This blog post is also worth noting: https://ciechanow.ski/gps/

Great explainer. The part about atomic clock synchronization always gets me — the satellites carry atomic clocks accurate to 1 nanosecond, and the system has to account for both special AND general relativistic effects (the satellites experience different gravity AND they're moving fast enough that time dilation matters).

The correction factor is about 38 microseconds per day — small enough to ignore in everyday life but catastrophic for GPS accuracy if unaccounted for. No other engineering system relies on relativistic corrections in its day-to-day operation quite like this.

Always makes me laugh when you get some dimwit that claims the Earth is flat, but then uses Google maps in his car. Magic!

GPS are amazing. If you understand how they work, and how they reliably know the time etc. you'd think you live in the future; and yet it's everywhere, in our pockets.

For anyone interested in a more detailed account of (general-)relativistic effects in GPS and other positioning systems, I really liked this article: https://pmc.ncbi.nlm.nih.gov/articles/PMC5253894/

Very cool to see these browser-native interactive 3D visualizations! Gives this such a different energy than a regular blog post would have had.

I'm guessing those visualizations wouldn't be in this post if it weren't for AI. The interesting question is what happens when ed-tech ships this pattern at scale. Exciting future.

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Pretty cool. Would be nice to have the equation system as well in a recap, and the math not collapsed by default. Also had to look up other resources to understad that time correction refers to correcting a relatively short window of time, as it was not clear that receiver clock is actually accurate enough for short periods (milliseconds) to treat as affine.

So the trick, as always, boils down to engineering approximations, haha.