There’s a history of using local Martian solar time in the past, driven by the need to operate in the Martian daytime for rover safety. They even made special watches that ran “slow” compared to earth times so that they kept correct Martian solar time for some of the missions.
However for “absolute” chronological records you would be looking at using Barycentric Coordinate Time, which is what we get when we do a bunch of corrections to subtract the effects of the sun and earth’s (and the other planets) mass and motion, leaving us with a virtual “clock” that is suitably common for anything in the solar system.
To quote one definition of Barycentric Coordinate Time - ”It is equivalent to the proper time experienced by a clock at rest in a coordinate frame co-moving with the barycentre of the Solar System: that is, a clock that performs exactly the same movements as the Solar system but is outside the system’s gravity well.”
The ELI5 I normally use is roughly: It’s what we get if we take the Solar System in its normal orbit around the Milky Way, with some fancy magic we subtract away all the stuff, sun, planets, moons and all the asteroids and comets we can count, and then with a little more fancy magic, we put a super accurate clock that doesn’t weigh anything at all back at the center of where all the solar system stuff used to be.”
1) Latitude on another planet is straightforward: take the rotational equator, divide into 90 degrees north and south, done. But what about Longitude? Here on Earth, the prime meridian is Greenwich, because reasons. On Mars, it's indexed to a certain crater. But on the gas giants? Yeah, we still don't have a good plan about that.
2) Paul Krugman's thesis (yes, that Paul Krugman) is on relativistic economies. As in, my planet is in a deep gravity well, your's isn't. My clocks pas a lot slower. Now, how do I calculate interest? What about letters of credit for ships traveling between places to ship goods? His conclusion: let's hope there isn't money by then, because interest can't work between relativistic time frames.
In reality: Even if in a few hundred years we have the capability to travel at FTL to other solar systems, we will still be using GMT as "ship's time".
However for “absolute” chronological records you would be looking at using Barycentric Coordinate Time, which is what we get when we do a bunch of corrections to subtract the effects of the sun and earth’s (and the other planets) mass and motion, leaving us with a virtual “clock” that is suitably common for anything in the solar system.
To quote one definition of Barycentric Coordinate Time - ”It is equivalent to the proper time experienced by a clock at rest in a coordinate frame co-moving with the barycentre of the Solar System: that is, a clock that performs exactly the same movements as the Solar system but is outside the system’s gravity well.”
The ELI5 I normally use is roughly: It’s what we get if we take the Solar System in its normal orbit around the Milky Way, with some fancy magic we subtract away all the stuff, sun, planets, moons and all the asteroids and comets we can count, and then with a little more fancy magic, we put a super accurate clock that doesn’t weigh anything at all back at the center of where all the solar system stuff used to be.”