1986: THE DARIAN CALENDAR AND THE GANGALE CLOCK
Before stumbling quite by accident upon the work of Aitken,
and then that of Levitt as well, I had already
published my own Martian chronometric system in a paper entitled
"Martian Standard Time",
which was published in the June 1986 issue of the Journal of
the British Interplanetary Society. It was only after discovering
these two other Martian calendars that I set out in search of
the others.
In my system, 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 solar
years there are 6,685.921 sols, the difference thus being 0.079
sols, which necessitates two additional corrections: all years
divisible by 100 are short, except for those divisible by 500.
The remaining theoretical 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. Theoretically,
however, years following those divisible by 10,000 would contain
669 sols. (Note: this is a correction to earlier papers,
and is based on information supplied by Michael Allison.)
As discussed previously, the orbital periods of Phobos and Deimos
are quite useless as far as a calendar is concerned. However,
the month that is based on the orbit of the Moon around Earth
is such useful and familiar a unit of time, and it can be quite
easily tailored to the new system. Admittedly, the Martian month
will be an artificial rather than natural division of time, but
this is also true in terrestrial solar calendars, where months
have nothing at all to do with the phases of the Moon. On Earth,
because of the relationship between the lunar cycle and the solar
cycle, calendars have nearly always consisted of twelve months.
Considering that the Martian year is nearly twice as long as the
terrestrial solar year, I elected to divide the Martian year into
24 months, exactly twice the number as in a terrestrial year.
The other obvious approach would have been to retain the division
of the year into twelve months, which would be nearly twice their
terrestrial duration. There are several reasons why I chose not
to do this. First of all, this would result in essentially a new
and unfamiliar unit of time which really ought not to be called
a month, since it would not in any way approximate the lunar cycle.
Secondly, it is more logical to successively divide the year by
numbers that are as similar as possible, just as we divide the
hour into 60 minutes, then in turn divide the minute into 60 seconds.
If we are to divide the year into two successively smaller units,
the number of divisions within those units should be as close
as possible to the square root of the value of the year in terms
of the smaller unit (sols). For instance, the hour is divided
into 3600 seconds, and the square root of 3600 is 60; thus 60-minute
hours and 60-second minutes. Since the number of sols in a Martian
year is 668.5921, and the square root of this is 25.85715, 24
months of approximately 28 sols each is a balanced, two-tiered
division of the year. A final point, one that has been overlooked
by other writers on the subject of Martian timekeeping (which
I suppose is forgivable given that so far all of us have been
male), is that a period of 28 sols closely approximates the human
menstrual cycle (the name of this cycle comes from the Latin mensis,
meaning "month"). Until the first women live beyond
the Earth-Moon system for an extended period of time, there will
be no data on what changes, if any, may occur. However, there
is nothing that suggests that this essential human biological
cycle will be radically different on Mars; therefore this human
cycle should be incorporated into a calendar meant to be used
by humans living on Mars.
In my proposed calendar for Mars, years of 669 sols consist of
21 months of 28 sols and three months of 27 sols. Years of 668
sols contain 20 months of 28 sols and four months of 27 sols.
In all years the short months -- spaced at regular six-month intervals
-- are the 6th, 12th, and 18th, and in 668-sol years the 24th
month is also short. The variable sol is therefore the last sol
of the year. It can immediately be seen that such an arrangement
is as symmetrical as possible in that the 668-sol year divides
into exactly equal quarters of 167 sols. By contrast, the quarters
of the Gregorian calendar are 90, 91, 92, and 92 days.
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. 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 proposed calendar, twelve of the months bear
the commonly used Latin names of the zodiacal constellations.
The remaining twelve months bear the Sanskrit names
of the same constellations, and each appears in the calendar following
its Latin counterpart. (Note: I recently changed the names of some of these months to reflect the predominant usage in the Hindu Solar calendar and Vedic astrology.)
In modern times we always think of Mars as the planet named for
the Roman god of war. However, before the Roman state and its
religion became heavily militarized, Mars was the god of vegetation
and fertility in early Roman religion, and his festivals signified
the return of life to the land. The original Roman calendar began
with the vernal equinox, and the first month of the year (now
the third month, which we call March) was named for Mars, the
provider and protector of the Roman people. The calendar I propose
for the Martian colonies is intended to symbolize the beginning
of life on the planet named for Mars, and so the vernal equinox
is chosen as the beginning of the Martian year. A further rationale
for selecting this astronomical event to begin the Martian calendar
year is that on Earth, the vernal equinox marks the prime meridian
of celestial longitude, and at the moment of the vernal equinox,
ephemeris time, which expresses the difference between mean solar
time and sidereal time throughout the year, is defined as 00:00:00.
One can imagine that future Martian astronomers may adopt similar
conventions for their world. Thus by beginning the calendar year
at midnight on the sol of the vernal equinox, it would correspond
to the beginning of the astronomical year to within a few hours.
The present position of the Martian vernal equinox is on the western
edge of the constellation of Sagittarius. The first month of the
Martian calendar year is therefore named Sagittarius, and the
rest follow in their appropriate order as listed in the table.
Still another convenient and familiar unit of time can be exported
from Earth to Mars: the seven-day week, a unit of time whose sociological
importance was amply demonstrated by the failure of the French
and Soviet calendars. In fact, with a very minor adjustment, the
seven-sol week can be made to work even better on Mars than on
Earth, for obviously 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", Latin for "day". is replaced by "sol". (Note: In earlier papers, the word "dies" was retained. Also, Sol Lunae was called Dies Phobotis, and Sol Martis was named Dies Terrae.)
Each month begins on Sol Solis, so that regardless of the month,
a given sol of the week can only occur on four invariable dates;
for example, Sol Jovis will always be either the 5th, 12th, 19th,
or 26th of any month. No one on Mars will ever have to pause to
consider, "Now let me see, the 14th of next month is Sol
Saturni, isn't it?" It could not possibly be anything else.
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 all 27-sol months end on Sol Veneris,
and that the following Sol Saturni be skipped over, resulting
in only a six-sol week in this special case. The last week of
a short month therefore ends on Sol Veneris, and the next sol,
being the first sol of the following month, is Sol Solis. This
will happen at most only once every six months, so this small
and infrequent deviation from the traditional seven-sol week should
still satisfy the chronometric needs of Martian civilization.
Almost certainly, the last sol of each short month will be a holisol
by Martian custom so that they will not be deprived of the normal
two-sol weekend. The superstitious may be loath to migrate to
Mars, however, since on this calendar the thirteenth of every
month falls on Sol Veneris, the Martian analog of Friday.
In my view, the similarity in nomenclature of any Martian calendar
to the Gregorian calendar is an invitation to great confusion,
and I have purposely avoided this in my calendar. I have exported
to Mars the concepts embodied in the Gregorian calendar where
possible, and improved upon them where I saw the opportunity;
however, I have changed the names of the months and the sols to
give the Darian calendar a distinctive Martian flavor and eliminate
any possible confusion with Earth's timekeeping nomenclature.
I might suggest here that even the names of the Martian chronometric
units themselves may be changed to avoid any confusion with their
terrestrial counterparts. The Martian solar day has already been
dubbed the "sol" by the scientific community, and since
Martian nomenclature is primarily Latin, the Martian month and
week might be called the "mensis" and "vicis".
Alternatively, Martian units of time might be named for some of
the writers on the subject: the Martian month might be called
the "heinlein", for instance, since Heinlein was the
first to devise Martian months of roughly the same duration as
our own. The Martian week might be called the aitken, after the inventor of the first Martian calendar to contain weeks, and the Martian year might be called the "lowell".
Possibly Burroughs' Barsoomian words "zode", "xat",
and "tal" might come to denote the Martian hour, minute,
and second, or Martians might adopt Robert L. Forward's
terms "mear", "maur", and "marmin"
for the Martian year, hour, and minute. Similarly, the Martian
second might become known as the "marsec". On the other hand, the Martian hour might be known as the levitt, in honor of the inventor of the first working Mars clock.
What Martian year should be chosen to begin this calendar? There is no real need to express dates in Martian terms before the occurrence of the first human event directly related to Mars, yet although largely unrecognized as such, this event has already taken place even though the first manned landing is still many years away. In a vicarious sense, humans landed on Mars on 20 July 1976, and during the three Martian years of Viking lander operations, a group of people lived and worked according to the cycle of day and night on Mars. This was the true beginning of Martian chronology. This need to keep account of Martian solar days will recur as future unmanned landings are made, and so for this reason also it appears best to establish the use of a formal Martian calendar immediately rather than await the first human expedition or permanent settlement. Given this, the Viking 1 landing, a human event by extrapolation, is the appropriate beginning for the calendar. That Martian year, the year 0 M.E., began with the Martian vernal equinox on Wednesday 17 December 1975 according to the Gregorian calendar, when midnight on the Prime Meridian of Mars occurred at 22:47:43 Universal Coordinated Time. One hundred ninety-four sols later Viking 1 landed in Chryse Planitia. On Earth that date was Tuesday, 20 July 1976 A.D.; on Mars the date was Sol Saturni, 28 Pisces 0 M.E. (Note: this is a correction to earlier papers, and is based on Mars Pathfinder mission data and information supplied by Michael Allison.)
However, while the idea of beginning the Darian calendar with the first remote presence on Mars is a straightforward one, it has recently been called to my attention that this choice may have nationalistic overtones which some might find objectionable. An alternative would be to adopt Robert Zubrin's idea of beginning the Martian epoch with the most recent Martian vernal equinox which occurred at the beginning of a Gregorian year. This occurred on 1 January 1707, which would make the current Darian year 155. This calculation was independently confirmed by Alan Hensel.
Now that the description of the new calendar is complete, it must
have a name. To the men and women who watch over the robot explorers
of Mars, to the crews of the first human expeditions, and to the
settlers who shall follow them: should any of you choose to adopt
the calendar I have proposed, I wish it to be known as the Darian
calendar, which I name for my son Darius. This calendar, like
the planet Mars itself, belongs to his and future generations.
My June 1986 paper "Martian Standard Time"
also included a brief discussion on the Martian clock. I considered
two options: that of stretching the Terran second, minute and
hour to fit the slightly longer Martian sol, and that of dividing
the Martian sol by powers of ten to create a "metric"
clock. The metric clock would have ten hours per sol, 100 minutes
per hour, and 100 seconds per minute. I decided upon the "stretch"
approach, however, since the stretched Martian units of time would
be less than three percent longer than their earthly counterparts,
and no one would have to learn a new system. As I discovered later,
this was also the approach favored by Levitt,
Richardson, Lovelock and Allaby, and other
writers. However, the next writer on the subject made a persuasive
argument in favor of the metric clock.
An HTML version of my paper, "Martian Standard Time",
published in the June 1986 issue of the Journal of the British
Interplanetary Society, is available on Jim Kelley's web site.
An HTML version of my paper, "The Darian Calendar",
to be presented at the Founding Convention of the Mars Society
in August 1998, is available on the Martian Time Web Site. Also on the Martian Time Web Site, "The Calendars of Jupiter" duscusses four variants of the Darian calendar for the Galilean moons: Io, Europa, Ganymede, and Callisto.
1987: THE MACKENZIE CLOCK
Bruce A. Mackenzie's paper, "Metric Time for Mars", which was presented at the Case for Mars III Conference at the University of Colorado in Boulder in July 1987, is the most thorough discussion on the Martian clock to date. He too saw the need for a distinct Martian chronometric nomenclature, especially in the case of stretching the Terran clock to fit the Martian sol:
Unfortunately, all technical measurements must account for this 1.0275 conversion factor. For example, specifications for machinery and electronics are in units of meters/second, cycles/second, microseconds, megahertz, etc. If the units are stretched, it is critical to give them different names so that a person knows if the conversion factor has been factored in.
Mackenzie briefly considered four other options for a Martian
system before settling into a detailed description of his metric
system. He began by dividing the sol into 100 centidays, but also
observed that four centidays are about the same duration as the
terrestrial hour, so with a nod to ancient custom, he invented
the intermediate unit of time "hora", 25 of which form
a Martian sol. The centiday then would be analagous to a quarter
of an hour, and so he also referred to the centiday as a "quarter"
(note that in Terran usage, a "quarter" refers to a
quarter of a year, whereas Aitken used the
term to denote a quarter of a "season", which was itself
a quarter of a Martian year). A milliday, which he named "mil",
would be analogous to a Terran minute. Finally, 10 microdays,
which he called a "beat", is about the interval between
human heartbeats.
Mackenzie pointed out that a clock based on powers of ten was
an original part of the metric system developed in revolutionary
France two centuries ago and failed to gain acceptance. Possibly,
the Martians will be more open to the idea.
An HTML version of Mackenzie's paper, "Metric Time for Mars",
presented at the "Case for Mars III" conference in 1987,
is available on the Martian Time Web Site.
1988: THE FORWARD CALENDAR AND CLOCK
Robert L. Forward was in the process of working out his own system
of Martian timekeeping when he read my "Lost Calendars of Mars"
article in the July 1988 Spaceflight. So he wrote to me
care of the British Interplanetary Society, and our common interest
in the subject led us to an interesting exchange of letters.
In his letter of 31 July 1988,
Forward explained that in his latest novel, Martian Rainbow,
the first Martian colonists were scientists, and it is to them
that he would attribute the invention of the Martian chronometric
system. As with the Lovelock-Allaby calendar,
there are no months, but rather the mear (Martian year) is merely
divided up into 95 numbered, seven-sol weeks, with four seasonal
"holisols" outside of the weekly calendar, for a total
of 669 sols. These holisols are spaced unevenly in the calendar
to reflect the lopsided seasons of Mars. The Forward calendar
has a southern hemisphere bias, and thus the calendar period called
"Spring" is 20 weeks long, "Summer" is 22
weeks, "Fall" is 28 weeks, and "Winter" is
25 weeks. Intercalation is effected by dropping a holisol -- either
"Springsol" or "Fallsol" -- every two and
a half mears. At this point, Forward specified that the zeroth
mear of this calendar should coincide with the Gregorian year
2000, but he had not worked out an exact date.
On the subject of the Martian clock, most previous writers had
been content to simply stretch our terrestrial units of time to
fit the slightly longer Martian sol. I think we all assumed that
it would be acceptable for the Martian physical scientists to
keep their Terran second in the laboratory while the rest of Mars
used the Martian second for civil purposes. But Forward, being
a physicist, was resolved to somehow fit the standard terrestrial
second into a Martian clock. "A second is a second is a second!"
His first shot at a Martian clock had 24 "maurs" (Martian
hours) per sol, 43 "marmins" (Martian minutes) per maur,
and 86 terrestrial seconds per marmin. Forward noted that this
"legal sol" of 88,752 seconds was shorter than the physical
sol by 23.238 seconds, but at this point felt that this was too
small a discrepancy to cause any problems.
In my letter of 13 August 1988,
I pointed out that these 23 excess seconds accumulate to one maur
every 168 sols, which is roughly a quarter of a mear. I also asked
whether he intended to begin his calendar mear with spring or
some other season, noting that although he wished mear 0 to coincide
with year 2000, MARSOFT (my software implementation of the Darian
calendar) showed that the nearest vernal equinoxes of the southern
hemisphere would take place on 6 August 1999 and 23 June 2001.
I wondered if instead Forward might have arbitrarily picked 1
January 2000 for the beginning of his calendar without regard
to where this date might fall in relation to the seasons of Mars,
and discovered that this would be a fortuitous choice, since it
would correspond to the southern hemisphere's summer solstice
to within a few hours! (Note: the Earth dates given in
this paragraph are late by seven days, according to Mars Pathfinder
mission data.)
In his letter of 19 August 1988
Forward mentioned that is would be nice if there were a method
of designating equinoxes and solstices that didn't depend on which
hemisphere was assumed for the seasons, and for this purpose coined
the terms "apsolstice" and "perisolstice"
to represent the solstices nearest the aphelion and perihelion.
Thus apsolstice would refer to the beginning of summer in the
northern hemisphere and the beginning of winter in the southern
hemisphere.
Forward abandoned his 24/43/86 clock and came up with a revised
scheme. He still had 24 maurs to the sol, but now resigned himself
to the time-honored (and more mathematically elegant) 60-marmin
maur. It is his method of fitting the standard terrestrial second
into these marmins that was so ingenious. He now proposed that
in each Martian hour (maur), the zeroth, first, and all Martian
minutes (marmins) divisible by three be 61 seconds in duration,
while all others be 62 seconds, for a total of 88,776 seconds
per sol. Additionally, three out of every four sols had the second
marmin of the zeroth maur containing 61 seconds rather than 62,
for a 88,775 second sol. The remaining discrepancy between the
average statutory sol and the physical ephemeris sol was tiny
enough to be figured in as part of the annual leap-second correction.
Thus the physical scientists in Forward's novel were happy because
they had kept their precious Terran second, and the social scientists
and ordinary citizens were content because this complicated algorithm
was programmed into their electronic timepieces and they did not
have to bother with it much. Forward's determination led him to
look at the problem of the clock a lot closer than other authors
on Martian timekeeping did, and he came up with a compromise which
reconciles the two approaches to timekeeping: the physical and
the sociological. In his final version of his Martian clock, few
people would care whether a minute contained an extra second or
two, especially since we have the technology in hand to handle
the details automatically. Forward was able to preserve the sanctity
of the second and all the physical units derived therefrom (the
newton, the watt, et cetera), and at the same time work out a
practical method of integrating in into the civil chronometric
system of Mars. Nicely done! I wish I'd thought of it!
In my letter of 2 September 1988
I added to Forward's idea of coining new words to define the equinoxes
and solstices by suggesting the terms "apequinox" and
"perequinox" (although Forward's letter of 11 September
would change the latter to "periequinox" on the recommendation
of his English Lit wife, the Latin prefixes per- and peri-
having very different meanings). I also supplied him with MARSOFT-generated
tables listing the Gregorian dates of numerous Martian equinoxes
and solstices. These tables showed that the best choice for the
beginning of the Forward calendar
was the perisolstice on which midnight on the Martian Prime Meridian
will occur at 15:31 Universal Coordinated Time on 24 December
1999. (Note: this is a correction to earlier papers, and
is based on Mars Pathfinder mission data.)
1988: THE CHILDS CLOCK
Another response to "The Lost Calendars of Mars"
appeared in the December 1988 issue of Spaceflight.
In this letter, David Childs proposed yet another Martian clock
based on the Terestrial second. This one had 25 hours per sol,
50 minutes per hour, and 71 seconds per minute, which as Childs
noted ends up being short of the physical sol by 25.2 seconds.
He proposed to correct this discrepancy by redefining the Martian
second as 1.00028 terrestrial seconds.
1993: THE ROBINSON CALENDARS AND CLOCK
In Part 1 of Kim Stanley Robinson's novel Red Mars,
he described the Martian clock devised by the first one hundred
colonists:
And then it was ringing midnight, and they were in the Martian time slip [the author's bow to Philip K. Dick's novel], the thirty-nine-and-a half-minute gap between 12:00:00 and 12:00:01; when all the clocks went blank or stopped moving.
A Martian calendar was described at the beginning of Part 3 of
Red Mars:
Mars's year was 668.6 local days long, and to tell where they were in this long year it took the LS calendar. This system declared the line between the sun and Mars at its northern spring equinox to be 0°, and then the year was divided into 360 degrees, so that LS = 0°-90° was the northern spring, 90°-180° the northern summer, 180°-270° the fall, and 270°-360° (or 0° again) the winter.
Since it takes a bit less than two sols for Mars to travel an arc of one degree in its orbit around the sun, typical dates on Robinson's calendar are "the first day of LS = 266°," followed by "the second day of LS = 266°" and "the first day of LS = 267°." However, since spring lasts 194 sols, there would have to be 14 "third day of LS" dates added. On the other hand, summer, which lasts 177 sols, would need three more "second day of LS" dates subtracted toward the end than there were "third day of LS" dates added early in the season. Similarly, autumn and winter would have 38 and 24 "second day of LS" dates subtracted, respectively. The LS calendar in the table is a speculative layout.
As a Martian society developed in the later novels of the series, Green Mars and Blue Mars, the LS calendar was augmented by a calendar containing weeks and months. Although not mentioned in the text of Red Mars, at the beginning of Part 3 was a diagram of Mars' orbit. The legend described the year being divided into 24 months generally numbering 28 sols, with every eighth month having one less. According to this diagram, the Martian year 1 occurs in 2027 AD. The nearest Martian vernal equinox corresponding to this will occur on approximately 29 September 2026. Dates mentioned throughout Green Mars and Blue Mars such as Friday, LS 101, 2 July 2, M-year 52, imply a seven-sol week, and twelve pairs of months, with the months of each pair preceded by "1" or "2". Robinson's 24-month calendar does not begin on the northern vernal equinox, however, as the date LS 4, 2 March the 22nd, M-year 32 shows more clearly. Rather, the vernal equinox would occur on about the 13th sol of the 2nd March. I was unable to find a reference to the placement of the leap sol, but since there are so many Gregorian features to this calendar, I suspect that it would occur at the end of the 2nd February.
A brief description of Robinson's Martian clock and 24-month calendar
are included in Frans Blok's "Red, Green & Blue Mars Site".
1993: THE ZUBRIN CALENDAR AND CLOCK
In his article "A Calendar for Mars", published in the November/December 1993 issue of Ad Astra, the noted astronautical engineer an President of the Mars Society Robert Zubrin proposed a calendar which reprised several ideas found in earlier calendars: a year beginning on the vernal equinox and divided into twelve months, with each month representing a 30° arc in Mars' orbit about the sun, and each month named for a constellation on the ecliptic. There's a odd twist, however; instead of the each month being named for the constellation in which the sun appears (as seen from Mars) at that time of year, each month was named for the constellation in which Mars appears as seen fron the sun. The Zubrin calendar began with the year I (he used Roman numerals for counting years) on 1 January 1961, noting that it was after this date that spacecraft from Earth began exploring Mars (although several Soviet spacecraft were launched in 1960, they failed to leave Earth orbit). Zubrin made no mention of weeks in his calendar, nor did he specify an intercalation sequence.
Zubrin devised an algorithm for converting Gregorian dates to his system, the heart of which is the following equation:
In this equation, the Earth date is expressed as:
year + ((the numeric value of the Gregorian month x 30.4) + the numeric day of the month) / 365)
The Martian date in day/month/year format must by extracted from the numeric value resulting from the basic equation. The Martian year equals the integer value of the numeric Martian date. The fractional value of the numeric Martian date is then multiplied by 669, and the resulting numeric sol value must be looked up in a table to determine the Martian month. The numeric day of the month is then calculated by subtracting the numeric sol of the year on which that month begins (from the lookup table) from the numeric sol value from the previous calculation, then adding 1 (since months don't begin with 0).
Several approximations in Zubrin's algorithm accumulate to induce significant errors in his calendar. First of all, the length of the Martian year is derived from the ratio of 15 Earth years to 8 Martian years, resulting in the value 1.875 Earth years per Martian year. The actual value is 686.98 Earth days/Martian year / 365.2425 Earth days/Earth year = 1.88 Earth years per Martian year, making Zubrin's Martian year a bit short. Secondly, Zubrin assumed 365 days per Earth year, whereas the actual value is 365.2425. Since the length of the Martian year is tied directly to the length of the Earth year via the 8:15 ratio, this short value for the Earth year has the effect of further shortening the Martian year. The combined error results in a Martian year of only 684.375 Earth days. Another, albeit smaller, error induced by Zubrin's assumed value of 669 Martian sols per Martian year (the actual value being 668.592) has the effect of shortening the length of the Martian sol in Zubrin's algorithm. The cumulative effect of these errors is that the average length of Zubrin's Martian sol is only 24 hours, 33 minutes, 5.6 seconds, 6 1/2 minutes short of the true duration of 24 hours, 39 minutes, 35.2 seconds.
These problems account for the large discrepancy between the epoch of Zubrin's calendar and the actual date of the first Martian vernal equinox of the 1960s. The next vernal equinox will occur on 14 July 1998, which is Julian Day 2,451,008.5. This should begin Zubrin's Martian year XXI. Multiplying the number of Earth days in a Martian year by twenty (he began his calendar with the year I, there being no Roman numeral for zero), then subtracting this number from the Julian Day above:
JD 2,451,008.5 - (687 x 20) = JD 2,437,268.5
The Gregorian date for this Julian Day was 30 November 1960. Since Zubrin calculated that the vernal equinox occurred on 1 January 1961, the beginning of his calendar is off by 32 terrestrial days, or 31 Martian sols. Alan Hensel and I have determined that the most recent New Year's Day on which a Martian vernal Equinox occurred was in 1707.
Zubrin, following many other authors, based his clock on stretching the hours, minutes, and seconds to accommodate the longer Martian sol.
These problems are easily corrected, of course. The epoch of my
own Darian calendar was originally off by seven sols.
An HTML version of Zubrin's article is located on Jeff Roche's web site.
The Zubrin Calendar is also discussed on Paul J. Thomas's
web site.
In October 1994, William H. Becker sent a letter to Christopher P. McKay regarding his proposal for a perpetual Martian calendar. Becker's calendar is very much like the Rohrer calendar in that it consists of nineteen months of thirty-five days each. This amounts to 665 sols, so Becker inserts an intercalary sol (i.e., not counting as a sol of the week) at the beginning of each quarter. Thus the year begins on the first intercalary sol, called "Mars Sol", which occurs on the northern hemisphere's winter solstice. Since 19 is not divisible by 4 (or any other number), the remaining intercalary sols are embedded in the fourth week of the fifth month ("Phobos Sol"), the third week of the tenth month ("Horos Sol"), and the second week of the fifteenth month ("Deimos Sol"). Horos Sol, which is the mid-year intercalary sol, only occurs in leap years.
Becker takes the length of the Martian year to be 668.62 sols, which causes his intercalation formula to be off by one sol in 36 years: odd-numbered years, decennial years, years ending in 66, and years ending in 32 in even-numbered centuries are all leap years. However, he's very creative with his month names, starting with the sun and moving sequentially through the solar system with names taken from several different languages, and ending with Universe. Coincidently, two of these, Ceres and Zeus, appear in Heinlein's calendar.
Becker begins his calendar with the same approximate epoch as the Gregorian calendar, and uses the ratio of 0.5316514 Martian years per Earth year to arrive at the statement that the winter solstice beginning the Martian year 1064 occurs in the Gregorian year 2001 (about 8 November). Calculating back, the Martian year 1 would have begun on or about 2 August 1 B.C.
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