Jan 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002iaf..confe.514c&link_type=abstract
IAF abstracts, 34th COSPAR Scientific Assembly, The Second World Space Congress, held 10-19 October, 2002 in Houston, TX, USA.,
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Scientific paper
Looking at the planets in a coordinate system based on the "Invariant Plane" of the solar system, it is possible to find a single sinusoidal wave of a specific wavelength by which the motion of all ten planets can be approximated - not just their orbital motion, but the inclination of their axes and their direction of rotation. The significance of this geometric solution is evident in the context of Celestial Mechanics. In the Three Body Problem it is known, by analytical geometry, that when creating the zero velocity curves the equilibrium points happen when the curves associated with the two primaries meet. There are three colinear points and two triangular points. There is also a equilibrium line from L4 to L2 to L5; formed as the two curves expand beyond the L2 intersection. This line is, in non-rotating coordinates, the helical wave that has been derived. It can now be postulated that there exists a gravity ellipsoid, in which this equilibrium line is the unstable third principal axis and the axes of the Three Body Problem are the other two (stable) principle axes. Just as the Lagrange Points are five equilibrium points; the line is an equilibrium continuum; and the surface of the ellipsoid is an equilibrium surface. That is, solutions to the problems of 4 Bodies, 10 Bodies, and N Bodies; respectively.
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