This paper discusses two options for a calendar based on the astronomical cycles of Mercury to regulate any future long-term human activity on that planet. The orbital period of Mercury is divided into three months. Each month is in turn divided into 28 “circads” of approximately 25.13 hours, organized into four weeks of seven circads each. Option 1 scales the calendar year to the approximate duration of the terrestrial year: 12 months, for a total of 336 circads (351.8770 Earth days). Option 2 scales the calendar year to the approximate duration of the Martian year: 24 months, for a total of 672 circads (703.7541 Earth days). The circad is organized into sub-units according to a stretched 24:60:60 clock, the precedent set on Mars. Synchronization with the Gregorian (Earth) or Darian (Mars, the Galileans, and Titan) systems is considered and rejected in favor of a purely Mercurian system. Although the desirability for a Mercury-based timekeeping system is assumed for the purpose of this exercise, there is no convincing case to be made for it versus retaining the Earth-based Universal Time, Coordinated (UTC) and the Gregorian calendar.
During the past 125 years, more than 80 calendars have been invented for Mars, which, after the Moon, is the most likely planet for future human exploration and settlement. With the subject of Martian timekeeping now fairly well covered, calendar-makers have begun to set their sights on other bodies in the solar system. It is difficult to say if or when humans will find Mercury useful enough that there will be a substantial long-term human presence on that planet. However, that has not deterred a few people from devising timekeeping systems for organizing human activity on the innermost planet in the solar system, well in advance of any conceivable need.
Mercury is the one planet in the solar system on which the diurnal and annual cycles synch up exactly, and the ratio of their durations is a simple fraction. Mercury is so close to the sun that solar tidal forces have forced the planet into this synchronization. Its rotational period (sidereal day) is 58.646225 days, which is 2/3 of its 87.969257-day period of revolution (NASA 2003).
On any planet, there is always one less solar day (referenced to the sun) than there are sidereal days (referenced to a fixed star) in a year. On Earth, there are 366.2422 sidereal days (23h 56m 4s each) in a tropical year, but of course only 365.2422 solar days (24h each). In one day Earth travels approximately one degree in its orbit, and the direction from Earth to the sun (referenced to a fixed star) also changes by about one degree. It takes about four minutes for Earth to rotate through the extra one degree from the star-referenced direction to the sun-referenced direction. In the course of a year, these approximately one-degree discrepancies add up to 360 degrees, or a complete rotation, and thus there is one less solar day than there are sidereal days.
Similarly, on Mercury, there are 1.5 sidereal days per revolution, but only 0.5 solar days. In other words, in the course of a day and a night Mercury travels twice around the sun! Obviously, such a long day isn’t at all useful in terms of human circadian rhythms. And, of course, the environmental conditions on Mercury are problematic in terms of human habitation. Even if there were sufficient incentive to go to the trouble to establish a long-term human presence on Mercury, it is not clear that a timekeeping system based on Mercurian astronomical cycles would be preferred to UTC and the Gregorian calendar, the standard for timekeeping on Earth.
Assuming the former, however, the Mercurian solar day would need to be divided into smaller segments to serve the human circadian rhythm (the term “circad” was coined in Gangale 1998). Also, if possible, commonality with a previously established timekeeping system should be designed into a Mercurian system. An obvious choice for commonality is Earth’s Gregorian calendar. Another option to consider is the Darian system, which is currently defined for Mars (Gangale 1986; 1999), the Galileans (Gangale 1998), and Titan (Gangale 2003). Originally designed for Mars, the Darian system happened to fit more conveniently with the natural cycles of Io, Europa, Ganymede, and Callisto than did the Gregorian calendar. Furthermore, it can be speculated, as Isaac Asimov did in “The Martian Way” (1952), that the natural resources of the outer solar system may be more accessible and more valuable to a Martian economy than to the terrestrial economy. Having extended the Darian system to the Galileans, a further extension to include Titan was logical. The same logic does not necessarily apply to Mercury, however, which is closer to Earth than to Mars. The average Earth-Mercury travel time would be shorter, but this would be only one of many factors to consider in the calculation of total transportation costs. Other considerations would be the comparative per-unit cost of propellants, the difference in ΔV (change in velocity) requirements between the average Earth-Mercury and Mars-Mercury voyage, and the relative need for Mercurian resources. Since it is impossible to predict whether Earth-Mercury or Mars-Mercury trade relationships will be stronger, both the Gregorian and Darian systems should be considered.
Taking the Gregorian system first, four revolutions of Mercury around the sun could constitute a calendar year (351.8770 Earth days). Dividing this calendar year into the customary 12 months, each month would constitute 1/6 of a Mercurian solar day (1/3 of a revolution, 1/2 of a sidereal day). One could divide the month into 28 circads (four weeks of seven circads each. Having an integral number of weeks in a month allows each month to start at the beginning of the week, rather than letting the days of the week haphazardly float through the months as in the Gregorian calendar (the goal of commonality does not necessarily imply an uncritical propagation of inconvenient features in the original model). The calendar year would therefore contain 12 x 28 = 336 circads. The length of the circad would be 351.8770 / 336 = 1.047253 Earth days (25h 8m 2s). Since the human circadian rhythm is somewhat longer than the 24-hour terrestrial solar day, this should not be an insurmountable physiological problem. How often does it seem that there just aren’t enough hours in a day!*
The elegance of this system is that January 1 could be set at solar midnight on the prime meridian of Mercury, sunrise would occur on February 15, noon on April 1, and sunset on May 15. This solar cycle would repeat with midnight on July 1, sunrise on August 15, noon on October 1, and sunset on November 15.
If a timekeeping system based on the Mercurian solar cycle is adopted and the circad is substituted for the terrestrial day in regulating human activity, the problem of dividing the circad into smaller units must be considered. The most straightforward solution is to divide the circad the same way that the terrestrial day is divided: 24 hours per circad, 60 minutes per hour, and 60 seconds per minute. Each of these units would simply be stretched to fit the longer Mercurian circad. The precedent for this concept is established on Mars, where space scientists have long referred to the time of day at a given location on Mars in terms of a stretched 24-hour clock.
To go from a Gregorian to a Darian structure, it is only necessary to double the length of the year and the number of months: 24 months, or 672 circads (703.7541 Earth days). The principal points of the solar diurnal cycle would similarly be set to either the 1st or 15th of the month, at 42-circad (6-week) intervals.
However, designing further commonality into the system presents problems to which there do not appear to be elegant solutions. A fully integrated Mercurian system would require synchronization with either the Gregorian or Darian systems. Four Mercurian revolutions are 13.3655 days shorter than the average Gregorian year of 365.2425 days. Uncorrected, the starting date of the Mercurian calendar year would drift around the Gregorian year (much as the Islamic calendar of 12 lunar months does), and the discrepancy would accumulate to a full year every 26 Gregorian years (27 Mercurian calendar years). As a result, dates written in the Mercurian system might look like Gregorian dates, but the two systems would actually have no relationship to each other. Similarly, eight Mercurian revolutions are 16.7830 days longer than the average Darian year of 686.9711 Earth days, and although dates written in the Mercurian system might resemble Darian dates, they would be completely out of synch. Attempts at synchronization with the Gregorian system while maintaining some relationship between the principal points of the solar cycle and the calendar months would be problematic. For instance, adding a 28-circad month approximately every other year would mean that solar midnight on the prime meridian would shift from January 1 to December 1, then to November 1, et cetera. Similarly, synchronization with the Darian system might involve subtracting a 28-circad month approximately every other year. In either case, the relationship of the principal points of the solar cycle to the calendar dates would constantly shift, and the whole point of devising a Mercurian system in the first place would be lost. It would be better to abandon the idea of a timekeeping system based on Mercurian cycles and use either the existing terrestrial or Martian systems outright. Otherwise, we are left with the choice of either a 12-month system that is not synchronized with Earth or a 24-month system that is not synchronized with Mars, the Galileans, and Titan. Either way, there is no point to giving names to Mercurian months and circads that resemble the Gregorian or Darian names. Such a Mercurian system would need to be distinct in its nomenclature to preclude confusion with the other systems.
*This system has similarities to those worked out by Shaun Moss (2002) and Blort (2003). Blort’s “Two by Three by Four” Mercury calendar divides the Mercurian solar day into six months, each containing four weeks of seven “turns;” however, this makes for a calendar year of only 175.9385 Earth days. The calendar year outlined by Moss is based on two Mercurian solar days (four revolutions = 351.8770 Earth days); however, he divides the months into 30 “M-days” of 23h 27m 30s, and makes no mention of weeks. Blort’s “Two by Three by Three” Mercury calendar also divides the month into 30 segments, organized into three weeks each, but again the basis of the calendar year is two revolutions rather than four.
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