mfb said:
For the discussed system with one star far away, close to the seasons on Earth (maybe more or less extreme depending on the axial tilt). For the other orbits... it's complicated.
I guess every cycle would get its own unit - similar to days, months (not exactly, but close to the period of the moon) and years on earth. Days would still be the rotation of the planet (unless it is tidally locked), and you would probably get two kinds of years, one for the sun close to the planet, and one less important year for the orbit of the sun far away. This second year could be significantly longer than the lifetime of your calendar-making species and also less important, but the motion of the second sun relative to the stars would be easy to track.
I think you should call the distant star period something else than a year. It is necessarily very different in both its length and importance.
And the motion of the second sun relative to stars will not be directly that easy to track, nor that important. With effort you can make out the brighter stars around Moon. But who cares if Moon is in Capricorn, apart from astrologers? Whereas full Moon, new Moon, waxing or waning Moon are easy to spot and also of immediate practical importance. Sure, if Moon is in Capricorn and so is Sun then it therefore is new Moon. But the immediate logic of tracking, if you do care where Moon is, is opposite - new Moon, winter (Sun in Capricorn that is invisible in sunlight) - therefore Moon in Capricorn.
Now imagine that Proxima is on Jupiter´s orbit, and as bright as Moon.
The relevant period for the immediate practical use of Proxima would be the period of Proxima relative to Sun. But, since Proxima is moving much slower than Sun, this period is close to the period of Sun (that is, Earth orbit around Sun). This period, therefore, is the (solar) year - unlike the case of Moon which moves much faster than Sun and whose period therefore is close to its orbital period and very different from the year.
Now, assume that Proxima also orbits in prograde direction as Jupiter does - the same direction as Moon orbits and Earth rotates.
Note that, looking from Sun, a full moon overtakes Earth, whereas Jupiter is overtaken by Earth.
Jupiter is brighter than any stars in the sky except Venus which never gets far from Sun. It follows that the opposition of Jupiter is easy to track, but of no practical importance: Jupiter outshines any single star, but not the combined light of all stars and skyglow, so Jupiter in opposition does not shine significant useful light on ground the way full moon does.
So imagine Proxima instead of Jupiter - slightly brighter than full Moon.
Then the exact opposition of Proxima would be both conspicuous and practically important.
Moon circles the Earth in 24 hours 50 minutes, so it rises 50 minutes later each day. Fixed stars, and Jupiter, circle the Earth in about 23 hours 56 minutes, so they rise 4 minutes earlier each day.
For an evening owl, exactly full moon would rise at sunset, and climb higher in the east as the twilight fades in the west, so there would not be real darkness at full moon - or before full moon, under waxing gibbous moon. But the next evening after full moon? Twilight gets as dark as the light of full moon when Sun is 9 or so degrees under horizon, so in tropics where sun sets vertically or nearly so, it would get quite dark in 40 minutes or so after sunset. Unless full, or waxing gibbous, moon is in the sky. One night after exact full moon, and all of a sudden evenings get quite dark before Moon finally rises 50 minutes after sunset - and even then it takes time to climb higher from horizon and spread useful light on horizontal ground.
Now imagine Proxima. As bright as Moon, but unlike Moon its rise gets 4 minutes earlier each evening. So on the exact opposition, it rises at sunset, and you can watch the opposition approach over a period of something like ten days, as it rises progressively earlier in dusk and is correspondingly higher as the twilight fades. Something that is both easy to detect and immediately practically important. And which happens not 12 times a year, each month, but just once a year.
Approximately. Because Jupiter does orbit Sun relative to stars, with period of about 12 years. The motion relative to stars is somewhat harder to detect in case of Proxima, and less practical importance. But what does matter, actually, is the motion relative to Earth axis.
Because the Sun still rises and falls in sky. Days get longer and shorter, at sufficient latitude disappear altogether. The warmth of the Sun varies with its height and day length, and winds and rains follow.
If, one year, Jupiter reaches exact opposition on 1st of January, or Proxima does and shines useful light on otherwise long and dark winter nights then on the next year, it does not do the same. It reaches exact opposition in early February instead. In 6 years, Proxima will be in opposition/full in summer nights when the nights are short and light anyway, and in winter nights it is in conjunction/new, so winter nights are about as long as dark as on Earth for that year.
So, the seasonality of Proxima´s oppositions and conjunctions will regularly change with its orbit, and that is a significant cycle of about 12 years. How about, Year of Rat?
But the orbital cycle will not be exactly 12 or some other integer number of years. The orbital period of Jupiter is actually 11,8618 years.
So suppose you want to fix the cycle to years to the seasonality of Jupiter´s orbit. So that Year of Rat always means Jupiter is in opposition in January, Year of Ox always means Jupiter is in opposition in February, et cetera.
In 12 years, Jupiter has accomplished one orbit, but also is about 0,138 years into next. If one Year of Rat, Jupiter opposition was on exactly 1st of January, then in 12 years, it will be about 5th of January.
So the result will be that in about 90 years you will need a, well, leap year. One Rat Year had Jupiter opposition in the very end of January. The result will be that 11 years after that Rat Year, Jupiter will be in opposition in the beginning of January, and in 12 years after such Rat Year, in beginning of February.
So you will have to skip a year. Which one?
There are 12 cycle designations. Rat, Ox, Tiger, Hare, Dragon, Snake, Horse, Goat, Monkey, Cock, Dog, Pig.
Would you designate a specific year as the leap year - so that it is always, for example, Pig Year shipped after 84 or 96 years when Jupiter is far enough from cycle that you must skip from Dog Year to Pig Year? Or would you do the leap year at any year of the cycle, whenever the accumulated deviation reaches one month?
