TAB 5

A LOCUTUS AT BARYCENTER

This report attempts to establish a physical phenomena to resolve the "error" in the second term of the trigonometric series representation of the ellipse ( 1 ). As illustrated, the deviation of second order is a cosine function of twice the frequency and a fraction of the amplitude as the first term. The two perturbations together produce a result accurate to at least eight significant digits (i.e. for e=.01, the maximum permissible). Given all the other unknowns in a system of many bodies like the solar system, this is the best approximation one should reasonably expect since anything more accurate would be inconsistent with the situation and the natural order of things.

Imagine a simple 3BP consisting of an object in Earth orbit. Since 99.5 % of all satellites are in nearly circular orbits, e<.01, it is reasonable to suppose the alleged sinusoidal variation from the unit circle orbit is bona fide.

The error in the ellipse has the same pattern and frequency as the motion of the barycenter in a sun/planet/satellite 3BP. That is, if the planet were in a low eccentricity orbit, this orbit could be modeled accurate to eight significant digits by simply ignoring the motion at barycenter - i.e. fixing the distance from the origin for larger primary body near the sun, and varying the motion of the planet by just the first term of the series representation of the low e orbit. (1)

Another solution to this 3BP is an anomaly within the sun, in the same plane as the planet's orbit, moving in such a way as to result in a 3BP solution to the circular coplanar problem.

A combination of these two alternatives would explain the evolution of a stable planet. An unstable circular orbit initially creates a virtual singularity in the sun, around which an anomaly develops over time (like a pearl around a grain of sand in an oyster) as the planet's orbit becomes stable and elliptical.

This kind of scheme is suggested by the "vortex" at the origin of the symmetric plane ( 2 ). Any new body or cloud of mass entering the solar system would assume a circular orbit initially, a very dangerous even for the dynamically delicate solar system (circular orbits being a singularity). Instead of initiating a point singularity within the sun itself (a uniform hoop of mass is a point gravity source) - a disastrous calamity - the asymmetric origin of the symmetric plane simulates a non-circular orbit, until such time as overall equilibrium can result for the solar system as a whole in the presence of this new massive body.

At the same time, this symmetric plane makes the solar system seem a point source from a long distance (e.g. a "black hole"), thus allowing it to attract mass and energy sufficient to make it a self sustaining system. Conversely, as the star weakens the invariant plane weakens, and the symmetric plane strengthens until it reaches the point where the vortex overcomes the point singularity inclination and the system explodes and then the process starts all over again, the anomaly in the sun forming the core for the brand new star. With each iteration, the solar system becomes more and more complex (ours is likely among the very oldest star systems - with only one gas giant remaining), until eventually the star can possibly switch over without altering gravity, leaving one or two planets unchanged: Earth is like that.

Precession of Mercury's Perihelion

 

NOTE: By fractal theory, if the L6 point causes anomalies in gas giants - Jupiter's Red Spot and Uranus' Dark Spot - then it should also cause anomaly within the sun as posed here.

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© 2004 WH Clark