If one has the luxury of designing a calendar from scratch, it might be good to put leap day at aphelion, where its angular value is least.

I got yet another wacky idea for a Martian calendar. Start with 24 months of 28 days each. Drop one day from every seventh month (so that a given month is short in one year out of seven), and add one day every 48 years. The result is longer than the mean tropical year by one day in 6176 years.

An analogous calendar for Earth: start with 12 months of 30 days, add 3 days to every 7 months (so the cycle is 30 30 31 30 31 30 31), and add one day every ten years; this is long by one day in 219130 years.

Most proposed calendars for Mars have 24 months, and various systems have been offered to name them. Here’s one more: use the names of the 24 brightest stars, in order of longitude right ascension (relative to the rotation axis of Mars), so that each star is conspicuous at night in the month named for it. ( . . more . . )

A Martian year is 668.6 Martian days; that’s 3.4 less than 24×28. I asked myself, how should the short months be arranged for best ‘balance’? I ran all combinations and this is it:

The three big dots represent the missing days in short months; the smaller dot represents the sometimes-missing day in the variable month; and the diamond, slightly left of center, is the center of gravity of the dots.

Then I thought, what if I were designing a calendar for a world where the number of days in a year is 5¼ off from a multiple of 12?

If I were Pope Gregory’s advisor, I’d urge this: all months to have 30 days until the first (or last) of some month falls on a solstice or equinox; thereafter, alternate 30, 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 30¼.

Unrelated link: Questioning 7/4

A little-appreciated advantage of the French Republican calendar: only three months have no R.