The next big step came in 1824, when the German astronomer Friedrich Bessel extended the Newtonian approach of thinking about eclipses using the laws of gravity. He envisioned the moon’s shadow cast onto an imaginary plane running through the center of the Earth. You could then project that shadow back up to the surface of the globe to see exactly where and when the shadow would strike, a process that eventually required thinking about the Earth as not a sphere but a lumpy, bumpy, spinning object. After Bessel, many nations had the global, imperial reach to chase down those shadows, said Deborah Kent, a math historian at the University of St. Andrews. By doing so, they could further refine their calculations in a battle for scientific soft-power supremacy.

Over the next century, eclipse expeditions helped settle one of the biggest mysteries in science: Was Mercury’s odd orbit due to an undiscovered sun-hugging planet (which would presumably become visible during an eclipse)? Or, as turned out to be the case, was there some problem with Newton’s understanding of gravity? These stakes made eclipse prediction and observation even more important, with scientists dispatched to all corners of the Earth with strict instructions on where exactly to be and which data to record. They then filed dry reports punctuated by the occasional “eruption of awe,” Kent said. “In almost every single one of them, there’s kind of two paragraphs of rhapsodic, Victorian, over-the-top description.”

In the 20th century, the problem transformed yet again. A proper prediction of eclipses always had to wrestle with the fact that the moon and everything else in the solar system are constantly tugging at each other. This wasn’t just the famously unsolvable “three-body problem”; it’s an N-body problem. When NASA began to launch people and robots toward solar system bodies, the need to know where these bodies were and where they would be in the future took on new urgency — and it became easier to figure out.

Because of mirrors left on the moon by the Apollo astronauts, we know where the moon is relative to Earth to within a couple of meters, according to Ryan Park, who leads the Solar System Dynamics group at NASA’s Jet Propulsion Laboratory. And with multiple spacecraft beaming back ranging data as they buzz around the solar system, we know the sun’s position with high accuracy, too. Park’s team feeds the lunar and solar position data — alongside similar parameters for the planets and hundreds of asteroids, and corrections for things like pressure from the solar wind, and not just the laws of Newton’s gravity but the subtler tweaks of general relativity — into a computer model. Then the model churns out a list of the predicted positions of everything, including the moon. And then, periodically, the JPL team updates their model and publishes new lists.

These positions, overkill for the task of predicting eclipses, are meant to be good enough for space travel. “I’m a little surprised,” said Park, when space mission developers ask about whether they’ll have to spend time figuring out where exactly the moon will be and how it moves. “I’m like, no, no, no, no, we solved the problem years ago.”