Mercury has resonant sidereal rotation to revolution resonance of 2:3, so 3 days equals 2 years on Mercury. The Mercurian calendar is trivially **one day** **plus one leap day** exhibited **every second year** per year.

We’ll get back to the Venusian calendar at the end, and you’ll see why there.

The Martian year is 686.97 Earth days long, and the Martian day is 24.62 Earth hours long. There are thus 669.67 Martian days in a Martian year. The Martian calendar should therefore have 670 days with one day deleted every three years. 670 has more factors (although only by a slight amount), so it should be used as the base amount for a calendar. For months, neither of Mars’ moons has a long enough orbital period to serve as a guide for month length, and thus year divisions would purely be optimized by mathematical philosophy. One reasonable division would be 10 months of 66 days plus 10 in-between month “special” days (or, 20 months of 33 days, or, if one doesn’t desire the in-between days, just **10 months of 67 days**). In all cases, **-1 day per three years**.

Jupiter’s year is 4332.59 Earth days long, with a 9.925 Earth-hour rotational period, for 10476.79 Jovian days in a Jovian year, calling for 10476 days in a calendar with all but every fifth year having one day added. Jupiter has four highly significant moons, the largest of which is Ganymede, which orbits Jupiter in 17.30 Jovian days. If we put 18 days in a month, Jupiter’s calendar would therefore be **582 months of 18 days** each, with **+1 day per four out of five years**.

Saturn’s year is 10759.22 Earth days long, with a 10.57 Earth-hour rotational period, for 24429.64 Saturnian days in a Saturnian year, calling for 24430 days in a calendar with every third year having one day deleted. Saturn’s most prominent moon, Titan, orbits Saturn once every 36.20 Saturnian days. Using 35 days for a month, Saturn’s calendar would **698 months of 35 days** each, with **-1 day per three years**.

Uranus’ year is 30799.1 Earth days long, with a 17.24 Earth-hour rotational period, for 42875.8 Uranian days in a Uranian year, calling for 42876 days in a calendar with with every fifth year having one day deleted. Oberon orbits Uranus in 18.74 Uranian days. Using 18 days for a month, Uranus’ calendar would be **2382 months of 18 days** each, with **-1 day per five years**.

Neptune’s year is 60190.0 Earth days long, with a 16.11 Earth-hour rotational period, for 89668.5 Neptunian days in a Neptunian year, calling for 89668 days in a calendar with an extra day every other year. Triton’s revolutionary period of 8.76 Neptunian days is rather short, and the next moon out, Nereid, orbits Neptune in 536.5 Neptunian days, which is too long and not close enough to any divisor of 89668, so let’s not consider moons and give Neptune a calendar of **773 months of 116 days** each, with **+1 day per two years**.

Back to Venus. Venus is special because its revolutionary period is shorter than its rotational period. They are 224.70 Earth days and 243.02 Earth days, respectively. In addition to this, Venus rotates retrograde, but that doesn’t affect our calendar, although if anyone thinks of a way to incorporate this further abnormality, go ahead and mention it. There are 0.9246 Venusian days in a Venusian year, for **one day**, with **+3 years every 37 years**.

For outer planets, perhaps we need something between year and month to avoid three-digit number of months. People hate big numbers.

I considered that possibility, but I’m already using quantities regarding the outermost significant moons, so any division of time in between will have a clashing reason for existing from the other division, in which case one would probably be better off approaching the entire problem mathematically. Whether this is better or worse than the moon-parametrized system is likely different to the tastes of different people.

For what it’s worth I understand one of the final issues of The Journal of Calendar Reform put out a perpetual calendar for Mars. It had eight months of 56 days each, and four months of 55 days, with three leap days every five years, omitted every tenth century year. The last week of the year would omit a Saturday.

I haven’t run across examples of perpetual calendars for other planets.

Thanks for posting this. Interesting stuff. Would you happen to know a resource that charts actual sunlight hours for the planets during their respective “years?” Something along the lines of The Old Farmer’s Almanac and sunrises/sunsets? I apologize if I sound like a rube.

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