The saros is a measurement of time equal to 6585 days (plus one third of a day). It is the time between identical eclipses.
Eclipses are predictable. With enough astronomical knowledge, you can chart exactly when, where, and how they will appear. The calculations involved are a little complicated, because you need to take into account three different cycles: the synodic month, the anomalistic month, and the draconic month.
The month you know best, the time between two new moons, is the synodic month. The anomalistic month is the time between those points when the Moon as close to the Earth as it can be. And the draconic month is time between those points (“nodes”) when the orbital plane of the Moon crosses the orbital plane of the Earth.
Can we just take a moment to appreciate that there is actually a term in astronomy called the “draconic month”? That’s metal, man.
Anyway, those three months are all ever so slightly different: the synodic is 29.53059 days, the anomalistic is 27.55455 days, and the draconic is 27.21222 days. For an eclipse to occur, they all have to line up in particular ways. An eclipse can only happen, for example, when the Moon and the Earth are on intersecting orbital planes – those nodes in the draconic calendar – because those are the only times that the Moon, Sun, and Earth all line up in a row. An eclipse can only happen on a full or new moon, because those are the times when the sun is directly behind or in front of the moon (from the perspective of Earth)… which is where the synodic month comes into play.
Those three weird months all have different durations, but every now and then they all reach the same point in their cycles at the same time. Think of it like three clocks moving at three different speeds: they’re all ticking according to their own unique tempo, but every so often they must all end up at 12 o’clock at the same time.
How long does it take all three months to line up, to metaphorically all reach 12 o’clock at the same time? 6585 days (plus one third of a day). One saros.
What this means, in practical terms, is that a saros represents one big repeating cycle that takes into account the three month types. If you take any given day and add 6585 days (plus a third) you’ll find yourself at the same point in the synodic, anomalistic, and draconic monthly cycles. And that’s where the magic happens: because those months determine when an eclipse can occur, if you take an eclipse and add 6585 days (plus a third), you’ll get another eclipse.
In one saros, roughly forty eclipses occur. The next saros will contain the same eclipses, of the same types. The eclipses will unfortunately appear in slightly different places (the reasons are complicated, but we can blame that pesky “third of a day” part), but are otherwise completely cyclical and predictable.
As is always the case, I’m glossing over some of the details in this explanation, and some other relevant units that help to predict cyclical eclipses. Read about the inex, if you want to know more! But I wanted to leave you with one mind-blowing fact: the Antikythera mechanism, that famous Ancient Greek analogue computer, could apparently calculate the saros cycle.
The Generalist Academy 
