[scjosh]

Most of the data is typically in a two-line element format [0]. You can grab it here https://www.space-track.org or here https://celestrak.com/NORAD/elements/

(although I believe the celestrak data comes from space-track, correct me if I'm wrong)

The satellite positions are then estimated using an algorithm such as sgp4 implemented in quite a few languages:

* https://github.com/joshuaferrara/go-satellite (<-- disclaimer: this is mine)

* https://github.com/brandon-rhodes/python-sgp4

* https://github.com/shashwatak/satellite-js

Check out Dr. Kelso's (he works for AGI now) original work here in Pascal, plus a few links to C++ works: https://celestrak.com/software/tskelso-sw.php

[0] https://celestrak.com/columns/v04n03/