You can still use those. As long as the other planet is reasonably close to a sphere, then we can say it’s 360 degrees around it in latitude or longitude, and a minute of arc will still be 1/60 of a degree and a second of arc will still be 1/60 of a minute of arc. (Nothing to do with time.)
The distance on the ground that each of those represents will differ, depending whether the other planet is bigger or smaller than Earth (or maybe, by a miracle, exactly the same size) but the arc measurements make sense for any fairly-round thing.
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