[teraflop]

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...

[wlesieutre]

If I did my math right that's 0.178 seconds per year. As long as everyone's handling time the same way you shouldn't have a problem, but it's enough to be noticeable if someone forgets about it.

I suppose the more noticeable oddness for most people would be that the speed-of-light delay in communications from Earth to Mars varies so much. Around 3 light minutes up to 22 depending on where they are in their orbits.

[Rebelgecko]

That's around what I got from my back of the envelope Math too (well, I got around 300ms/year). Small enough where you can adjust a leap second everyone few years to take care of the drift. Kind of like converting between UTC, TAI, and UT1.

It may need to be compensated for when receiving transmissions between the planets, but I don't know enough about RF to judge how meaningful the difference is. There was a spacecraft (I think Huygens?) that actually had problems with Doppler shift. I think in that case they forgot to take it into account entirely, so it wasn't that they just forgot the relativistic component.