The dr / dtheta Comparison

This is a particularly interesting and important result, the graphics here vividly illustrate the effect of special relativity. The overall conclusion is the Lorentz covariant ECE2 theory allows the use of the familiar equations of special relativity, notably the hamiltonian and lagrangian. A numerical method of solution developed by co author Horst Eckardt leads to results that cannot be obtained analytically. This situation is similar to molecular dynamics or Monte Carlo computer simulation, where results can be obtained that are intractable analytically. So the numerical solution of the lagrangian of special relativty produces the true orbit. This method also produces the true orbitals of the Sommerfeld atom, the first relativistic quantum theory. The Einstein theory produces a ridiculously incorrect orbit if we expand our horizons form the seconds of arc perspective to the complete orbit. The Marion / Thornton approximation to Einstein gives a completely unphysical orbit that diverges. The x theory produces a precessing ellipse initially, but as x increases the orbit of x theory becomes the fractal conical sections, also discovered by the AIAS group. The fractal conical sections are mathematically valid, but they do not give the true orbit. So mainframes and supercomputers should be used to try to give a precise comparison of special relativistic precession with experimental data. Given the new principle of special relativity of recent UFT papers that v0 squared is bounded above by c squared / 2, special relativity gives light deflection by gravitation exactly. So these are historic advances in physics and cosmology. Special relativity also describes the fundamentals of the velocity curve of a whirlpool galaxy, where Einstein fails completely. So I will now proceed to write up UFT328, Sections One and Two.

To: Emyrone@aol.com
Sent: 28/09/2015 21:41:51 GMT Daylight Time
Subj: PS PS: p/L and other quantities in relativistic context

PS PS: I forgot the dr/dtheta comparison. It can be seen that this
changes sign, therefor the doubled structures. In polar diagrams,
negative functional values are represented by an argumen t schift of 180
degrees.
Horst

Am 28.09.2015 um 22:32 schrieb Horst Eckardt:
> PS: it makes less sense to compare orbital radii between different
> theories directly because precession leads to large differences. You
> would have to subract the precession anyhow to make differences in
> orbital curvature comparable for example.
>
>
> Am 28.09.2015 um 22:28 schrieb Horst Eckardt:
>> I compared the results of the Newtonian Lagrange eqautions with those
>> of the relativistic Lagrangian. Initital conditions were the same,
>> and angular momenta were also the same. It is not possible to use L0
>> in the relativistic equation because this is not a constant of motion
>> there.
>> From Fig.7 (orbits) it can be seen that the relativistic orbit is
>> significantly larger for the same intial conditions. This is a hint
>> that it makes no sense to use an equation for the non-relativistic
>> orbit (p0 in note 328(5)) in a relativistic context.
>> Fig. 10 shows gamma(theta), this varies only between 1.00 and 1.03.
>> However the orbital precession is significant, see Fig. 7. The
>> quantities rdot, theta dot, v/c resemble each other, there is a bend
>> at the aphelion. This also holds for p/L (Fig. 13).
>> I will see which anlaytical results can be compared with these
>> curves, for example extracting a precession parameter.
>>
>> Horst
>

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