Yup, it was also posted in the other thread on GPS the other day and it is quite a bit better than OP's article, particularly because it doesn't give a false account of the involved relativistic effects:
> Satellites at the GPS altitude travel at the speed of about 2.4 mi/s relative to Earth, which slows the clock down, but they’re also in weaker gravity which causes the clock to run faster. The latter effect is stronger which in total results in a gain of around 4.4647 × 10−10 seconds per second, or around 38 microseconds a day.
> Unfortunately, this is where many sources make a mistake with their interpretation of that result. It’s often erroneously claimed that if GPS didn’t correct for these relativistic effects by slowing down the clocks on satellites, the system would increase its error by around 7.2 mi per day as this is the distance that light travels in those 38 microseconds.
> Those assertions are not true. If relativistic effects weren’t accounted for and we let the clocks on satellites drift, the pseudoranges would indeed increase by that amount every day. However, as we’ve seen, an incorrect clock offset doesn’t prevent us from calculating the correct position.
(Nevertheless there are of course relativistic effects to account for, which Ciechanow proceeds to mention and which are explained in more detail in the other link I shared here: https://news.ycombinator.com/item?id=47861535 )
You don't need to belittle someone else's work. It's a series of articles, and author has 2 more articles that aren't related to articles Ciechanowski wrote at all.
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.
It's not that AI is necessary, but it's that one may not choose to (or have the skills to) spend a whole weekend hand-coding a 3D interactive visual. But one might spin up Claude Code and build whatever the explanation actually calls for in 15 minutes.
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.
> Satellites at the GPS altitude travel at the speed of about 2.4 mi/s relative to Earth, which slows the clock down, but they’re also in weaker gravity which causes the clock to run faster. The latter effect is stronger which in total results in a gain of around 4.4647 × 10−10 seconds per second, or around 38 microseconds a day.
> Unfortunately, this is where many sources make a mistake with their interpretation of that result. It’s often erroneously claimed that if GPS didn’t correct for these relativistic effects by slowing down the clocks on satellites, the system would increase its error by around 7.2 mi per day as this is the distance that light travels in those 38 microseconds.
> Those assertions are not true. If relativistic effects weren’t accounted for and we let the clocks on satellites drift, the pseudoranges would indeed increase by that amount every day. However, as we’ve seen, an incorrect clock offset doesn’t prevent us from calculating the correct position.
(Nevertheless there are of course relativistic effects to account for, which Ciechanow proceeds to mention and which are explained in more detail in the other link I shared here: https://news.ycombinator.com/item?id=47861535 )
for that I'd recommend this youtube series https://www.youtube.com/watch?v=i7JPjgHa7_A
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.
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.
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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.
So the trick, as always, boils down to engineering approximations, haha.