A Critique of Robert Zubrin’s Martian Calendar
Abstract
Robert Zubrin published his ideas for a Martian calendar in the November/December 1993 issue of Ad Astra, the National Space Society’s magazine. He also described his calendar in his 1996 book, The Case for Mars. Due to his position as President of the Mars Society, Zubrin’s calendar proposal continues to attract the interest of the Mars enthusiast community. Unfortunately, his work contains egregious technical errors. Moreover, even if these flaws were corrected, the basic concept of his calendar is such that it would be very difficult for a society on Mars to put into practice.
The primary author of this article wrote a personal correspondence to Dr. Zubrin in 1998 regarding the errors in his work; however, Dr. Zubrin did not respond. This article was first offered to Ad Astra, then to the Mars Society's online magazine, New Mars. The authors have yet to receive a response from either publication.
Technical Errors
Robert Zubrin set the Martian vernal equinox (referenced to the northern hemisphere) as New Year’s Sol on Mars. Also, he reasoned that it would be convenient to begin the Martian era when the Martian year and the Earth (Gregorian calendar) year began simultaneously. According to his calculations, the last time these two events coincided was on 1961 January 1.
Zubrin devised an algorithm for converting Earth dates to his Martian system, the heart of which is the following equation:
Mars date = (8 / 15) x (Earth date  1961) + 1
In this equation, the Earth date is expressed as:
year + [(the numeric value of the Gregorian month  1) x 30.4
+ (the numeric day of the month  1)] / 365
The Martian date in yearmonthday format must be extracted from the numeric value resulting from the basic equation.
Several approximations in Zubrin's algorithm accumulate to induce significant errors in his calendar. First of all, he derives the length of the Martian year from the ratio of 15 Earth years to 8 Martian years. This is not terribly accurate. Earth’s year, measured from one vernal equinox to the next, is 365.2424 days. A Martian year, measured from one vernal equinox to the next, is 686.9710 Earth days. This means that in 15 Earth years, there are only 7.975062 Martian years. This doesn’t sound like much of a discrepancy, but it is, as you will see in a moment.
Another error in Zubrin’s calculations is that he assumes there are 365 days per Earth year, whereas the actual value is 365.2424. Since the length of the Martian year is tied directly to the length of the Earth year via the 15:8 ratio, this short value for the Earth year has the effect of further shortening the duration of the Martian year in Zubrin’s algorithm. The combined error results in a Martian year of only 15/8 x 365 = 684.375 Earth days in Zubrin’s calendar.
When considering a Martian calendar, one needs to talk in terms of the Martian solar day (known as the “sol”), which is 2.75 percent longer than an Earth day. There are 668.5907 sols in a Martian year, measured from one vernal equinox to the next. Because he uses the inaccurate 15:8 ratio and assumes 365 days in an Earth year, Zubrin’s calendar really has only 15/8 x 365/1.0275 = 666 sols in a Martian year.
The Gregorian calendar replaced the Julian calendar because the old calendar had three days too many in 400 years. By comparison, Zubrin’s calendar is missing nearly three sols every Martian year. This adds up to a big problem over just a few years. One of the primary purposes of a calendar is to keep in step with the seasons. Zubrin’s calendar is clearly intended to do this, since each year supposedly begins on the Martian vernal equinox. However, because it is based on a highly inaccurate formula, it fails to achieve this purpose.
For instance, although the next New Year’s Sol may occur on 2004 February 15 according to Zubrin’s calendar, the actual Martian vernal equinox will not occur until March 5, nineteen days later. You can confirm this by consulting next year’s Astronomical Almanac, a joint publication of the Greenwich and U.S. Naval Observatories, or you can consult NASA Reference Publication 1349, “Geocentric Planetary Ephemeris for Mars, 20012006.”
The displays below show the time and date on Mars using two different systems, both of which are intended to begin the Marthian calendar year on or near the northern hemisphere's vernal equinox. Because of the difference between the Darian calendar's simple intercalation algorithm and the complex variation in the length of the Martian year, the actual vernal equinox can occur either a sol before or after the first sol of the calendar year, but is generally on the first sol of the year (similarly, the date of the vernal equinox on Earth ranges from March 19 to 21, but is usually on March 20). The Darian clock/calendar display shows the number of sols since the beginning of the Martian year. The Zubrin calendar display also provides this number. Note that the number provided in the Zubrin calendar display is approximately 19 sols ahead of the Darian calendar display.
As another example of the calendar’s inaccuracy, Zubrin’s formula led him to believe that a Martian vernal equinox occurred on 1961 January 1. Zubrin used this date to begin counting Martian calendar years since, according to his calculations, the beginning of the Earth year and the beginning of the Martian year occurred simultaneously. However, the real Martian vernal equinox occurred 31 days (30 sols) earlier on 1960 December 1. Again, you can confirm this by consulting the Astronomical Almanac for that year.
To recap, New Year’s Day on Zubrin’s calendar has gone from being 30 sols late in 1961 to being 19 sols early in 2004, a total discrepancy of 49 sols over that time. Indeed, Zubrin’s calendar was only briefly in synch with Mars in 1993, when he published his original article in Ad Astra.
Practical Problems
Even if these technical defects were corrected, Zubrin’s calendar would still be problematic to put into practice. He casually dismisses the idea of having months of equal duration. “Such equipartitioned months don’t work for Mars because Mars’ orbit is elliptical, which causes its seasons to be of unequal length.” While it is true that Mars’ seasons are unequal in length, it does not logically follow that “equipartitioned months don’t work.” For whom would they not work, and why? Zubrin does not explain this. Another vague assertion is, “In order to predict the seasons, a calendar must divide the planet’s orbit not into equal divisions of days, but into equal angles of travel around the Sun.” Why must it? Earth’s Gregorian calendar does not divide the planet’s orbit into equal angles. The arc of Earth’s orbit that is represented by February is only 27.6 degrees, while March occupies 30.6 degrees, a variation of more than ten percent. Yet anyone can predict with great confidence that the first day of spring will occur on or about March 20 every year.
Zubrin declares that “if we want months to be useful units and choose to retain the terrestrial definition of a month as a twelfth of a year, then a month really is 30 degrees of travel around the Sun.” Two observations can be made here. First of all, this is exactly the opposite logic from the design of the modern clock. One could argue that we should define an hour as one twentyfourth of a day (or sol on Mars), in which case an hour is really 15 degrees of travel of the Sun across the sky during the day. The problem is that the terrestrial day (and the Martian sol, for that matter) varies in length in the course of the year, and so that 15 degrees of travel takes slightly longer at some times of the year than at others. Of course, we don’t have hours that are sometimes 59 minutes long and at other times 61 minutes long. This is because the modern clock is based on the length of the mean solar day, averaged over the span of the entire year, rather that being based on the variable rate at which the sun travels across the sky. So, why should Martians inconvenience themselves with months based on the variable rate at which Mars travels around the sun?
Secondly, one should ask, “For whom would Zubrin’s equalangle months be useful units?” Suppose you are living on Mars, and you just got paid for the month. You got by fairly well in late autumn in the northern hemisphere, when the months lasted less than 50 days, but now it is late spring, so you are going to have to somehow make that paycheck last 66 days. The problem is, you can only buy enough heating fuel and food for about 50 days, and you will have to shiver and eat shoe leather for the last couple of weeks. There would be cold comfort in the fact that Mars traveled 30 degrees around the sun that month, just as every other month. People live from day to day and from paycheck to paycheck, not from angle to angle.
One could counter that Martians could get paid more at one time of the year than at another. Monthly rents could also be seasonally adjusted, along with a million other prices in a cascade effect throughout the entire Martian economy, just so we could have a diagrammed calendar (which Zubrin calls the “Areogator”) that traces immaculate 30degree angles in planetary space. One can begin to imagine the administrative costs that this complex system would impose, not only on every commercial enterprise on Mars, but on every field of human endeavor on the Red Planet.
The success of sustained human habitation on Mars will depend on such settlements becoming selfsufficient as rapidly as possible. It is a matter of debate whether the first Martian colonies will be funded by terrestrial governments, private investors, or a partnership of both. In any case, the startup costs leading to a sustainable Martian economy will be huge, and the patience of either taxpayers or investors will not be inexhaustible. In all realms, the critical concern will be the shortest path to profitability consistent with human safety. Profitability requires efficiency, which in turn requires that all things be made as simple as possible.
Zubrin’s calendar is far from simple. Only two of the twelve months contain the same number of sols. Here on Earth, we use a short mnemonic poem to help us figure out which months on the Gregorian calendar have 30 days and which have 31. Imagine how long a poem describing Zubrin’s calendar would be, how long it would take to memorize it, and how long it would take to mentally recite it each time one needed to determine how many sols were in a particular month: 61, 65, 66, 65, 60, 54, 50, 47, 46, 48, 51, or 56? Imagine these mental exercises being performed over and over by every person on Mars, sol after sol, year after year. What a monumental waste of time!
Zubrin’s characterization of “the terrestrial definition of a month as a twelfth of a year” is arguable. There are three natural units of time on Earth: the day, the month, and the year. A day is the time in which Earth completes one rotation relative to the sun, and a year is the time it takes for Earth to complete one revolution about the sun. The third natural unit of timethe monthis the time in which the Moon completes one revolution of Earth relative to the sun: 29.53 days. “The terrestrial definition of a month as a twelfth of a year” is an abstraction, meant to rationalize the lunar cycle with the solar year. There is no reason why a month on Mars must be “a twelfth of a year.” In the absence of a large moon orbiting Mars on which to base a new unit of time, it makes sense to keep the concept of a month to approximately the same duration of time that we are familiar with on Earth: 29.53 days, which is 28.74 sols. Abstracting from the natural unit, it might be convenient to divide the Martian year into 24 nearly equal months of 27 or 28 sols, since 24 is divisible by many numbers. Also, a 28sol month would be exactly four 7day weeks.
This segues to another deficiency in Zubrin’s work. He never even mentions the concept of a week. This is a glaring oversight, for nearly every calendar ever used on Earth has included some unit of time shorter than a month, consisting of a handful of days, in order to regulate commercial and social activity. Without this, any description of a calendar is incomplete.
A final criticism of Zubrin’s calendar is that nowhere does he discuss the necessity of leap years, much less in what pattern these should occur.
Conclusion
Zubrin designed his calendar from the perspective of a space scientist. The irony is that space scientists do not even use the civil calendar in their work because it lacks the necessary precision. Knowing only the time of day and the day of the year, one can only determine the position of the Earth in its orbit to about one degree of solar longitude, because some calendar years have 365 days and some have 366 days. For this reason, space scientists instead use precise astronomical tables called ephemerides. Similarly, on Mars, some calendar years would have 668 sols and some would have 669 sols; meanwhile, space scientists would use ephemerides to obtain the desired precision. In contriving to make all the months fit equal angles, Zubrin attempted a solution for which there never was a problem, and in so doing created a huge inconvenience for future Martian society at large. Furthermore, even as a work of space science, Zubrin’s calendar fails “to predict the seasons,” since the Martian vernal equinox slips nearly three sols during each of his Martian calendar years.
Zubrin acknowledges, “The idea of a Martian calendar and timekeeping system is not original, and many have been designed in the past.” This body of work should not be summarily dismissed; rather, it deserves to be carefully researched for the valuable ideas it may contain. We invite you to visit the Martian Time website, where you will find information on more than 80 Martian calendars dating from 1880 to the present.
A successful calendar cannot be a product of vague reasoning and approximate astronomy. Furthermore, a grounding in exact astronomical relationships, while a necessary starting point, is still not sufficient. Calendrics is a subject where space sciences and social sciences intersect. A Martian calendar cannot simply be designed on the basis of the planet’s periods of rotation and revolution, but must be carefully crafted to serve the common needs of the many walks of life in an emerging society struggling to make a go of it on a new world.
