The definition of a second is as follows [0]: The second is defined by taking the fixed numerical value of the caesium frequency ∆ν, the unperturbed ground-s

The definition of a second is as follows [0]: The second is defined by taking the fixed numerical value of the caesium frequency ∆ν, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s−1 But with the Moon's lower gravity, time flows very slightly faster (a moon-second is 0.99999999999848 of an earth second according to a sibling post). I'm no physicist, but my assumption is that the SI definition of a second would still be true on the moon (at least relative to the moon's reference frame). So it would make sense to me to leave a second defined as a SI second, regardless of your reference frame because that's how humans, science & technology measure time passing. I think the bigger calendar problem with space travel is the differences in the length of a day (or sol), as we know it's 24hrs on earth, Mars is 24h 37m (not sure about the moon since it's tidally locked its ~27x24hrs). The drift of days between Mars and Earth is going to be far more noticeable than a tiny fraction of a second due to relativity. [0] https://www.npl.co.uk/si-units/second https://www.npl.co.uk/si-units/second