Center 4 CM

Ten Body Problem

It has been shown in the paper "The Invariant Plane" that a higher order of symmetry of the Solar System is obtained by transforming into a new coordinate system. This transformation results in two distinct schemes for the planets which are pi radians out of phase. Two planets, Venus and Pluto, are out of phase with all the others, and these are the only two planets that exhibit retrograde rotation. It is therefore logical to postulate that the entire solar system, in some context, can be regularized into a Three Body Problem using the so-called Szebehely Equation: the sun, plus the two sets of planets distinguished by their direction of rotation. A helical equation is assumed for the combined solution to the Ten Body Problem and, when substituted into the formula for the regularized Three Body Problem, there results a closed form solution. Having thus proven the solution, the analysis validates a mechanical analog to the imaginary number, "j" as a rotational motion with a "complex" ordinate of the Invariant Plane itself. This is proven graphically as well as analytically.

You can download the complete paper in PDF format here.