I don't think the relativistic effects would be a problem in practice. You can synchronize clocks on other planets to the UTC or TAI reference time, which are already specified in terms of the Earth's reference frame.

Because of relativity, clocks on other planets would very slowly drift relative to UTC on Earth. But the drift is on the order of a few parts per billion (see e.g. [1]) which is comparable to what you'd expect anyway, even from a very high-quality temperature-controlled crystal oscillator. So it doesn't add any new clock synchronization difficulties that you wouldn't have anyway.

For the most demanding applications -- the ones that require atomic clocks -- you would still need to take relativity into account. You can either measure time passing at the local rate (in cases where you need to know locally elapsed time to high precision) or you can measure UTC, which allows you to assign a consistent ordering to events on different planets. But for most ordinary purposes, the distinction is irrelevant.

[1]: https://space.stackexchange.com/questions/33590/time-dilatio...

>"Seconds according to who?"

According to a very accurate pulsar, of course.

https://en.wikipedia.org/wiki/Pulsar#Precise_clocks

https://en.wikipedia.org/wiki/Pulsar_clock

GPS satellites already control for relativistic effects. Their required accuracy is so high that they wouldn't work without doing so.

You would simply also correct for relativistic effects caused by the orbits of different planets, and boom, you have a pretty consistently defined time that is valid across the entire solar system.

Seconds according to the atomic clocks at NIST. People operating clocks moving at relativistic speeds will apply the necessary corrections, as GPS satellites already do.

Note that GPS compensates for relativistic effects to allow GPS receivers to act as very accurate clocks (GPS time receivers are considered stratum 0 clocks). If you didn't care about using GPS time receivers you wouldn't have to care about relativistic effects with GPS at all (because all satellites are more-or-less exposed to the same relativistic effects), because a 3D/4D fix already synchronizes the receiver to the satellite's clocks.

Relativity compensation in GPS satellites does not increase spatial accuracy.