THE DARIAN SYSTEM

Abstract

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

The Darian calendar is a complete timekeeping system for the 24-hour, 39-minute, 35.244-second sol and the 668.5907-sol vernal equinox year on Mars. Features include:

• 24 months, normally containing 28 sols, with three to four 27-sol months spaced regularly throughout the year to total either 668 or 669 sols.
• A nominal seven-sol week, with six-sol weeks ending the 27-sol months, thus allowing every month to begin on the first sol of the week. The numerical sol of any month always occurs on the same sol of the week.
• Since the new year always begins on the first sol of the week, there are only two types of calendar years: one common year and one bissextile or "leap" year. This is in marked contrast to Earth's Gregorian calendar, which actually comprises 14 different types of calendar years, one beginning on each of the seven days of the week for common years and leap years.
• The calendar year begins on the vernal equinox, a standard astronomical reference point.
• An intercalation formula keeps the calendar synchronized with the vernal equinox for up to 10,000 Martian years.
• A defined epoch allows the Darian date and local time on Mars to be calibrated with the Gregorian date and local time on Earth.
• A distinctive nomenclature for months and sols eliminates any possibility of confusion with Gregorian dates.
• Special calendar formats provide an easily understandable visual display of both Darian date and Gregorian date.

Moving beyond Mars, two systems of calendars for the four Galilean satellites of Jupiter are explored, one based on the terrestrial year and one on the Martian year. The orbital periods of the moons are divided into "circads" of approximately 21.3 hours. The relationship of the orbital periods of Io, Europa, and Ganymede leads to the adoption of eight-circad weeks. The natural cycles of the Galileans leads to a 13-month calendar based on the terrestrial year and a 24-month calendar based on the Martian year. Not only is 13 a prime number, which is inconvenient for subdividing the year into smaller cycles, but a 13-month calendar deviates considerably from the 12-month Gregorian calendar, thus commonality is lost. On the other hand, the Martian-year option represents less deviation from the Darian calendar. Thus, the Darian system is the preferred solution for the Galileans. Intercalation formulae out to 10,000 Martian years are provided, as well as epochs for calibrating this set of four Galilean calendars to the Darian calendar for Mars.

Finally, a timekeeping system for Titan based on the Darian system is explored. The orbital period of Titan is divided into 16 "circads" of approximately 23.95 hours. As with the Galileans, the relationship of the orbital period of Titan to the circad leads to the adoption of eight-circad weeks. The Martian vernal equinox year is used as the basis for Titanian years. Years are divided into 24 months, nominally containing 28 circads (four weeks), with rules for lengthening the months to 32 circads (4.5 weeks) as necessary. Common years contain 688 circads, and leap years contain 696 circads. Intercalation formulae out to 10,000 Martian years are provided, as well as an epoch for calibrating the calendar to the Darian Martian calendar.