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Does axial precession change what calendar months that the seasons are? Given a 26000 year precession cycle, will it be summer in December (2022 + 26000/2) in the northern hemisphere?
Axial tilt is responsible for Earth's seasons. It is summer in the northern hemisphere when the Earth tilts "towards" the sun. I figure in 26000/2 years that tilt should be the opposite way, i.e. "away" from the sun, i.e. winter, whence summer in December, according to the Gregorian calendar.
Our Gregorian calendar is designed so that the seasons remained (almost) fixed.
The Earth takes 365.256 days to orbit the sun. If the calendar was designed so that the average number of days in a year was 365.256, (you could have a leap year every fourth year, and then every 166th year you could have an extra leap year) Then the precession would cause the seasons to flip, eventually. After 13000 years it would be summer in December in the Northern Hemisphere.
But this is not the rule for the calender. Instead the calendar is designed to have 365.2425 days, on average. This is intended to approximate the tropical year of 365.24219 days, which is the period from one spring equinox to the next. The reason that we use the tropical year for the calendar, and not the orbital period is precisely to avoid the shifting of the calendar through the year.
Correcting this shift of season was the reason that the Julian calendar was replaced by the Gregorian one.
Eventually, as the calendar isn't exactly the same length as the tropical year, the seasons will, very slowly, shift. But it will take many millennia for the difference to become more than a day on average.
Ignoring that no fixed calendar is perfect, the primary effect of precession is to change the lengths of the seasons. The imprecision of the Gregorian calendar can be overcome by making leap days occur on an as-needed basis rather than formulaic. (This is exactly what the Solar Hijri calendar that is currently used in Iran and Afghanistan does.)
Currently, winter is the shortest season in the Northern Hemisphere and summer is the longest. That will flip in twelve the thirteen thousand years, when the Northern Hemisphere see long cold winters and short hot summers. A calendar done right will still make December to February be the months during which those long cold winters occur, and June to August be the months during which those short hot summers occur.
