TAB 27

THE ENVELOPE CURVE

Take the 2^nd order Ordinary Differential Equation (ODE) for the three bodies and form a 3x3 matrix, set the determinant equal to zero, and solve for the eigenvalues and eigenvectors. The eigenvectors will be the stable inertial axes of the gravity ellipsoid (bonding orbital orientations at the atomic level). The eigenvalues will be the "buckling modes" or the rate of vibration at which these molecular bonds will break. A stable vibration about these bonding orbitals will result in the controlled emission of bonding energies by E=mc² - heat. There are probably some materials that will emit energy directly as EM waves, or that can be made to do so as an energy source.

As a preliminary to the following derivation of the Law of Gravity used by Newton, consider the impact of Relativity - which adds a term to the Universal Law of Gravity

What does this imply? Geometrically, Relativity says straight lines are not straight, or the shortest distance between two points; circles aren't circles, mass isn't mass, density cannot be uniform, and angles cannot be measured accurately. This obfuscates every principle of analytical geometry and every notion of common sense.

Gravity

It is really quite elementary, how Newton derived the Universal Law of Gravity (Moulton, p. 104). He used just one figure:

The two spherical shells attract a particle p (at the apex of the lines) equally because any solid angle which includes part of one shell also includes a similar part of the other shell. The masses of these included parts are as the square of their distances, and their attractions are inversely as the square of their distances. Thus, you get the above equation (without R).

In the calculus, which Newton created later, you get

The correction due to Relativity is

where c is the speed of light; so the correction is admittedly exceedingly small. However, this does alter the geometry of the problem in such a way that Kepler's 2^nd Law works for eccentric orbits, even though the math is for circular orbits. Relativity, with this constant, presumes to change space AND time; when, in fact, the whole analysis here takes a much more rational approach, that time is invariant and only space is distorted because of extremely high gravity.

The Small Eccentricity Ellipse

The theory posed here argues for a geometric distortion in the neighborhood of the sun, for example, that for a small eccentricity ellipse puts the focus at the ellipse to be coincident with the geometric center of the ellipse, in such a way that the orbiting body is then acted upon by the usual inverse squared gravity force, plus the much more subtle 1/r force whose action causes the precession of the perihelion of the inner planets, most notably Mercury.

The 1/r force at work

The above illustration shows this affect in great detail; whereas an ellipse is a conic section, and the foci are each so close to the geometric center of the ellipse; whence the peculiar motion of the origin of the symmetric plane makes the foci and the center coincident during much of the orbit, the remainder being negligible - zeroing out over the long term.

What this means is that Relativity serves to correct a simple error in geometry by causing the local distortion of space and time, and - moreover - propagates this unnecessary distortion through the space sciences by actual altering the most fundamental law of them all, the Universal Law of Geometry. This has had the affect of making all the basic sciences more and more abstract and statistical, less and less realistic and practical.

To whit, any violation of this law of Relativity must do so using equally simple geometry - e.g. Kepler's 2^nd Law of Equal Areas, which has been shown to itself be flawed. It is not good science to justify a flaw with a flaw.

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© 2004 WH Clark