I have no knowledge of old-style satellites, but have worked on cubesats (low earth orbit) reasonably recently. Star trackers give you location in orbit and or

I have no knowledge of old-style satellites, but have worked on cubesats (low earth orbit) reasonably recently. Star trackers give you location in orbit and orientation of your satellite. I don't believe you can get absolute time from them, especially given that Earth time is somewhat decoupled from Earth's orbital dynamics. What you can do is get time using GPS, like you would on the ground. Not sure if that's possible for higher orbits, but definitely for low orbits. There have also been some experiments with laser-based synchronization (a PPS-style signal, I believe?) and you could get a coarse sync with a regular old radio uplink.