Perihelion initial year

[Geo]

I should stay out of this given my obvious astronomical numtiness but it’s an itch that won’t quit.

If the perihelion is the point in time when Alphas A and B are at their closest, then shouldn’t that be in the middle of the game’s 20 year period of perihelion?

Ideally, yes. But as with Earth seasons, they often start later or earlier then 'planned'. That, combined with whether Planet happens to orbit between A and B when the onset of perihelion happens or on the far side of A, gives us a random factor of a turn or two.