Also, we would like to fix an origin for this plane in a natural way. Physics tells us that the center of mass is the best choice, the point around which all of the system's mass is ``equally distributed'' in a sense. The center of mass is computed by taking the average of all the planets' positions, weighted by their respective masses:
A point in a plane with a fixed origin can be described by a complex number. This means we have reduced our description significantly to six, rather than nine, real numbers, with a linear relation between them effectively reducing it to four complex numbers. We'll call this state space :
In fixing this origin we are disregarding any of the motion of our system with respect to a ``stationary'' observer.