Center 4 CM

The Gravity Ellipsoid

Having established a new invariant plane for the solar system, the fundamental frequency is designated the "system wave" and is assumed to be the first sequence in a Fourier Series model of the solar system. This paper gives a theoretical significance to this "system wave" in the context of the circular restricted Three Body Problem (3BP). The "system wave," being the solution to the Ten Body Problem implies the planets exist in stable positions in the non-rotating problem. In the rotating problem this "system wave" reduces to an arc between Lagrange Points L4 and L5, thereby establishing a Lagrange Continuum with L3 at the center, on the intersection with the x-axis. This continuum of stability points is shown to coincide - and thus be proven by - the asteroid belt. The result is a presentation of the 10BP as a special case of the N Body Problem, here represented by the gravity ellipsoid.

You can download the complete paper in PDF format here.