[ELI5] How do we predict solar and lunar eclipse?
In: Mathematics
Orbital mechanics!
While not entirely true, you can imagine the moon and Earth as if they move on rails. Orbits are more or less the same every time, so we’ll treat them like rails (like railroad rails, if you’re unfamiliar with the terminology). Big invisible rails in the sky. They move at speeds which change slightly but the speed always depends upon the height of the rail. We’ve been observing the movement of the Earth and moon for a long time, so even if we didn’t have math to reconstruct these ‘rails’ we would have mapped them out pretty well by now. Since we know where the rails are and how fast the Earth and moon move along their respective rails, all we have to do is calculate when the two will align just right. For instance, the moon’s rail has to line up with the position of the sun when viewed from the Earth’s rail for either kind of eclipse. This will happen twice a year. I can’t really think of an intuitive proof for this without a diagram, alas. However, not only do the rails have to line up, but the moon must also be at a specific point on its rail for a lunar eclipse and the opposite specific point for a solar eclipse.
In modern times it’s orbital mechanics and geometry. We can predict where the Sun, Earth, and Moon are going to be relative to each other and draw lines from a potential viewer to the sun and moon to figure out what people would see with things in that position.
The moon orbits the earth about once a month. So if the earth moon and sun were all orbiting in the same plane you’d expect one solar and one lunar eclipse every month. Unfortunately they don’t orbit in the same plane, so there’s only an opportunity for an eclipse twice a year, when the intersection of these two planes (earth around sun, and moon around earth) aligns with the earth and sun. Though even this isn’t quite enough, because you also have to have a new moon when this happens to get a solar eclipse, or a full moon to get a lunar eclipse. And depending on how far away the moon is from the Earth, and how well it’s aligned, you might not get a total eclipse.
In ancient times they didn’t understand the orbital mechanics, but they did notice the patterns, see “antikythera mechanism”
The earth goes around the sun in a cycle.
The moon goes around the earth in a cycle.
The cycles are running together. So if you looked over a long enough time, you’d realize they’re two parts of a much bigger cycle.
So if you wrote down what the moon and the sun were doing at a particular point in the cycle, you’d know what it would be doing at a that same point in the next cycle.
And the sun or moon suddenly disappearing from the sky is something a lot of people would write down.
This is how ancient peoples were able to predict eclipses, long before they figured out that the earth was going around the sun, and sun was going around the earth. They noticed the cycle.
The difference from modern is that now we know what causes the cycle and we’ve measured the things more exactly.
You observe the position and speed of the moon, sun, earth with a telescope.
You input that into a physics model and run the simulation like a billion years forward and have the computer note every single lunar eclipse.
I don’t know how sophisticated these models need to be, but even a very simple two body Newtonian gravity model would probably be 99% accurate over 10 years.
Like you can do super basic and it still works fine for the most part,
https://www.compadre.org/osp/EJSS/4690/384.htm
Because we know the speeds at which the sun, earth, and moon travel through space. We know the current location, and also the path that they take. From there it’s just math.
It’s basically the stereotypical math question “If two trains are 100 miles apart, one is heading south at 50mph and the other is heading north at 50mph, how long will it take them to collide?”
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