Awesome. This is a side project I never got around to making myself. For all the questions of "How do you know where the satellites are", there are published TLEs (old punchcard format) that describe orbital parameters, and you can use those to estimate the position within ~10km (good enough for this).

https://celestrak.org/NORAD/elements/

The no-account and on-device location approach feels exactly right for this kind of app; how often is the orbital data refreshed?

where do you get satellite orbits from?

How do you calculate the next passes over a given position?

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