ABSTRACT
Martian clocks and calendars have been discussed in the writings of various authors over the past one hundred years, although the need for a Martian timekeeping system was often perceived as being so far off in the future that the subject was treated in a cursory manner. However, several very sophisticated Martian calendars have been developed. Now, at the close of the twentieth century, the prospect of vigorous programs for the robotic exploration of Mars by several nations is near at hand, programs which will ultimately lead to human expeditions and settlements early in the next century. Thus the implementation of a standardized Martian clock and calendar has at last become a practical and immediate concern. This article recounts the history of Martian timekeeping from 1880 to 1998, and discusses the work of:
Anyone having knowledge of other work on the subject please send
e-mail to the above address. In particular, I would like to give
credit to whoever invented the term "sol".
23 May 1999 -- 26 Taurus 12
5 February 1999 -- 6 Mina 12
26 January 1999 -- 24 Pisces 12
6 December 1998 -- 16 Kumbha 12
15 September 1998 -- 6 Capricornus 12
22 August 1998 -- 11 Dhanus 12
14 July 1998 -- 1 Sagittarius 12
15 June 1998 -- 1 Vrishika 11
3 June 1998 -- 17 Scorpius 11
5 April 1998 -- 16 Libra 11
28 February 1998 -- 9 Kanya 11
10 January 1998 -- 16 Asleha 11
7 December 1997 -- 11 Leo 11
27 November 1997 -- 1 Leo 11
6 September 1997 -- 5 Mithuna 11
THE NATURAL CYCLES OF MARS
In the next century, when humans begin colonizing Mars, they will
leave behind the familiar 24-hour day and the 365-day year. Theseare cycles that are peculiar to Earth, and as a product of billions
of years of evolution on this planet, we are designed to operate
by them. However, these earthly cycles will have no physical meaning
on Mars. On other planets in the solar System that humans may
settle in the coming decades and centuries, there will be inevitable
conflicts between the natural cycles of the new worlds and those
of human biology. Humans will have no use for diurnal periods
that are hundreds of hours long, nor will years of twelve or twenty-nine
times the duration of the terrestrial year be of any practical
use; on the moons of Jupiter and Saturn, the current time-keeping
conventions of Earth -- Universal Time and the Gregorian calendar
-- will probably do quite nicely. But, paradoxically, human colonists
on Mars will have to abandon Earth's system because the cycles
of Mars itself are so Earthlike!
On the Moon, for instance, where the alternation of day and night
takes over twenty-nine terrestrial days to complete, this cycle
can be pretty much ignored as far as its utility in regulating
the day-to-day affairs of humanity -- no one is going to stay
awake for two-thirds of a lunar day and sleep the remaining third!
On the other hand, the Martian solar day (now known as the "sol")
of 24 hours, 39 minutes, 35.2 seconds is so very close to our
own on Earth that it would be entirely impractical to ignore it.
There would be absolute chaos on Mars if one tried to reckon time
by the 24-hour terrestrial solar day. Suppose that on a given
date and at a specified point on Mars, local midnight coincides
with Greenwich Mean Time midnight (00:00 GMT, in terms of 24-hour
time). On that sol the Sun rises at about 06:10 and sets around
18:30. The following local midnight does not occur until nearly
40 minutes into the next GMT day, and after another sol passes
the Martian sky lags the terrestrial clock by 79 minutes. Now,
try to imagine the situation a couple of weeks later when a Martian
executive opens her office in the middle of the night just because
it is nine o'clock in the morning in Greenwich. Still another
week later a young Martian is told he cannot play outside because
"it's too dark outside this afternoon and it won't be dawn
until past your bedtime". If you can't imagine having to
live like this then don't think the Martians will stand for it
either. They will have to live by the Martian solar day, not the
terrestrial solar day.
Similarly, the 365-day cycle of the seasons of faraway Earth will
be irrelevant on Mars. Mars has seasons of its own due to its
very Earthlike axial tilt of 24.936 degrees, but because it orbits
much farther from the Sun that does Earth, the Martian year is
nearly twice as long as the terrestrial year. Just as on Earth,
life on Mars will undeniably be dependent on the Sun, and the
Martian yearly solar cycle will have great influence on colonial
life. There will be Martian farmers who will need to know the
seasons of Mars: how to manage water and other resources throughout
the year, when to plant, when to harvest and expect an income,
when to expect the need to draw more power from Martian Edison
or the Valles Marineris Authority to supplement the winter Sun.
Martian farmers will need to be able to compare their cash flow
and cash reserves at any point in the present Martian solar year
with those recorded at the same point in previous years. Also,
if Martian utility companies derive a significant portion of their
power from the Sun, so much more so will the solar cycle drive
Martian economics. These and other activities directly depend
on the Martian annual cycle will have ripple effects throughout
the colonial economy. Certain businesses will be subject to significant
seasonal fluctuations, just as they are on Earth. In these pursuits,
of what use will the Gregorian calendar be to the Martians? This
strongly suggests that the Martians will require a calendar based
on the solar cycle of Mars.
1880: THE GREG CALENDAR AND CLOCK
We begin our historical exploration of Martian time with Percy
Greg's remarkable novel Across the Zodiac,
which was not only the first (as far as I know) fictional account
of an expedition to Mars, but also coined the term "astronaut"
(in this case, the name of the spacecraft).
Several paragraphs in Chapter 9 describe the organization of the
Martian clock and calendar:
The Martial day, which consists of about twenty-four hours forty minutes of our time, is divided in a somewhat peculiar manner. The two-hour periods, of which "mean" sunrise, and sunset are severally the middle points, are respectively called the morning and evening zydau. But for purposes of exact calculation, the day, beginning an hour before mean sunrise, is distributed into twelve periods, or antoi, of a little more than two terrestrial hours each. These again are subdivided by twelve into periods of a little more than 10m., 50s., 2 1/2s., and 5/24s respectively; but of these the second and last are alone employed in common speech. Tle uniform employment of twelve as the divisor and multiplier in tables of weight, distance, time, and space, as well as in arithmetical notation, has all the conveniences of the decimal system due to the greater convenience of twelve as a base. But as regards the larger divisions of time, the Martials are placed at a great disadvantage by the absence of any such intermediate divisions as the Moon has suggested to Terrestrials.
The revolutions of the satellites are too rapid and their periods too brief to be of service in dividing their year of 668 2/3 solar days. Martial civilization having taken its rise within the tropics--indeed the equatorial continents, which, only here and there extend far into the temperate zone, and two minor continents in the southern ocean, are the only well-peopled portions of the planet--the demarcation of the seasons afforded by the solstices have been comparatively disregarded. The year is divided into winter and summer, each beginning with the Equinox, and distinguished as the North and South summer respectively. But these being exceedingly different in duration--the Northern half of the planet having a summer exceeding by seventy-six days that of the Southern hemisphere--are of no use as accurate divisions of time.
Mars's orbit around the Sun is significantly more elliptical than
Earth's. The effect of this is that when Mars is further from
the Sun, it moves more slowly in its orbit, and conversely, when
Mars is closer to the Sun, it proceeds more rapidly in its orbit.
This effect causes the seasons to have markedly different lengths.
Mars reaches its farthest point from the Sun, or aphelion, during
last spring in the northern hemisphere, and its closest point,
or perihelion, in late autumn. Specifically, in the northern hemisphere,
spring lasts 194 sols, summer 177, autumn 142, and winter 156.
Time is reckoned, accordingly, from the first day of the year; the 669th day being incomplete, and the new year beginning at the moment of the Equinox with the 0th day.
Note that Greg did not specify which equinox begins the
calendar year. In Chapter 5, one of Greg's Martians stated:
"We date events from the union of all races and nations in a single State, a union which was formally established 13,218 years ago."
Taking the year that Across the Zodiac
was published, and subtracting 13,218 Martian years:
1880 - 13,218 x (686.9897 / 365.2425) = -22,982
we find that Greg's Martian calendar
began in 22,982 B.C., a time when there wasn't much interest in
either Mars or calendars here on Earth.
1895: THE LOWELL CALENDAR
The need for an entirely Martian system of timekeeping for any
inhabitants of that planet was recognized by astronomers of the
nineteenth century. In his 1895 treatise entitled simply Mars,
Percival Lowell described a very straightforward method for referring
to the Martian time of year. He took the Gregorian calendar of
Earth and simply stretched it to fit the longer Martian year,
stretching not only the months of our earthly calendar, but the
dates as well. In his system, then, the date on Mars changed slightly
more frequently than once every two Martian solar days. As such,
Lowell's system did not constitute a true Martian calendar, but
rather was intended only as a convenient shorthand for marking
a particular point in time in reference to the advance of the
seasons on Mars, for Lowell was keenly interested in espousing
the notion that there were regular, repetitive seasonal changes
in the surface features of that planet that were conclusive evidence
of life. Lowell could thus quote some date on Mars such as 25
August, and his readers would know that this was late summer in
the southern hemisphere of Mars (since the closest oppositions
of Mars always occur when its southern hemisphere is pointed toward
Earth, Lowell chose the southern rather than the northern hemisphere
for referencing the seasons of Mars).
1913-1914: THE BURROUGHS CALENDAR AND CLOCK
Edgar Rice Burroughs described a somewhat more detailed Martian
chronometric system in his 1913 novel The Gods of Mars.
He first divided the Sol into ten parts called "zodes".
Each zode consisted of fifty "xats", each of which in
turn comprised twenty "tals". Burroughs' approach was
similar to the idea of metric time, for while it was not strictly
based on powers of ten, it was at least based on multiples of
the powers of ten.
Burroughs mentioned in The Gods of Mars
that the Martian calendar year was divided into twelve months,
but did not go into detail as to how these months were organized
into days and weeks.
The similarity of the Sol to the terrestrial day caused Burroughs
to err when describing the length of the Martian year, and as
we shall later see, Burroughs was not the last to commit such
an error. In the beginning of his third Martian novel, Burroughs,
narrating as the protagonist John Carter, lamented the imprisonment
of the Princess Dejah Thoris in a chamber, located at the south
pole of Mars, which rotated in synchronization with the revolution
of Mars about the Sun. John Carter anticipated that he could not
free the princess until 687 days had passed, at which time the
cell's door would again be aligned with the tunnel's end. This
is in fact the number of terrestrial solar days, i.e., 24 hour
days, in a Martian solar year. Although The Warlord of Mars
was published in 1914, it was already at that time well established
that the Martian sidereal day is 24 hours, 37 minutes, 22.66 seconds,
or 24.622961 hours. While Burroughs mentioned this slightly longer
duration of the Sol elsewhere in his works, he failed to take
this into account when describing the number of sols a Martian
would experience in the course of a Martian solar year.
How long then is a Martian mean solar day, and how many are contained
in a Martian year? The figure generally given for the length of
the Martian sidereal year in terms of terrestrial mean solar days
is 686.9796. Multiplying by 24 hours gives 16,487.51 hours in
a Martian year, and dividing this value by the 24.622961-hour
Martian sidereal day yields 669.5990, the number of Martian sidereal
days in a Martian year. The number of Martian solar days in a
Martian year is exactly one less than this, or 668.5990 sols.
Dividing 16,487.51 hours by this number gives the length of the
Martian mean solar day: 24.65979 hours, or 24 hours, 39 minutes,
35.2 seconds. The mean solar day of any planet can be calculated
by this method. The general form of the equation is:
ysol
dsol = ----------------
ysol
---------- - 1
dsid
where dsid, dsol, and ysol are
sidereal days, solar days, and solar years, respectively, and
all quantities are expressed in consistent units.
Additional accuracy can be attained by taking the precession of
Mars' axis into account. The effect of this precession is that
the Martian tropical year on 668.5921 sols is somewhat shorter
than the sidereal year.
1936: THE AITKEN CALENDAR
It was in Patrick Moore's 1956 Guide to Mars
that I chanced across a passing reference to a Martian calendar,
which attributed the invention to the astronomer Robert S. Richardson
of the Griffith Observatory in Los Angeles. Eventually, I found
a copy of Richardson's 1954 book Exploring Mars,
only to find that he named Robert G. Aitken, Director Emeritus
of the Lick Observatory above San Jose, California, as the inventor
of the calendar. I later learned from Arthur C. Clarke
that Richardson first published an article on Aitken's work in
the August 1947 issue of Astounding.
Finally, I tracked down Aitken's own paper, "Time Measures
on Mars", originally published in 1936 in the Journal of Calendar Reform,
and reprinted in the Leaflets of the Astronomical Society of the Pacific
that same year.
Aitken began his discussion of a Martian calendar by entertaining
various methods of dealing with the fractional portion of the
668.6-sol year. The first scheme had common years of 669 sols
and every fifth year consisted of 667 sols. In the second method,
common years would be 668 sols and every fifth year would contain
671 sols. The solution Aitken settled on was to have the years
run alternately 668 and 669 sols and insert an extra sol in every
year whose number was divisible by ten. In Aitken's intercalation
sequence, the odd-numbered years were 668 sols long and his even-numbered
years 669 sols long, and therefore every tenth year had 670 sols.
The moons of Mars are such tiny objects and in such tight orbits
around the planet that the idea of basing months on their orbital
periods makes little sense. Only 20 kilometers in diameter, Phobos
orbits so close to Mars that it can be seen rising in the west
and setting in the east twice each sol, so that a month based
on the motion of Phobos would be less than half as long as a Martian
solar day! Having an orbital period of little more than a Martian
solar day, Deimos is half the size of Phobos and orbits far enough
away from Mars that from the surface of that planet the satellite
appears not much larger, and certainly far dimmer, than Venus
does from Earth. As the bases for natural divisions of time, then,
the moons of Mars can be ignored.
On the strength of this argument, Aitken dispensed with months
entirely on his Martian calendar. Instead, he first divided the
year into equal quarters of approximately 167 sols, which he called
"seasons" and named Spring, Summer, Autumn, and Winter.
Each "season" he quartered in turn so that each sixteenth
of a year contained either 41 or 42 sols. These subdivisions of
the "seasons" Aitken called "quarters", although
this term usually connotes a quarter of a year. Indeed, while
he chose not to call them months, in order to keep the terminology
in this paper consistent, one can think of them as such. It should
be pointed out here that because the orbit of Mars around the
Sun is highly eccentric as compared to the nearly circular orbit
of Earth, the naturally occurring seasons of Mars are not at all
of equal length. In the northern hemisphere, spring, summer, autumn,
and winter last 194, 177, 142, and 156 sols, respectively. Thus,
there would be a very poor correlation between the naturally asymmetric
seasons and Aitken's symmetric "seasons". Assuming that
Aitken's calendar began with the vernal equinox, he would have
his first sol of Summer 27 sols before the summer solstice, his
first sol of Autumn 37 sols before the autumnal equinox, and his
first sol of Winter 12 sols before the winter solstice.
Every culture on Earth has had to invent a period of time whose
length is shorter than a month but longer than a day. A society
functions more efficiently if a given day out of every five or
ten is set aside for bringing produce to market, social gatherings,
recreation, worship, et cetera. There is no natural cycle of Earth,
Moon, or Sun that satisfies this human sociological need, and
across the face of the Earth and the span of history, civilizations
have employed many methods for filling this void. Once the ancient
Sumerians discovered that there were seven objects that moved
through the skies -- the Sun, the Moon, Mercury, Venus, Mars,
Jupiter, and Saturn -- the number seven took on great metaphysical
significance. Archaeological evidence indicates that the Sumerians
began practicing the seven-day week as early as 5,000 years ago.
Each day of the week was named for one of these seven celestial
wanderers: the Sun, the Moon, and the five known planets. The
Egyptians, the Jews, and the Babylonians also adopted the seven-day
cycle. The number seven was held by all of these peoples to be
holy. The importance of the seven-day week in the religion of
the Jews was recorded by Moses in Genesis, according to
which God made the world in six days and rested on the seventh.
Although of religious origin, the seven-day week satisfies economic
and social needs; there are days of work and days of rest. It
has become so important as a regulator of human activities that
the two major attempts to change it, both of which were made by
revolutionary governments seeking to purge society of all religious
symbols, were complete failures. French revolutionaries attempted
to establish a calendar containing ten-day weeks, but Napoleon
Bonaparte abandoned it only thirteen years later. The early Soviet
government promulgated a calendar incorporating five-day weeks,
then replaced it three years later with a calendar of six-day
weeks, which in turn had a life of only eight years.
In view of this proven sociological need of some unit of time
consisting of a handful of days, and humanity's evident preference
for a seven-day week, Aitken incorporated such a unit of time
into his calendar. He also retained the same names of the days
of the week as we use on Earth. Being 41 to 42 sols in duration,
each sixteenth of a year thus consisted of roughly six weeks.
As shown in the table, Aitken
allowed the sols of the week to regress through his calendar over
a two-year period. His odd-numbered years began on Sunday, and
since each "season" was 167 sols -- one sol short of
being evenly divisible by seven -- his Summer began on Saturday,
Autumn on Friday, and Winter on Thursday. In even-numbered years,
Spring began on Wednesday, Summer on Tuesday, Autumn on Monday,
and Winter on Sunday. Since even-numbered years contained 669
sols, this last "season" was a sol longer than normal;
168 being divisible by seven, the following Spring also began
on Sunday to begin the two-year cycle again. Aitken's calendar
is thus a perpetual one, for each two-year period is the same
as any other. Another nice feature of the Aitken calendar was
that within each of the "seasons", all of the six-week
periods began on the same sol of the week. Aitken treated the
extra sol that he inserted every tenth year as an intercalary
sol -- having no "sol of the week" -- so as not to upset
his biennial cycle. The leap sol occurred at the end of Summer
-- halfway through the year -- so Aitken called it Mid-Year Day
and declared it a holiday.
Aitken's Martian calendar
is very well thought out, and except for one omission, it is a
complete system. Unfortunately, Aitken did not specify a starting
year for his calendar, and so it cannot be correlated with the
Gregorian calendar. Certainly he saw that it would be many decades
before there was any practical use for such a calendar, and perhaps
he thought it best to leave it for a future generation to fix
a beginning date for his calendar.
An HTML version of Aitken's paper, "Time Measures on Mars", and of Robert S. Richardson's article, "Calendar for Mars" are available on the Martian Time Web Site.
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