 47928*
MER-A Spirit contact lost 22 March 2010 4 Kumbha 213* 142553* 48424*
MSL Curiosity landing 6 August 2012 5:17 13 Rishabha 214 143398 49269 5:50
MAVEN entered orbit 22 September 2014 02:24 18 Cancer 215 144154 50025 8:07
Mars Orbiter Mission entered orbit 24 September 2014 02:00 20 Cancer 215 144156 50027 6:27
ExoMars Trace Gas Orbiter entered orbit, Schiaparelli EDM lander impact 19 October 2016 15:24 3 Simha 216 144892 51348 14:02
MER-B Opportunity ceased communication 12 June 2018 4 Cancer 217* 145477* 51348*
InSight landing, Mars Cube One flyby 26 November 2018 19:52:59 26 Kanya 217 145640 51511 05:14:37
Perseverance landing 18 February 2021 20:55 UTC 13 Sagittarius 219 146433 52304 10:54

*Mars dates are approximate where the exact (Earth) time of the event is not stated.

The Darian calendar in fiction

Gangale was inspired to create the calendar after reading Red Planet, a 1949 science fiction book by Robert A. Heinlein. In the book, Heinlein postulates a 24-month Martian calendar.

The Darian calendar is mentioned in several works of fiction set on Mars: