Figures and Tables

1.0 The Darian Calendar for Mars

1.1 Introduction

1.2 Years

1.2.1 An Extended Intercalation Scheme

1.3 Months and Seasons

1.4 Weeks

1.4.1 The Martiana Calendar

1.5 The Telescopic Epoch

1.6 Darian-Gregorian Calendar Displays

1.7 Children and Collateral Relatives

2.0 The Calendars of Jupiter

2.1 Introduction

2.2 Circads

2.3 Years

2.4 Weeks

2.5 Months

2.6 Intercalation

2.7 Calibration

2.8 Variations on a Martian Theme

3.0 The Darian Calendar for Titan

3.1 Overview of the Darian Calendar System

3.2 Astronomical Cycles on Titan

3.3 Circads and Weeks

3.4 Months and Years

3.5 Intercalation

3.6 Calibration

4.0 Conclusion

5.0 References

Appendix 1: Intercalation Precision on Mars

Appendix 2: Perturbations of Mars

Appendix 3: Martian Daylight Time


Copyright 1986-2005 by Thomas Gangale


Updated from Journal of the British Interplanetary Society, Vol. 42, pp. 337-340, July 1989

The eccentricity of Earth's orbit and the inclination of its spin axis to the plane of its orbit affect the apparent motion of the Sun along Earth's ecliptic and cause annual -variations in the correlation of Solar time to mean time. The sum of these effects constitute Earth's equation of time, shown in Figure 1. With a Martian calendar now fully developed, it may now be considered how the slightly greater inclination of Mars' axis and the far greater eccentricity of its orbit would affect sundials on Mars. Figure 1 also depicts the Martian equation of time and its two components. Solar time agrees with mean time on approximately Aquarius 7 (Sol 119) and Simha 16 (Sol 490). A Martian sundial will read about 39.5 minutes slow on Mithuna 21 (Sol 383) and approximately 52.5 minutes fast on Tula 28 (Sol 613).

Figure A3-1: The Equations of Time for Earth and Mars

Perhaps sundials will never be in vogue on Mars, and there will obviously be far more practical and accurate instruments for timekeeping on that world. While it is quite likely that early Martian technology will require that colonies be built below the surface, the Martians will surely move to the surface of their world as soon as technology permits. Thus, the shape of the Martian equation of time raises interesting questions with regard to the need for seasonal adjustments to the setting of clocks in the Martian colonies.

Since Mars has an axial tilt comparable to Earth's, it also experiences changes in the duration of daylight throughout the year. This suggests that the periodic alternation between standard time and daylight time might be practised in the Martian colonies, much as do many nations on Earth. Probably, since Mars is a much colder world than Earth, early Martian colonies will be clustered near the equator and the tropic circles. Just as in the tropics of Earth, the seasonal fluctuation in the length of day and night in minimal at these Martian latitudes. States situated in the tropical regions of Earth do not bother with daylight time for this reason, so one might deduce that this will be true on Mars as well.

It can be seen from Figure A3-1, that the effects of orbital eccentricity and axial inclination combine on Mars to produce a naturally occurring daylight time of up to 52 minutes in the southern hemisphere's summer and autumn. The reverse phenomenon happens during the other portion of the year, when Solar time can be as much as 31 minutes ahead of mean time. To anyone who recalls the brief experiment with year-round daylight time by the US in the early 1970s, it is disturbing to realise that this natural Martian daylight time occurs during winter in the northern hemisphere. Equally so is the revelation that there is a natural reverse daylight time in the northern hemisphere's summer. Based on these facts, the preliminary conclusion that, huddled between the tropic circles, the Martian colonies will have no need of a seasonal adjustment to their clocks, deserves to be examined in detail.

An alternate diagram to the equation of time is the analemma, which depicts the deviation of solar time from mean time along the x-axis, and the variation in the declination of the sun along the y-axis. Thus, it represents the figure of the sun's appearent motion from noon to noon throughout the year.

Figure A3-2: The Analemmas of Earth and Mars

Figures A3-3 through A3-6 depict deviations in the time of sunrise and sunset for various latitudes on Mars and Earth, throughout the year, from the average times of 06:00 and 18:00, respectively. One can see (Figures A3-3 and A3-4) that the combination of the equation of time and the seasonal variation in the duration of daylight causes the hour of dawn to be more stable in the southern hemisphere of Mars for, as the period of daylight lengthens, Solar time gets later with respect to mean time. The hour of dusk, however, fluctuates considerably more throughout the year in the Martian southern hemisphere. For example, Figure A3-3 shows that on Tropicus Virginis, the southern tropic circle of Mars, the Sun rises earliest at about 04:57 on Karka 23 (Sol 441) and rises latest on Capricornus 1 (Sol 57) at about 06:44, a variation of only 1h 47m. On the other hand, sunset on Tropicus Virginis varies from 16:51 on Aries 8 (Sol 231) to 19:26 on Libra 16 (Sol 573), a total fluctuation of 2h 35m. Meanwhile, in the northern hemisphere the situation is much the opposite in that the time of sunrise is more variable and that of sunset is more constant. On Tropicus Piscium, sunrise varies from as early as 04:51 on 8 Aries to as late as 07:26 on Libra 16 (a difference of 2h 35m) while sunset occurs at its earliest time at 16:57 on Karka 23 and at its latest on Capricornus 1 at 18:44 (a variation of only 1h 47m).

Figure A3-3: Variation in Times of Sunrise and Sunset, 24.936 Degrees Latitude, Mars

Figure A3-4: Variation in Times of Sunrise and Sunset, 40 Degrees Latitude, Mars

Figure A3-5: Variation in Times of Sunrise and Sunset, 30 Degrees Latitude, Earth

Figure A3-6: Variation in Times of Sunrise and Sunset, 40 Degrees Latitude, Earth

The intent of the civil use of daylight time on Earth is to make the hour of sunrise more stable throughout the year. For instance, Figure A3-5 depicts how the time of sunrise changes throughout the year on Earth at 30 north latitude, including the seasonal adjustment of daylight time as observed in the USA. Of the contiguous states, only those on the coast of the Gulf of Mexico are this close to the equator; yet at this latitude, even with daylight time helping to stabilize the time of sunrise, it may occur as early as 05:18 in the last week of April and as late as 07:14 in the last week of October - a fluctuation of nearly two hours. Figure A3-6 shows the variation in the time of sunrise on the 40th parallel, a latitude more representative of the USA. Here the Sun may rise as early as 05:02 and as late as 07:28, a difference of nearly two and a half hours. Bearing in mind that some areas of the contiguous USA are nearly as far north as 50, and that the 50th parallel cuts right through Western Europe, where a similar daylight time scheme is used, a variation of three hours serves as a reasonable benchmark for the maximum desirable change in the hour of sunrise.

In the case of Mars, Figure A3-4 shows the varying times of sunrise and sunset at 40 north and south latitude. At this latitude in the southern hemisphere, sunrise fluctuates from 04:25 on Leo 17 (Sol 463) to 07:19 on Kumbha 17 (Sol 154), a change of 2h 54m, and sunset varies from 16:10 on Mina 9 (Sol 204) to 20:01 on Kanya 28 (Sol 557), a difference of 3h 51m. As in the example of the tropic circles of Mars, the total change in time of sunrise and sunset are reversed at 40 north latitude, where dawn is at its earliest at 04:10 on 9 Mina and at its latest at 08:01 on Kanya 28, a difference of nearly four hours, and dusk varies from as early as 16:25 on Leo 17 to as late as 19:19 on Kumbha 17.

Martian demographics of the 21st century and beyond is difficult to predict, but even if there is a significant percentage of the population living as far south as the 40th parallel, a fluctuation in the time of sunrise throughout the year of up to 2h 54m will probably be acceptable, as against inducing the complication of civil daylight time to reduce this variation.

Between Tropicus Piscium and 40 north latitude, however, the total annual change in the hour of dawn varies between 2h 35m and 3h 51m, which suggests that daylight time might be legislated for these latitudes if there is a sizable population located near or north of the 40th parallel. On the other hand, if the significant Martian population centres are confined to well south of the 40th northern parallel, daylight time might be dispensed with altogether. As shown in Figure A3-3, were daylight time to be instituted on and north of Tropicus Piscium from Makara 1 (Sol 85) to Gemini 28 (Sol 362), the earliest dawn on the northern tropic circle would occur at 05:17 on Gemini 28, limiting the total annual fluctuation to 2h 9m on Tropicus Piscium. Similarly, Figure A3-4 shows that the earliest sunrise on the 40th parallel of the northern hemisphere would take place on Makara 1 at 05:11, limiting the total annual variation to 2h 52m at this latitude. The institution of daylight time north of Tropicus Piscium from Makara through Gemini thus brings the annual change in the hour of sunrise to about the same value as that experienced below Tropicus Virginis.