Spaceflight, July 1963, Vol 5, No. 4, pp. 138-141

The Martian Calendar

by M. Vertregt, F.B.I.S.
edited by Thomas Gangale, 2003 July 25

The basis of terrestrial chronology is the Mean Solar Day, which is subdivided into 24 hr. of 60 min. of 60 seconds. Relative to the stars, the Earth makes a complete revolution in 23 hr., 56 min. and 4 sec.; this time interval is called the Sidereal Day. This day is not suitable as a basis for chronology because time reckoning in civil life depends on the course of the Sun and not of the stars.

In the temperate zones, where the greatest part of the world’s civilization is situated, the times of sunrise and sunset deviate more than 4 hr. throughout the year, and as it is very difficult to change the time of beginning daily activities, the result is that in winter we go to our offices when it is still dark and in the summer we sleep hours in the morning when the Sun is shining. We try to correct this situation by the introduction of Summer Time, but, of course, this is only a very inadequate remedy, because a change of 1 hr. is insufficient and people would not readily appreciate an abrupt change of, say, 3 hr. Therefore, Prof. Van den Bergh of Amsterdam proposes to introduce summertime, as it were not in one lump, but by little bits, namely by advancing the clock 50 sec. every day in winter and in spring, and by retarding them 50 sec. every day in summer and in autumn. An alternate solution proposed by the author of this article is to change the course of the clocks continually according to a sine-function, making them gain in winter and in spring, and lose in summer and in autumn. This could be done by introducing a rather simple mechanical device into our clocks and watches. In this manner we could ensure that our clock-time of sunrise would be practically constant throughout the year.

An advantage of this system is that it works imperceptibly, people would soon become accustomed to it and would accept it as the normal state of affairs.

Of course, this method of time measurement is only for civil use; astronomers will have nothing to do with days, hours, minutes and seconds of variable length, and their tables will be expressed in true time.1

We must use a Mean Solar Day because the length of the real solar day changes throughout the year. The eccentricity of the Earth’s orbit around the Sun, and the inclination of the Earth’s axis cause the longest solar day to be 31 minutes longer than the shortest one. Therefore, a simple sun dial gives the correct time only four times a year, namely on 16 April, 14 June, 1 September, and 25 December. On 12 February, the Mean Solar Day is 14.3 min. longer and on 3 November, 16.4 min. shorter than the real solar day.2

The second unit of chronology is the year. We have several kinds of year, the most important being the Sidereal Year and the Tropical Year. The Sidereal Year is the time the Sun needs to make a complete circle around the ecliptic, starting from a star and returning to the same star. But to serve as a practical basis for our chronology, we want the time that the Earth needs to return to the same place in its orbit around the Sun.3 These 2 years are not equal, because of the fact that the terrestrial axis has no constant orientation relative to the stars, but describes a cone with an angle of 23.5° in 26,000 years. This causes the precession of the equinoxes, which are the two points where the celestial equator and the ecliptic intersect. These two points advance an amount of 50.3? per year, causing a lengthening of the year by 20 min. and 27 sec., which means 1 day in 70 years.

Origin of Calendars

In ancient times the requisites of a good chronology were: firstly to fix the dates of the beginnings of the seasons, secondly the dates of the Christian feasts,4 and thirdly to give a basis for the counting of the years.

Using the Sidereal Year, the dates of the beginning of the seasons would advance by 1 day every 70 years, which would soon become perceptible in the course of the centuries. Therefore the Tropical Year should be used for civil purposes. For civil use a year must have an integer number of days, but as a matter of fact the Tropical Year has 365.2422 mean solar days. Therefore, when the normal duration of the year is fixed at 365 days, an extra day must be inserted at fixed intervals to get the exact mean duration. The first to introduce a solar year of 365 days were the Egyptians, and they, too, were the first to see the necessity of inserting a leap day every 4 years.

In the time of Julius Caesar the Roman calendar, which was based on the Moon, was in a chaotic state, and when he became dictator he decreed that in the future a year of 365 days with one leap day every 4 years would be used. By this means the average length of the year became 365.25 days, which is a fair approximation, but a little too long. At the end of the sixteenth century the difference between the official and the real date had become 11 days. Pope Gregory XIII, whose pontificate occurred from 1572 to 1585, issued the Bull “Inter gravissimas,” decreeing that, beginning on 24 February, 1582, a new chronology would be introduced. Every fourth year would be a leap year, excepting the secular years, of which the number of centuries is not divisible by 4. Thus the year 1600 would be a leap year, but the 1700 would not. At the same time the date of the month was advanced 11 days to set the new calendar right. This last measure caused not a little trouble on the part of workers, who felt themselves swindled out of their rightful wages. The Easter date was fixed on the first Sunday after the first full moon in spring.5 The Catholic countries accepted the new calendar at once; the Protestant countries waited a long time. England introduced the Gregorian calendar in 1752 and Russia6 only changed to the new calendar in 1917.

The length of the mean Gregorian year is 365 + 1/4 - 1/100 + 1/400 days = 365.2425 days, while the length of the mean solar year is 356.2422 days.7 Thanks to the ingenious arrangement our chronology will be in error by only 1 day after 3000 years.8

Other time units we use are the week and the month. The meaning of these units is to divide the year into shorter, more convenient periods. But the main difference of dividing the year consists of the number of days, 365, which is divisible only by 5 and 73. Therefore there are two methods of dividing the year. We can divide it into an integer number of periods of varying duration, or we can use a period of fixed duration that does not go an integer number of times into a year. Both periods are used: the first is called a month, the second a week.

The great advantage of the week is that it gives an unbroken sequence of periods of equal duration, which is of great importance for chronology. The disadvantage of the week is that the same date falls on different weekdays in different years.

The division of the year into months of 28, 29, 30 and 31 days is the most unsystematic and unsatisfactory part of our calendar. This month is a remainder of the ancient Moon-calendar, and through the ages chronologists have tried unsuccessfully to adapt this old calendar to the new Sun calendar.

Many religious feasts, for instance, Easter, are based on the moon calendar. The fixation of the Easter date has been a controversial point in Christian churches for centuries and has led to accusations of heresy, even to persecutions.9

There has been no lack of reformers in the past, of course, who tried to ameliorate the shortcomings of the calendar. The number 364 has more divisors than the number 365; it is divisible by 4, 7, and 13. This leads to a calendar in which the year is divided into 13 months, each of 4 weeks of 7 days. At the end of the year an extra day and in leap years two extra days are attached.10

Another proposal called the World Calendar is to divide the year into four seasons of 91 days each. Each season consists of three months of 31, 30, and 30 days of 13 weeks each. An extra day is attached at the end of the year, and in leap years another extra day is inserted between June and July.

Of course, both systems (where the regular sequence of weeks is interrupted by extra days) will never be accepted by chronologists. How simple would be our calendar if only our year counted 360 days!

Extra-terrestrial Calendars

The foregoing is an introduction to give the reader an idea of the foundations of our chronology and to serve as a guide for the construction of extra-terrestrial calendars. We should, of course, avoid the inconsistencies of our calendar and try to adapt the planet’s calendar rationally to the planet’s special conditions.

In order to visualize those special circumstances, let us imagine that we are passengers in a spaceship destined for Mars. It is not the intention to pay a short visit, but to found a permanent colony on that planet.

As soon as we leave Earth, the ideas of day, night, season and year become meaningless. At the sunside of the spacecraft it is day and at the shadowside it is night. In infinite, eternal space, any chronology is as good as the next, so we use our own terrestrial calendar. Our clocks show Universal Time, we call 24 hr. a day, and we count the days according to our terrestrial calendar, as if we had never left Earth.

As soon as we arrive on Mars the situation changes completely. Let us assume that the spaceship lands at the moment that the Sun is exactly at its culmination in that place. Then it is midday and when our clocks show 6 hr. U.T., we should advance the hands 6 hr., if we insist on having noon at 12 o’clock. We can raise this local time to Standard Martian Time, if we call the meridian over our settlement the zero meridian of Mars.11

A Martian solar day is 40 min. longer than a terrestrial solar day, and therefore, if we keep to terrestrial hours we should set the clock back 2 hr. every 3 days. Soon this will become too troublesome, and we will construct a rational chronometry, adapted to Martian circumstances. A well organized expedition would have done this before the beginning of the voyage.

For the construction of the Martian calendar we free ourselves of every earthly tradition; thus, for instance, of the notion that a day should have 24 hr., an hour 60 min. and a minute 60 sec.12

We decide that a rational chronology should be based on the decimal system. Thus, we divide the Mean Solar Day of Mars into 10 Mars-hours, abbreviated hM, each Mars-hour is divided into 100 Mars-minutes, abbreviated mM, and each Mars-minute into 100 Mars-seconds, abbreviated sM. Thus a Martian day counts 100,000 Mars-seconds.

If we call the corresponding terrestrial units hE, mE and sE, then the Martian mean Solar Day expressed in terrestrial units is 24 hE, 39 mE, 35.0 sE or 88775.0 sE.13

Of course, on Mars, we don’t use those unsystematical expressions like “a quarter to two,” or half past five,” but we say: It is 6.73 or 4.82. Our clocks will have no hands, but show the numbers of the hours and the minutes on a dial, like modern clocks on Earth. Still, one of our clocks will show Terrestrial U.T., because all our astronomical tables are calculated in this time-system.

Now we have to decide which year we will chose: the Tropical Year or the Sidereal Year. The Gregorian calendar dates from 1582 and has never been revised since. In the meantime, many changes have taken place in society, and many things that were important then have lost much of their importance now. We saw that the Tropical Year was chosen as the basis of chronology because of the necessity of medieval society and religion to regulate the seasons of Christian feasts.14

In the first place man has become much less dependent in the seasons. The farmer nowadays does not have to look at his calendar to know when it is time to plough or to sow; he can hear that on the radio from the office of Agricultural Information.15 For glass-house horticulture the seasons mean much less and less as the technique of growing fruit and flowers out of season is more and more perfected. For millions of city dwellers the only season that interests them is summer, because of the holidays.16 The second reason for the Tropical Year, the fixing of the dates of the church feasts has lost all importance for a large part of the population, and as to the third reason, the fixing of the years, the Sidereal Year serves as well as the Tropical Year. Moreover, the exact length of the Martian Tropical year is not known, because we do not know in how much time the Martian polar axis makes a complete revolution among the stars.17

Finally, we should take into account that on Mars we are still less dependent on the seasons tan on Earth because we live in big bubbles of translucent plastic, surrounded by an artificial atmosphere that is quite independent of the atmosphere outside. Inside the bubble we have no seasons, or, if we prefer so, we can fabricate our own seasons, that have no relation whatever with the current Martian season.18

Therefore on Mars the tropical Year has little importance for us and we shall base out chronology on the Sidereal Year. The duration of the Martian Sidereal Year is 686dE, 23 hE, 30 mE, 41 sE, or 5,355,041 sE. This is equal to 66,860,086 sM, or nearly exactly 668.6 dM.19 The number 668 is as poorly divisible as 365, the factors being 4 and 167.

We don’t need months, which are such imperfect time-units on Earth,20 but we want weeks to divide the year into shorter periods, and following our principle of using the decimal system we give a week 10 days.21 The most important feature of the week is that the continuity of periods of fixed duration gives an easy means to count the days and name them. We must add three names to the names of the earthly week, and mindful of the fact that the last day of the week is called Saturday after the planet Saturn, we call the following days Uranusday, Neptuneday and Plutoday.

Now we have to invent a kind of leap year system, but with the additional condition that the number of weeks in the year must be an integer and that consequently the number of days in the year is a decuple. Thus the number of days in the common year will be 670 and that of the leap year 660. In this manner the same date in different years will always fall on the same weekday.

Fifty Martian years count 33,430 days, and we can distribute this number in the following manner:

33,430 =7*(6*670+1*660)+1*670

Thus a period of 50 years, a pentakontade, is divided into seven parts of 7 years, called heptades, following by 1 year. Every heptade contains six “long” years of 670 days and one “short” year of 660 days. Thus a pentakontade contains 43 long years and 7 short years.

As the true duration of the year is 668.6 days, the first civil year will be 1.4 days too long. After the second year this difference is 2.8 days and after the sixth 8.4 days. Then a short year intervenes and at the end of the first heptade the calendar is only 0.2 day fast. At the end of the seventh heptade of the 49th year, this difference is augmented to 1.4 days, but at the end of the pentakontade the difference is zero again. It takes about a thousand years to produce an error of one day in the system.

As we do not bother about seasons is does not matter much that the years are unequal in length; in any case the astronomers will take care that their chronology stays faultless by simply counting the days from a certain starting date. On Earth they call this the Julian era, not after Julius Caesar, but after Julius Scaliger, a celebrated scholar of Leyden, who lived in the sixteenth century. Scaliger chose as the staring date of his era,22 Monday the first January of the year 4713 before Christ, which day got the ordinal number zero. According to this counting the first January, 1963, is Julian day 2,438,031. It is not certain which day the astronomers will chose as the starting day for the Martian chronology. They could not do better than to choose the earthly date of 28 November, 1659.23 On that day at 19 hr. the Dutch astronomer Christian Huygens made the first sketchy map of Mars, on which however the Syrtis Mayor [sic] is clearly discernible, thus linking for the first time Martian and Terrestrian [sic] chronology, and enabling present day astronomers to calculate the duration of the Martian day with an accuracy of 0.01 sec.

How the Christian feast-days could be fitted into a year of 668 days is the concern of the theologians and it will not be easy to find a solution that satisfies all parties. It will certainly cause lively discussions in theological circles, and may lead to much showing of the well known odium theologicum.

Of course, on Mars we will not make the error of giving the first year of the era the ordinal number one. The first year of the Martian era will get the ordinal number zero, as well as the first week of the year and the first hour of the day. One sees immediately that the date 0.53.8 means the eighth day off the 53rd week of the year zero. The date 25.0.9 means the ninth day of the year 25 of the era.

The last thing to do is to fix the beginning of the year. On Earth this is now the first of January, about the time the Earth goes through its perihelium [sic]. Formerly 21 March was often used to mark the beginning of the new year;24 at that date the Sun enters the Vernal Equinox.

For the Sidereal Year we use on Mars, it would be rational to choose for the beginning of the year the moment when the Sun is exactly 180° distant from the meridian of a bright star, for instance α Leonis.25 This star, called Regulus, is of the first magnitude, has a small proper motion (0.25° per year) and a small parallax (0.049°). The star is situated -0.27’ from the terrestrial and -1.9’ from the Martian ecliptic. Perhaps when the length of the Martian Tropical Year is better known, this year may be used instead of the Sidereal Year, but though many objections can be raised against this proposed Martian Calendar, I think it would satisfy the simple needs of a colony for a long time.

1 Astronomical tables are expressed in mean time, not true time. Mean time averages the seasonal variation in the length of the true solar day, as the author attempts to explain in the next paragraph.

2 It is not true that longest solar day is 31 minutes longer that the shortest day. Rather, the total change in the length of the solar day amounts to considerably less than a minute. However, these changes accumulate, e.g. a day that is 10 seconds longer than the mean length causes the next day to begin 10 seconds late, the third day begins 20 late, et cetera. As a result, the deviation of the time of true solar midnight (or noon) from the mean varies by 31 minutes. On Mars, because of the greater eccentricity of its orbit, the variation is more than 94 terrestrial minutes (see “Martian Daylight Time”).

3 In fact, the sidereal year is the most objective measure of the time it takes to return to the same point in an inertial reference frame. The tropical year is based on a rotating reference frame.

4 Good calendars were devised in ancient times by non-Christian peoples.

5 This basic definition of Easter arose during the years immediately following the crucifixion of Jesus, although the exact algorithm, called the computus, is more complex, involving a conscious effort to prevent Easter and Passover form occurring simultaneously.

6 Russia is an Orthodox, not a Protestant country. On the whole, Orthodoxy was as loath to adopt the Catholic reform as was Protestantism.

7 Tropical year.

8 The common assumption is that the Gregorian calendar is intended to approximate the tropical year, which is actually an average of the changing relationships of all equinoxes and solstices with respect to the sidereal year. However, the principle purpose of the Gregorian reform was to stabilize the date of the vernal equinox, since this figures into the computus of Easter. Given this, the proper standard to apply to the Gregorian calendar is the vernal equinox year, which is the time from one vernal equinox to the next. The current length of the vernal equinox year is 365.2424 days, which would imply that an extra day would not be needed for 10,000 years.

9 There were some heated controversies among the various dioceses of the Christian church in the 4th and 5th centuries regarding the computus, but it is arguable whether these rose to the level of “persecutions.” These were arguments over methods of calculation, not over matters of theology.

10 The Positivist calendar and the International Fixed calendar.

11 The Martian prime meridian was generally agreed upon by the scientific world in the mid-19th century. It is extremely unlikely that the prime meridian will be redefined based on the location of a future settlement.

12 This assumption has proven not to be the case. Percival Lowell referred to local time on Mars by the stretched 24:60:60 clock in Mars, published in 1895, and it may not have been his invention. At least since that time, astronomers have used the stretched 24:60:60 clock to describe perceived diurnal phenomena on Mars. Also, since 1976, the human race has had a periodical telepresence on Mars in the form of robotic vehicles. During the operation of these missions, both the operators of the vehicles and the investigators of the returned data have used the stretched 24:60:60 clock for Mars. The precedent is well established. It is unlikely that when humans physically go to Mars, they will change from a system they have used for Mars for many decades.

13 The precise length of the Martian solar day, now known as the “sol,” is 88,775.24409 seconds.

14 By 1582 the Renaissance had been underway for several centuries. European society was well beyond “medieval.”

15 But where does the “office of Agricultural Information” get its information? In the end, someone must know the relationship of the calendar date to the season of the year. Invoking an “office of Agricultural Information” only passes the buck.

16 First of all, less than half of the human race lives in urban settings. Secondly, even those who do are affected by weather. The fact that millions of lives are disrupted or destroyed every year by droughts, floods, forest fires, famines, tropical storms, and arctic storms belies the assertion that “man has become much less dependent in the seasons.”

17 The Martian tropical year is now known to be 668.5921 sols.

18 Power demand to maintain the comfortable environment in the plastic bubble will vary seasonally on Mars, just as it does on Earth. Everyone turns up the heat during a cold snap. Furthermore, if terraforming Mars turns out to be possible, humans will have an even grater need to be cognizant of the Martian seasons.

19 The current value of the sidereal year is 686.9797 days (668.5991 sols).

20 Nearly every culture on Earth has reckoned time according to months. There is overwhelming evidence for the social utility of this unit of time, and hardly any evidence against it.

21 The historical evidence is that this idea will prove unpopular. The 10-day week was a feature of the French Revolutionary calendar, which few people accepted, and which had to be abandoned after a few years. The Soviet Union made several attempts to deviate from the seven-day week, with similarly dismal results.

22 It is called the Julian period, and Julius Caesar Scaliger had nothing to do with it. The Julian period was invented by his son, Joseph Justus Scaliger. It is often written that Joseph named the Julian period in honor of his father; however, in his De Emandatione Temporum, Joseph Scaliger wrote: "We have termed it Julian because it fits the Julian year," by which he meant the 28-yeat cycle over which the days of the week repeat in relation to the start of the year. The Julian period is the product of this cycle plus two others, the 19-year Metonic cycle of lunisolar years and the 15-year indiction cycle of Roman taxation; 28 * 19 * 15 = 7980 years. The last time these three cycles were synchronized was on -4712 January 1, which is the beginning of the Julian period. Even so, Joseph Scaliger did not invent the Julian Day system; rather, it was invented by John W. F. Herschel (son of the discoverer of Uranus) in 1849.

23Julian calendar. Being a Protestant state, the United Provinces did not convert to the Gregorian calendar until 1701.

24 March 21 has never marked the beginning of the calendar year. Originally, the Roman year began on March 1 (which made Quinctilis through December the fifth through tenth months, as their names suggest). Later, the beginning of the year was changed to January 1. Still later, Christians moved the beginning of the year to March 25, nine months before Christmas, in celebration of the Conception.

25 Having chosen the historical event to mark the start of Martian chronology, as well as the point in Mars’ orbit at which to begin the calendar year, the author could have calculated the epoch (reference date) for his calendar in terms of the Earth date. The right ascension of Regulus is 10h 08m 22.3s. Converting to degrees results in a longitude of 152.093°. The vernal equinox of Mars located at 85.061° longitude. Thus, in terms of Martian heliocentric longitude, Regulus is located at LS = 67.032°. Mars most recently passed through this longitude on JD 2452529.23. The date and time of Huygens’ observation of Mars on the night he drew Syrtis Major, 1659 December 8 (Gregorian), 19:00, translates as JD 2327339.29. The difference between the two dates is 125189.94 days. Dividing by the sidereal year of 686.9797 days results in 182.23 Martian years. Rounding up to the next integer and multiplying by 686.9797 days results in 125717.29 days. Subtracting this from JD 2452529.23 yields JD 2326811.95, which was 1658 June 29 (Gregorian), at about 10:50 UTC. The passage of Mars through LS = 67.032° (the meridian of Regulus) occurred at about 21:30 Airy Mean Time (on the prime meridian of Mars). The previous AMT midnight on Mars corresponded to 1658 June 28 (Gregorian), at about 12:50 UTC, or JD 2326811.03. This is Vertregt’s epoch.