Artemis II safely splashes down
https://www.cbsnews.com/live-updates/artemis-ii-splashdown-return/
NASA's Artemis II astronauts returned to Earth with a splashdown landing in the Pacific Ocean after making a high-speed reentry through the atmosphere.
I had to explain to my wife and kids (not that I'm in this field, but I also have to remind myself) that we are able to pinpoint where the craft will land, when it will land down to the minute, because of ... just ... math. And we're able to get them there and back because of science.
It all boils down to equations that describe the world accurately, and a way of experimentation, iteration, thinking that gets us all the way to do something this unbelievably complex.
The analogies for these things like "hitting a golf ball into a hole in one 5,000 miles away" are always fun.
I like starting from the fact that Ptolemy was able to get the accuracy of the "motions of the heavens" down so well that it took more than a thousand years to get observations that showed discrepancies. The math, it maths.
The first-order approximations are easy. When you start adding up all the other factors, it gets complicated fast. The solar wind, which isn't constant, affects trajectories. Earth's atmosphere is neither homogenous nor perfectly predictable along many dimensions: upper-level wind speeds and directions, air density, and temperatures, to name a few. The Moon's gravitational field is very lumpy. Earth's gravitational field, while relatively smooth compared to the Moon, also isn't perfectly uniform. Propulsion systems have tolerances. Same with parachutes. The location of the vehicle's center of gravity affects everything.
All of these factors and more have to be taken into account if you want your predictions to be accurate. Aside from telemetry processing, most of the computing power on the ground during a space mission is used for churning out navigation solutions.
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