Wondering what primary astronomical cycles there are that are greater than a year (which is a cycle around the sun), but less than 1000 years-ish (on that scale). There is the cycle of the moon phases too, and the cycle of the earth making a full rotation (a day). But I wonder if there are any cycles at a bigger-than-a-year scale, but not too big. I guess there's also the cycle of a stars life (but that is kind of a big scale, on the order of billions of years), but I am more wondering in terms of rotation what sort of cycles there are. I guess there is another one, Axial Precession, but that is a bit large such as on the order of tens of thousands of years. Maybe there are some cycles of the planets in which they are visible from earth, or of their moons, or of comets, or of nearby stars or that kind of thing.
If there were ones around each of these points that would be nice: 2, 5, 10, 20, 50, 100, 500, or 1000 years sort of thing.
Basically I am looking for "interesting" or "popular" cycles rather than just picking any of them (since every planet and moon has an orbital period). I am looking for ones that (a) we can observe most easily either directly without a telescope, or with a simple telescope/binoculars, and/or (b) have significance of some kind historically perhaps. If there is one that is historically significant or historically popular (say something Newton or Kepler talked about for example) but is difficult to see, that would be okay too.
For example, I vaguely remember hearing people mention "hey these x and y planets just aligned, it only happens every x years", so did a quick search and found this saying Jupiter and Mars align every 2-3 years. That is pretty interesting, since it is a small timeframe, bigger than a year, and you can see it pretty easily. I would like to find a few others though, spread over the scale (as mentioned above) from 1-1000 years. Here is another interesting one, a "Super Blood Blue Moon" as NASA is calling it, which hasn't happened since 1866 (so let's say ~150 years). Not sure if that will cycle every 150 years like that, but something that does cycle similar to this is also exactly the sort of "cycle" I am looking for.