Center 4 CM

The Inverse Problem of Celestial Mechanics

A least squares fit is used to generate a symmetric coordinate system for the planets in the solar system. The movement of each planet is uniform about this plane, each being in simple harmonic motion. A sinusoidal forcing function is assumed. The resultant linearized system analysis shows two distinct orbital schemes, one for the inner planets and one for the outer. These are interpreted to be the upper and lower portions of a prolate cycloid. Known astronomical phenomena validate the system. The sun-Jupiter Lagrange point, at the Trojan asteroids, links the inner and outer waveforms. The unique earth-moon system is indicated, as are new stable quasi-satellite orbits centered on Earth and Venus, and the location of the "Trojan" asteroids. Each body occupies a unique place on the system wave. The entire wavelength is occupied without duplication. Relative positions are indicative of the axial inclination and orbital ellipticity of the nine planets. Mathematical substantiation is developed by showing the system is a solution of the regularized three body problem. Reasonable assumptions made from the graphical study confirm this mathematical solution.

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