Re: Find Solar Calendar Seasons spreadsheet posted

Although the mean year of any particular leap cycle may not exactly match the mean year of an equinox or solstice, each reasonably accurate leap cycle has a mean year that is a stable match to one or two points in the annual solar cycle, which we can call "calendar season(s)" for that leap cycle. In the present era, such calendar seasons are stable for calendar mean years that are as short as about 365 days 5 hours 47 minutes 52 seconds or about 365+43/178 days to as long as about 365 days 5 hours 49 minutes 31 seconds or 365+25/103 days, a range of only about 1 minute 39 seconds, and that stability endures for about 10 millennia.

I dispute the lower end of this range 365+43/178 days , which I don’t believe has a stable season today (mean year about 365.241573).

In any given era the longest cycle mean year having a stable calendar season will match the mean year (in terms of mean solar days) at the ecliptic longitude of the Earth orbital perihelion, and the shortest cycle mean year having a stable calendar season will match the mean year at the ecliptic longitude of the Earth orbital aphelion. The advance of perihelion (and aphelion, always 180° away) together with the tidal slowing of the Earth rotation rate cause calendar seasons to evolve and migrate as the millennia pass.

They’ll migrate from aphelion to perihelion in opposite directions relative to them. The migration is fastest at start and end and slowest in the middle of the lifetimes of the calendar season. One season is stable because its migration towards the perihelion is in the opposite direction to the precession of the perihelion. I see that Irv explains some of this in more detail later on.

A leap cycle will not have any calendar seasons in an era in which its mean year is a few seconds shorter than the mean year at the ecliptic longitude of aphelion.

I don’t believe that any leap cycle will have any calendar seasons in any era in which its mean year is shorter than the mean year at the ecliptic of aphelion, but may have a season of drift slow enough to appear like a calendar season if the SD method is used to find it. There is no reversal of drift within the year nor does the graph of the present year have any  crossings with any nearby years.

With tidal slowing of the Earth rotation rate, however, eventually the mean year at aphelion will equal the cycle mean year, so a calendar season will appear at the ecliptic longitude of aphelion. With progressive tidal rotation slowing that calendar season will split into a more stable season that will migrate ahead of aphelion (to earlier solar longitudes) as well as a less stable season that will migrate after aphelion (to later solar longitudes). As tidal rotation slowing continues, eventually the average length of the solar cycle will approximately equal the cycle mean year, and then both calendar seasons will be optimally stable

I’d say are migrating at slowest rate towards perihelion (We have seen that the stable season is not most stable at this time).

and perihelion and aphelion will be situated approximately midway between them, with perihelion having the less stable calendar season behind it (prior solar longitude) and the more stable calendar season ahead of it (later solar longitude). Further tidal rotation slowing will cause the calendar seasons to converge towards perihelion, disappearing in later years when the mean year near the ecliptic longitude region of perihelion becomes longer than the cycle mean year. The region near perihelion having the longest mean year spans about 45° of ecliptic longitude, ranging from about 15° before to about 30° after the ecliptic longitude of perihelion, so both calendar seasons disappear before ever reaching perihelion.

Actually I think both calendar seasons speed up much as they approach perihelion, so become unstable enough not be detected by the SD method even if the step period (exposure time) is reduced.

Also I expect the initial spilt to be faster than the final merger and so a stable season would start (become stable)  further away from aphelion than it ends (ceases being stable)  from the perihelion.  This is because I’d expect a plot of the tropical year length beginning at a given time of year to resemble a sine wave, but have a sharper  peak to the perihelion and a flatter dip at the aphelion.

With that description, the reader might think that aphelion should eventually "catch up" to perihelion, but that can never happen because they both advance in unison around Sun, always 180° apart. As aphelion passes through each point of the solar cycle, however, that solar longitude has the shortest mean year, and the opposite solar longitude 180° away at perihelion has the longest mean year.