If the machine has the ability to jump in time and space (needed to land in the same spot) then it would be a real waste to use it only on earth.
So we would need a mathematical model of the entire universe that is accurate to the metre over all time. This N body is much harder than the 3 body problem.
Or we use gravity and other methods to track relative stationary position.
So, what other methods can be used to determine rotation?