Re: Complications
Except the second is defined for clocks sitting at the Earth's surface
Which is defined as g=9.81m/s^2
Which depends on the definition of a second
No,
"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom."
https://physics.nist.gov/cuu/Units/current.html
Nothing else is needed for the units system to be consistent, it'll work anywhere.
Now if you want to measure calendar time you need a frame of reference. I can't find in a quick search where ISO time incorporates this, but that's the point at which g matters.