On Earth, there is a table with leap seconds... and sometimes they're negative. That alone, is a good reason why writing time libraries is better left to people who specialize in writing time libraries.

The relativity part, also made me think: Luna orbits Earth at about 3600Km/h... but Earth's equator itself, "orbits" Earth's poles at 1600Km/h... so if one has relativity effects on time, half that speed must be having some relativity effects too, right...? Someone on the South Pole would also see a clock on the equator go some microseconds slower per day... and all the clocks at different latitudes, and everyone relative to everyone else, so you can't tell "precisely" the time on Earth without taking into account the exact location... 😬