THE DARIAN SYSTEM

1.0 The Darian Calendar for Mars

2.0 The Calendars of Jupiter

2.8 Variations on a Martian Theme

3.0 The Darian Calendar for Titan

3.6 Calibration

 Martian Time Martian Time Survey 2.2

# THE DARIAN SYSTEM

## 1.0 THE DARIAN CALENDAR FOR MARS

### 1.1 INTRODUCTION

Some time in the 21st century, there will be human settlements on Mars. Those pioneers will have left behind on Earth the familiar 24-hour day and the 365-day year, and they will be living and working according to the natural cycles of Mars. A work day will be 13 minutes longer than we're used to back here on Earth, but the work force on Mars will have an extra 26 minutes to show up the next morning. This is because Mars rotates a bit more slowly than Earth does. To devise a practical Martian clock, it's only necessary to take a terrestrial timepiece and slow it down sufficiently. The Martian clock therefore consists of the same units as we are used to on Earth -- 60 seconds per minute, 60 minutes per hour, and 24 hours per sol -- however, each of these Martian units of time are just slightly longer (2.7 percent) than their terrestrial counterparts. Most of the Martian clock applications on the World Wide Web use this system, although some authors, such as Bruce A. Mackenzie, have proposed Martian "metric" clocks based on powers of ten.

### Figure 1-1: Length of Terrestrial and Martian Days

A much bigger difference is the length of the year on Earth and Mars. Because Mars is nearly 80 million kilometers further from the sun, it takes nearly twice as long for Mars to travel once around in its orbit. It will not seem at all odd to the Martians that ten-year-olds have the vote, or that the retirement age is 35. This difference between years on Earth and Mars will require a new calendar to mark the progress of the Martian year.

Mine is just one of several dozen calendars that have been devised for Mars. First described in a paper published in 1986, I chose to name it the Darian calendar for my son Darius. Hopefully, his generation will be the first to reach Mars.

### 1.2 YEARS

While the Martian clock may be a "slam dunk", constructing a practical calendar for Mars is a bit more of a challenge. Astronomy tables give the length of the Martian year as 687 days. WARNING: these are Earth days, not Martian sols! The correct figure to use in expressing Martian time in consistently Martian units is 668.5907 sols per vernal equinox year (Note: earlier papers specified the 668.5921-sol tropical solar year). Now, just as Earth's Gregorian calendar uses a combination of common years of 365 days and leap years of 366 days to account for the 365.24219-day terrestrial tropical solar year, the same methodology can be applied on Mars to develop an accurate calendar. Of course, since the fractional amount of sols in a Martian vernal equinox year of 668.5907 solar days is different than in a terrestrial solar year, the sequence of common years and leap years will necessarily be different. In the Darian calendar, all even numbered years are 668 sols except for those divisible by ten. All other years are 669 sols, so that in ten calendar years there are 6,686 sols. In ten Martian tropical solar years there are 6,685.921 sols, the difference thus being -0.079 sols. A further correction is therefore needed every 100 years, and so every year divisible by 100 is 668 sols instead of 669. With this correction, there are 66,859 sols in 100 calendar years, while there are 66,859.21 sols in 100 tropical solar years. Finally, by making every year that is divisible by 500 a leap year, there are 334,296 sols in 500 calendar years, and the remaining error is only 0.05 sols. Theoretically, this error amounts to only one sol in 10,000 Martian years; however, the actual error will depend on the changes in Mars' orbital elements, rotational period, and the rate of the precession of the pole vector over this period of time.

To summarize, the intercalation formula is (Y-1)\2 + Y\10 - Y\100 + Y\500, where the backslash indicates integer division.

### 1.2.1 An Extended Intercalation Scheme

Since the Darian calendar year begins with the vernal equinox, the calendar should be based on the mean vernal equinox year rather than on the mean tropical year (for a discussion on the various astronomical years, see Michael Allison's "What is a 'Year' (on Earth or Mars)?"). At present, the mean vernal equinox year is 668.5907 sols; however, Allison estimates that the mean tropical year is increasing by 0.00042 sols per 1,000 Earth years, which times 1.88 (Earth years/Martian years) = 0.00079 sols per 1,000 Martian years. A simple intercalation formula of (Y-1)\2 + Y\10 - Y\100 + Y\1000 results in a mean calendar year of 668.5910 sols. This is a bit too long compared to the current mean vernal equinox year, so the calendar will slowly lose time at first. However, the rate at which the calendar loses time will slowly decrease until the mean vernal equinox year equals the mean calendar year. This will occur about the year 600 of the Telescopic period. The calendar will then begin to gain time at an ever-increasing rate as the vernal equinox year lengthens, eventually becoming off by more than one sol. Before this happens the intercalation formula will need to be changed, and as the year continues to lengthen, the intercalation formula will need to be changed again and again. The series of formulas in Table 1-1 would keep the date of the vernal equinox stable for 10,000 Martian years, as shown in Figure 1-3, assuming that the rate of increase in the vernal equinox year is constant. However, this is certainly not the case. Refinement of the intercalation series will need to await the determination of a value for the second order term for the variation of the Martian vernal equinox year. The table and figure are presented as an example of the accuracy that is achievable over long periods of time with simple formulas as our knowledge of Mars' solar orbit improves.

### Table 1-1 Extended Intercalation Formula Series

 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

### Figure 1-3: Cumulative Error of the Darian Calendar

See Appendix 1 for a discussion of the precision of the 10-year intercalation cycle versus a 5-year cycle and the 4-year Gregorian cycle.

See Appendix 2 for a discussion of the variation in the length of various Martian astronomical years due to gravitational perturbations, and their affect on the dates of annual astronomical events.

### 1.3 MONTHS AND SEASONS

Several of the calendars that have been devised for Mars stretch the months asymmetrically to reflect the changing angular velocity of Mars in its eccentric orbit around the sun. Such months would span equal arcs in Mars' orbit rather represent than equal spans of time. While this might appeal to the astronomical purist, it must be pointed out that, in all probability, as on Earth, comparatively few people on Mars will be concerned with astronomy. And let us be clear that we are discussing a civil timekeeping system, not a planetary ephemeris. No civil calendar will have the accuracy required for use by the space science community because of the need to insert leap sols. A timekeeping system is at least as much a societal construct as it is an astronomical one, and to be practical for the full spectrum of society, including those who can't program a VCR, a timekeeping system should be as simple as possible and as symmetrical as possible. As an analogy, here on Earth, few of us care, or even know, that on only four days of the year does the sun cross on the meridian at the precise moment that our clocks strike noon. We do not add or subtract minutes and seconds to our clocks throughout the year to adjust for the variable length of the solar day; rather, we set our timepieces according to the length of the mean solar day and let it go at that. Likewise, on Mars, we will find months whose lengths are nearly equal divisions of the tropical solar year to be far more useful than a system in which the longest month is nearly 50 percent longer than the shortest month. The stretched Gregorian calendar (Table 1-2) is a typical example of these wildly changing months. Imagine the difficulty of working out monthly budgets in such a variable system, or trying to remember how many sols each month contains. A mnemonic poem would be of epic length!

Since a Martian year is nearly twice as long as an Earth year, a logical approach to dividing the Martian year into smaller units is to give the calendar twice as many months. An alternative would be to maintain the division of the year by twelve and have months that are nearly twice as long as they are on Earth; however, a 24-month calendar year is more desirable for several reasons. The mean Earth month of 30.4368 days is already a familiar cycle the humans. Dividing 668.5907 by 24 results in a mean month of 27.8579 sols, or 28.6238 Earth days, so the difference between the mean Martian month and the mean Earth month would be only 6 percent. It will be much easier for humans to adjust to a slightly shorter month than to accept one that is nearly twice as long. Furthermore, although a 28-sol month has no astronomical basis on Mars, it will nevertheless be meaningful to human experience on Mars, since the statistical average of the human menstrual cycle is about 28 days. The purpose of a calendar is to mark the passage of time in human terms, so the more human factors that are designed into a calendar, the better.

In the Darian calendar, common years of 668 sols contain 20 months of 28 sols and four months of 27 sols. The 27-sol months occur at the end of each quarter. In leap years of 669 sols, the last month of the year (which also ends the fourth quarter, of course), instead of containing 27 sols, is a normal length of 28 sols. The leap sol is therefore the last sol of the year, rather than being stuck somewhere in the middle as it is on Earth's Gregorian calendar.

On the question of naming the 24 Martian months, the idea of using the names of the constellations of the zodiac naturally came to mind. Indeed, Robert Zubrin later adopted this idea for his own Martian calendar. These are the constellations through which the sun appears to pass as seen from Earth during the course of a year. This annual apparent path of the sun is called the ecliptic. Since Mars' orbit is inclined to Earth's by less than two degrees, as seen from Mars, the sun appears to pass through these same constellations along a very slightly different Martian ecliptic. There are only twelve such constellations, however, so two names must be used for each one. In the Darian calendar, twelve of the months bear the familiar Latin names of the zodiacal constellations. The names of the remaining twelve months are the Sanskrit names of these same constellations, and each appears in the calendar following its Latin counterpart. The nomenclature of the Darian calendar is thus a blend of Eastern and Western influences. Admittedly, the Sanskrit names are a bit difficult to remember, and to make it even worse, I recently changed the names of some of these months to reflect the predominant usage in the Hindu Solar calendar and in Vedic astrology.

In early Roman religion Mars was the god of vegetation and fertility, and his festivals signified the return of life to the land (this was before Rome became an imperial power, and Mars the farm boy got drafted into the army). Back in that more pastoral era, Romulus chose to begin his calendar with the vernal equinox, and the first month of the year was named for Mars, the provider and protector of the Roman people. In this same vein, the Darian calendar is intended to symbolize the beginning of life on the planet named for Mars (or if ancient life once did flourish there, the return of life to Mars), and so the vernal equinox is chosen as the beginning of the Martian year. Furthermore, on Earth the vernal equinox is a standard astronomical reference point that marks the beginning of the astronomical year, and it seems reasonable to carry this idea to Mars. The present position of the Martian vernal equinox is on the western edge of the constellation of Sagittarius. The first month of the Darian calendar year is therefore named Sagittarius, and the rest follow in their appropriate order as listed in Figure 1-4.

### Figure 1-4: The Darian Months

The current positions of Earth and Mars are shown.
Click on any month name in the diagram to view a calendar for that month,
or click inside the diagram to view the calendar for the full Martian year.

Because of the eccentricity of the Martian orbit, its seasons are of unequal lengths. Mars' furthest point from the Sun, known as the aphelion, occurs in late spring in the northern hemisphere (Kumbha 12). In accordance with Kepler's laws of orbital motion, Mars is at that time traveling at the slowest angular velocity in its orbit. This has the effect of making spring the longest season, and because aphelion occurs only 42 sols before the summer solstice, summer is the second longest season, beginning on Pisces 27. Similarly, perihelion, at which time Mars makes its closest approach to the Sun and attains its greatest orbital velocity, occurs 27 sols prior to the winter solstice (Simha 12). Autumn and winter are therefore the shortest and second shortest seasons, respectively. Spring in the northern hemisphere lasts 194 sols, and so the first sol of summer does not occur until the 28th of Pisces. Summer lasts 177 sols, so that although the autumnal equinox is in the constellation of Gemini it does not occur in the month of Gemini but on the 11th sol of Mithuna, the Sanskrit name of that same constellation. After 142 sols winter begins on Virgo 14 and lasts 156 sols. Of course, just as on Earth, the seasons in the southern hemisphere of Mars are exactly the opposite of those in the northern hemisphere, thus in the south of Mars, Sagittarius 1 marks the beginning of autumn, which lasts 194 sols, and so on.

### Table 1-3: The Martian Seasons

 Season Sols Spring 193.30 Summer 178.64 Autumn 142.70 Winter 153.95

### Table 1-4: Annual Astronomical Events (Nominal Dates)

 Event Date Vernal Equinox Sagittarius 01 Aphelion Kumbha 12 Summer Solstice Pisces 27 Autumnal Equinox Mithuna 11 Perihelion Simha 12 Winter Solstice Virgo 14

The actual dates of these events varies due to intercalation. The dates of annual astronomical events for specific years are given in the following tables:

These dates were calculated from Meeus 1995. The error in the table may occasionally be as large as about 3 minutes of clock time. Note that the date of perihelion becomes progressively later (by one sol per 42 years) due to the anomalistic year (668.6146 sols being longer than the vernal equinox year (668.5907 sols).

Dates of synodic events are given in Table 1-10 (oppositions of Mars) and Table 1-11 (conjunctions of Mars).

### 1.4 WEEKS

Still another familiar unit of time can be exported from Earth to Mars: the seven-day week. In fact, with a very minor adjustment, the seven-sol week can be made to work even better on Mars than on Earth, for there are exactly four such weeks in a 28-sol month. Now since Martian sols are longer than terrestrial days, it follows that a seven-sol Martian week is longer than its earthly counterpart. For this reason weeks on Mars will rarely and only briefly match up with weeks on Earth, and it will create confusion if on Mars the names of the sols of the week remain the same as on Earth; Monday on Mars might be Tuesday on Terra. In order to avoid this problem the Latin names of the days of the week are prescribed as a starting point: Dies Solis, Dies Lunae, Dies Martis, Dies Mercurii, Dies Jovis, Dies Veneris, and Dies Saturni. Since these names are the antecedents of those used in many of the European languages spoken today, they possess the familiarity that will enable their ready recognition by a large number of the cultures of humankind, yet being in the form of a language no longer spoken generally anywhere on Earth, they will not be mistaken to mean terrestrial days of the week. However, for Mars, the word "dies", which is Latin for "day," is replaced by the word "sol". (NOTE: In earlier papers, the word "dies" was retained. Also, Sol Lunae was called Dies Phobotis, and Sol Martis was named Dies Terrae.)

### Figure 1-5: Names of the Days of the Week

And now for an unusual feature. Each month begins on exactly the same sol of the week: Sol Solis, which is the Martian equivalent of Sunday. The direct result of this is that regardless of the month, a given sol of the week can only occur on four invariable dates; for example, Sol Jovis, the Martian Thursday, will always be either the 5th, 12th, 19th, or 26th of the month... any month. No one on Mars will ever have to pause to consider, "Now let me see, the 10th of next month is Sol Martis, isn't it?" It always is! This has the great advantage of eliminating the sloppiness we on Earth have had to put up with in the Gregorian calendar. However, this arrangement requires that a 27-sol month end on Sol Veneris (the Martian equivalent of Friday), and that the following Sol Saturni (Martian Saturday) be skipped over, resulting in only a six-sol week in this very infrequent case. The next sol, being the first sol of the following month, is Sol Solis. This will happen at most only once every six months, sometimes only once in twelve months, but since no one wants a one-sol weekend, the last sol of the month should be a "holisol". That means that these unusual six-sol weeks will contain only four work sols, and not many people are going to object to that! It has been pointed out, however, that this system guarantees the Martian equivalent of Friday the 13th every month. Think of this as a plus, as it will surely dissuade the superstitious from emigrating to Mars. But does this unusual arrangement violate the Biblical commandment to observe the Sabbath every seven days? Well, to be very literal, there are no days on Mars, there are sols. Nevertheless, it turns out that this scheme actually keeps the average length of the Martian week closer to that of the terrestrial week. The occasional short week almost perfectly compensates for the longer Martian sol, resulting in an average Martian week that is less than one percent longer than the terrestrial week.

Table 1-12 shows the layout of the calendar for the entire Martian year.

### 1.4.1 The Martiana Calendar

Table 1-13 shows a variant of the Darian calendar that uses a modified form of Robert G. Aitken's scheme for reconciling the months and the sols of the week into a repeatable pattern. In Aitken's system, developed in 1936, both the biennial leap sol and the decennial epagomenal sol occurred in even-numbered years. This results in calendar years of three different lengths: 668 sols for odd-numbered years, 669 sols for even-numbered, non-decennial years, and 670 sols for decennial years. In the Martiana calendar, the leap sol is moved to odd-numbered years, which therefore contain 669 sols as do decennial years, while even-numbered, non-decennial years contain 668 sols. The other departure from Aitken's scheme is that the decennial epagomenal sol is moved from mid-year to the end of the year.

In the Darian calendar, each month begins on Sol Solis. This requires the last week of each 167-sol quarter to be shortened to only six sols, which is the same solution that was developed by I. M. Levitt in 1954 to devise a perpetual Martian calendar. The Martiana calendar uses Aitken's solution, in which 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. In even-numbered years, all six months of spring begin on Sol Solis, those of summer on Sol Saturni, of autumn on Sol Veneris, and of winter on Sol Jovis. In the even-numbered years, the months of spring, summer, autumn and winter begin, in order, on Sol Mercurii, Sol Martis, Sol Lunae, and 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 and is 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 (see the summary table).

### 1.5 THE TELESCOPIC EPOCH

The need to keep a Martian calendar of even a rudimentary form began with the landing of the Viking 1 spacecraft in July 1976. The sol of the landing was designated "Sol 0", and the sols that followed were numbered successively. With the landing of this first unmanned spacecraft, humans began working on the surface of Mars, albeit by proxy, and thus it was that humans began working by Martian time. Originally, the epoch (year zero) of the Darian calendar was set to the northern hemisphere vernal equinox prior to the Viking landings. There were several problems with this choice. First of all, celebrating the Viking landings was viewed in some quarters to have nationalistic overtones. A more substantive concern is the need to use a Martian dating system prior the these events. Although the Viking landers established the first sustained human remote presence on Mars, there are centuries of Earth-based observational data that it would be useful to organize in non-negative Martian terms. This is especially true for the observation of seasonally variable Martian phenomena. For example, Giacomo Maraldi noted the variability of Mars' appearance in the early 18th century. It was Maraldi who conducted the first thorough study of the poles. He observed white regions in both the north and south, and noted that these regions fluctuated in extent. Indeed, in 1719 August, which was late spring in the southern hemisphere of Mars (the Darian month of Leo), the south polar white spot disappeared entirely.

The Martian year corresponding to 1609/1610 is highly significant in the history of Mars. During this Martian year, Johannes Kepler published his first two laws of planetary motion. His work included years of studying the orbit of Mars in particular. The highly eccentric orbit of Mars provided the principle challenge to Rennaissance astronomy, forcing the abandonment of the theory of circular orbits and epicycles (to which even Nicholas Copernicus had clung). Also, accurate characterization of the elliptical orbit of Mars inspired Isaac Newton's Principia Mathematica, from which much of modern mathematics and science has flowed.

The 1609/1610 period also marked the beginning of the history of the observation of Mars by telescope (Galileo Galilei observed the phases of Mars in 1610 December). Thus, by choosing the Martian vernal equinox occurring on 1609 March 11 as the epoch for the Darian calendar, any recorded telescopic observation of Mars can be expressed in a common chronological reference system without negative values.

Additionally, it should be noted that Galileo's discovery of the four large moons of Jupiter in 1610 provided startling observational evidence that Earth was not the center of the universe, and that the Darian timekeeping system extends to the four Galilean moons of Jupiter.

Finally, the human history of Mars may be organized into four periods, defined in terms of how humans have thought about and acquired knowledge of Mars:

1. Mythic (Mars as experienced by the bicameral mind).

2. Gymnoptic (Mars as studied in naked eye astronomy).

3. Telescopic (Mars as observed through telescopes).

4. Telemetric (Mars as explored by robotic spacecraft).

There are no clear beginning dates for the Mythic and Gymnoptic periods, of course, and there is a great deal of overlap in any case. On the other hand, it is fairly certain that the Telescopic period began in 1610. Applying the 1609/1610 epoch to a Martian calendar not only celebrates the birth of the Telescopic Period, but also celebrates Kepler's laws as the crowning achievement of Gymnoptic astronomy.

The 1609/1610 epoch was discussed in the Martian Time Virtual Conference in 1999 October. It seems to have first been suggested by Peter Kokh in a private message to another member of the conference. Two years later, the Mars Time Group adopted this epoch for their Utopian calendar. Simultaneous with the Darian calendar and the Darian Defrost calendar adopting the Telescopic epoch, the Utopian calendar has adopted the equal-quarter structure of the Darian calendar. As a result of these changes, these three Martian calendars now have the same structure. The only differences among the three calendars are nomenclatural.

### 1.6 DARIAN-GREGORIAN CALENDAR DISPLAYS

Centuries from now, there may be Martian who have little to do with Earth in their daily lives, and for them a purely Darian calendar can be a simple display. However, for those who must contend with timekeeping on both planets, the Darian calendar must be a dual-calibrated display. In its basic calibration, it must relate the local date and time on the Martian prime meridian (Airy Mean Time) to Universal Coordinated Time on Earth. For most Earth-bound users this generic calibration will suffice. Figure 1-6 is an example of a Darian-calibrated Gregorian calendar, with the horizontal offset of the Darian dates in relation to the Gragorian dates denoting the occurrence of prime meridian midnight on the two planets.

### Figure 1-6: Gregorian Calendar Display, UTC and AMT, September 2005

Users on Mars, as well as some Earth-bound users, will need Gregorian-calibrated Darian calendars. Additionally, such users may be interested in calendars that are calibrated for specific points on Earth and Mars. For example, During a Mars surface mission, the Darian calendar display must relate the local date and time at the position of the surface vehicle to the local date and time at the mission control complex on Earth or for the location of some other user group. It must also express Martian sols as a numerical sequence beginning with the sol of the landing of the vehicle, as has been done during the Viking, Pathfinder/Sojourner, Spirit, and Opporortunity missions. This second example of a Darian calendar display takes us back to 2004 July, or the Darian month of 210 Aquarius (Figure 1-7). It expresses chronological information pertinent to the Mars Exploration Rover 1 (Spirit) mission in the format of the Darian calendar. For each Martian sol, local mean Martian midnight at the Columbia Station is expressed in terms of local Earth date and time at the Jet Propulsion Laboratory in California. The numerical sequence of sols for the mission is also displayed. Note that terrestrial days of the week appear in their normal positions only occasionally on this Darian-formatted display, so in order to readily orient the Earth-bound user, these are color-coded: Sunday -- red; Monday -- orange; Tuesday -- yellow; Wednesday -- green; Thursday -- blue; Friday -- indigo; Saturday -- violet. Also note that periodically a terrestrial day drops out of the calendar (Monday, June 28 in this case) as a Martian midnight occurring late in the evening of one terrestrial day is followed by the next Martian midnight striking early in the morning two terrestrial dates later. This results in a shifting to the left of the columns of terrestrial days of the week.

An additional display that is available on the Martian Time website is a real-time clock showing the date and time on both Earth and Mars.

### 1.7 CHILDREN AND COLLATERAL RELATIVES

Although I read Robert A. Heinlein's Red Planet as a boy, by the time I developed the Darian calendar in 1985 I had forgotten his passing reference to a Martian calendar. It was only as I was putting the finishing touches on an article (see "The Lost Calendars of Mars") for the British Interplanetary Society's magazine Spaceflight (published in 1988 July) that this information surfaced from my unconscious:

And with these proud strokes of the word processor keys I thought I was finished writing this article. I had looked through every astronomy book about Mars I could find, but could uncover no more calendars. The next morning, in the last REM period before waking, I dreamt of a calendar in Robert A. Heinlein's 1949 Red Planet, a juvenile novel I had not read in 20 years. I bounded out of bed in the predawn gloom, flipped on the light in our study, and instantly found the book, for I had earmarked it for re-reading as part of the research for a future writing project of mine. Sure enough, in the course of a conversation in Chapter 1:

Jim thought back over the twenty-four months of the Martian year. 'Since along toward the end of Zeus, nearly November.'

'And now here it is the last of March, almost Ceres, and the summer gone.'

Thus it was Heinlein who originated the 24-month Martian calendar in 1949, and his idea must be included in the genealogy of the Darian calendar (see the summary table).

Although not a 24-month calendar, I. M. Levitt's 12-month 1954 calendar must also be acknowledged as an antecedent. If one were to bisect each of the 12 months, the resulting structure would be nearly identical to the Darian calendar. The exceptions are that the first sol of the calendar year is tied to the beginning of the Julian period, and that Levitt's intercalation sequence provides for three leap years out of ever five years (see the summary table and the calendar table). I did not discover the Levitt calendar until after I had published my 1986 June JBIS article. I acknowledged Levitt's work in my 1988 July JBIS article, "The Lost Calendars of Mars."

Kim Stanley Robinson's 1993 Red Mars also outlines a 24-month Marian calendar, which he probably developed independently of my work. In Robinson's calendar, the year begins on the fictional date of the first human landing on Mars, and the 27-sol months occur at the end of each trimester (every eighth month), with no provision mentioned for the leap sol. The names of the months are simply duplicated from the Gregorian calendar: 1 January, 2 January, 1 February, 2 February, et cetera (see the summary table and the calendar table).

Josef Šurán published his article, "A Calendar for Mars," in the peer-reviewed journal Planetary and Space Science in 1997. As with Robinson's calendar, this was probably developed independently of the Darian calendar. Šurán's calendar year begins on the northern hemisphere's winter solstice. In the leap sol/skip sol version, his months all contained 28 sols, except for the 12th month, which contained only 21 sols. His calendar included an epagomenal sol (i.e., not counted as one of the seven sols of the week) at the end of each quarter, with the sol at the end of the year being a leap sol. The calendar is thus perpetual, with each year beginning on the first sol of the week. The ten-year intercalation sequence is the same as the Darian calendar; however, further adjustment occurs on a 160-year cycle rather than a 100-year cycle (see the summary table and the calendar table). In the leap week/skip week version, an epagomenal week is added to the 12th month in leap years, which occur every even-numbered year and in the year before those divisible by 70 (see the summary table and the calendar table).

Miguel Angel Serra Martín published his two Martian calendars on the World Wide Web in 1997. The first option is a 12-month calendar, similar to Levitt's. The second option is a 24-month calendar beginning on the northern hemisphere's winter solstice. All months contain 28 sols except that the last month contained 25 sols in common years and 28 sols in leap years, which occur every five years (see the summary table and the calendar table). This was probably developed independently of the Darian calendar.

While a cadet at the United States Air Force Academy in 1997, Mickey D. Schmidt outlined a calendar similar to the Darian but independent of it. It uses a different intercalation scheme (involving 670-sol and 671-sol leap years), and does not have a defined epoch. The months of the year and the sols of the week are unnamed. The intercalation formula is 2 * Y\5 + Y\300 - Y\6000 - Y\36000 (see the summary table and the calendar table).

William Woods' 1997 calendar is an independent development of the Darian calendar. It uses the same pattern of 27-sol and 28-sol months; however, all weeks contain seven sols, making the calendar non-perpetual. Also, the calendar year begins 77 days after the summer solstice, instead of on the vernal equinox, and the intercalation formula is Y\5 + (Y-2)\5 + (Y-4)\5 - Y\100 + Y\500. Finally, the calendar uses an alternative system of month and sol names (see the summary table and the calendar table).

In 1998, Anton Sherwood outlined four 24-month Martian calendars. Three of them reflected to varying extents the asymmetry of the Martian seasons. Variant C, which was developed independently of the Darian calendar, is similar to it in structure; however, the 27-day months and the leap sol are placed differently. The months are unnamed, and there is no mention of a weekly cycle (see the summary table and the calendar table).

In 1998, Bill Hollon, who is well-versed in the many calendars of Earth and their history, independently created a Martian calendar that was structurally identical to the Darian calendar, with the exceptions that no epoch is specified and that in place of an intercalation formula, leap years are to be determined each year by astronomical observation (see the summary table and the calendar table). Hollon does not name all of the months, but suggests that they be "named in alpha sequence from Aldrin thru Zubrin."

The Darian calendar became available on the World Wide Web in 1997. Within a few years, other authors created nomenclatural variants of it. Alan Hensel suggested a new system for naming the months. Shaun Moss created a new set of names for the sols of the week (see the Areosynchronous calendar), which became the basis for the timekeeping system used in Scott Davis' Mars Simulation Project. Meanwhile, Frans Blok suggested a new naming system for both the months and the sols (see the Darian Defrost calendar). These alternative naming schemata are shown in the summary table and the calendar table.

Leon Heron's 2001 variant of the Darian calendar suggests yet another nomenclature scheme. It also moves the leap sol to the third month, with the other 27-sol months being the 9th, 15th, and 21st (see the summary table and the calendar table). The beginning of the calendar year is specified to be "at a point in Mars's orbit so that the seasons on Mars occur (approximately) during the same months as they do on Earth."

In 2001, Moss led a group of people who were interested in developing a common Martian calendar for three different websites, "VirtualMars," "The Republic of Mars," and "Martian Dreams." The Mars Time Group developed a calendar, called the Utopian (see the summary table and the calendar table), that is structurally identical to the Darian calendar, with the exceptions that they adopted the Telescopic epoch, and rather than having 27-sol months at the end of each quarter, the group decided to have the last month of the year contain 24 or 25 sols (with the last week of the year comprising only three or four sols). The Mars Time Group also developed a nomenclatural schema distinct from the Darian calendar. While the group's effort was independent of the Darian calendar, the final result is not a great departure from Moss' Areosynchronous nomenclatural variant of the Darian calendar. However, this attempt at a common solution was not entirely successful. The "Martian Dreams" website opted for a calendar with 27-sol months spread evenly throughout the year, as in the Darian calendar, but with different names for the months and sols from either the Darian or Utopian schemata (see the summary table and the calendar table). The "Martian Dreams" site's calendar also increments the year count on the terrestrial rather than the Martian annual cycle, which means that the number of the year change once or twice during the Martian year, and the dates on which these changes occur vary from year to year. The "Republic of Mars" website never implemented either calendar and eventually disappeared from the Web, leaving "VirtualMars" as the only site featuring the Utopian calendar.

In a subsequent effort to achieve a common Martian calendar, the Darian and Utopian calendars each made a change in 2002. The Darian calendar adopted the Telescopic epoch, which is the Martian vernal equinox that occurred on 1609 March 11. The Utopian calendar switched to the equal-quarter scheme, with 27-sol months at the end of each quarter (Shaun Moss has since renamed it the Kepler calendar). These mutual changes brought the two calendars into structural alignment, with the only remaining differences being nomenclatural. Other users of the Darian calendar have been notified of the change.

I created the Martiana variant to the Darian calendar in 2002. 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 (see the summary table). So far, there has been no popular support for this alternative intercalation method (either in discussions in the Martian Time Virtual Conference or in responses to the Martian Time Survey), and the Darian calendar, incorporating the Telescopic epoch and including the various alternative nomenclatural schemata, remains the preferred solution.

Terry Phelan's 2002 Chromium calendar, like the 2001 Utopian calendar, has the last month of the year containing 24 or 25 sols. The other 23 months have 28 sols. The last month has only three weeks, and the last three of four sols are epagomenal. The calendar begins on the summer solstice, and the intercalation formula is (Y-1)\2 + Y\10 - Y\100. The months are named for the first 24 elements of the periodic table (see the summary table and the calendar table).

In 2003, Rachel Ann Welton developed a Martian calendar independently of the Darian for a science fiction novel. The first 12 months have Roman names, and the names of the last 12 are abbreviated Roman names with the prefix "tu-". The second month (February) contains 27 sols, while the 14th month (Tufeb) contains either 26 or 28 sols. The intercalation formula is 2*Y\3 + Y\45. The calendar is mistakenly based on the number of Martian sidereal days in a Martian year, and there is no mention of a weekly cycle (see the summary table and the calendar table.

The Martian business calendar developed by Bruce Mills in 2005 eschews epagomental sols as being "unacceptable to Jews, Christians and Muslims because it interrupts the cycle of the seven-day week." Instead , Mills opted for a leap week solution similar to Šurán's. The leap week occurs at the end of the 24 month, which can contain either 21 or 28 sols. There are 39 long years in each 76-year cycle. The calendar uses the Telescopic epoch. The names of the month are derived from Woods' schema.

### 1.8 ADDITIONAL REFERENCES

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