[ahazred8ta]

Is there a big orbit registry somewhere? Yes. https://www.unoosa.org/oosa/osoindex/search-ng.jspx Each individual object is observed every few weeks, and then they estimate its current position with math and physics.

How do they track them? With big expensive radar systems, mostly paid for by the military. It's an international collaboration. https://en.wikipedia.org/wiki/Space_domain_awareness#Systems

[mlindner]

LEOlabs operates and pays for their own radars. They're a commercial company.