Phew, 23 days earlier your father would have had to code all timestamps in negative.
Joke apart, which OS did such satellites run? Unix? Probably not, since timestamps only started in 1970. Just "C"? Even today, how do you register time on satellites? With Unix timestamps (a long since 1970-01-01)? Can they synchronize based on objective points (stars or Earth position to the sun) or are satellites always resynchronized from Earth signals?
> In a 1970 survey, The New York Times suggested a consensus definition of a minicomputer as a machine costing less than US$25,000 (equivalent to $165,000 in 2019), with an input-output device such as a teleprinter and at least four thousand words of memory, that is capable of running programs in a higher level language, such as Fortran or BASIC.
I think it’s safe to say that the biggest issue with launching computers running UNIX into space in 1970 probably was not the lack of a standardized time stamp :-)
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.
IIRC there have been some proposals to use Pulsar signals on satellites/probes not just for time synchronization but more importantly navigation. Not sure if it's actually in production use yet.