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In "snow globe theory"
one must use the reciprocal of the scale change to calculate the local behavior of the scale in question from a distance.
In Wikipedia, under Laplace-Runge-Lenz vector, one can find a formula
for calculating the perihelion precession from a perturbation potential.
Δφ =1/kε•∫
r²ϐrΦ(r)cos(dφ) dφ von 0 bis 2π
Where in the one-body problem (Kepler's problem), m=1 and k=G•M are set. Unperturbed or with Newtonian potential,
the integral is zero (check it). In a gravitational field with potential P= -G•M/r (M is the central mass) and T=M•G/c²,
the reciprocal of the length scale contraction is equal to 1+T/r.
The reciprocal of the time scale extension is equal to 1/(1+T/r). The factor 1+T/r is also the factor for the "ghost mass"*.
In addition to the "ghost mass" the relative speed of light plays a role as a characteristic in the Keplerian orbit.
This has the reciprocal (1+T/r)². As with the deflection of light, it influences the potential.
The perturbation** therefore has the factor (1+T/r)³-1, (1+T/r)³ = 1+3T/r + O(T²/r²).
Thus, the perturbation potential is P•3T/r = -3k•T/r². An additional multiplication in the integral by (1+T/r)²
would have no effect, since only the factor 1 makes a significant contribution.
ϐrΦ(r) is then -2•-3k•T/r³=6k•T/r³.can be canceled by the denominator.
The total is now:
Δφ =1/kε•∫
6k•T•((1+ε•cos(φ))/a(1-ε²))•cos(φ) dφ
with r(ellipse)=a(1-ε²)/(1+ ε•cos(φ)).
The integral from 0 to 2π is zero for cos and π for cos².
Thus, the perihelion precession is:
T•6π/a(1-ε²)=6π•G•M/(c²•a(1-ε²))
This is the same formula that Einstein determined using spacetime curvature.
You can see: Everything Einstein's theory proves also proves my theory.
Note:
Ghost mass, potential change, and the Schwarzschild metric only apply from the perspective of the distant radius.
However, since the time relationships in the Sun's "weak" gravity do not change, the formula also applies at closer distances.
Why doesn't this derivation work locally?
A coordinate axis, for example, would be the line from the Sun to the center of the Milky Way.
A star far away would lie on this axis. From a local system near the Sun, this star would have negative ghost mass.
Its relative speed of light would be increased. Its apsidal line would move backward toward this local system.
The coordinate axis mentioned above therefore does not belong to the local system.
Locally, Newton's gravity and the "snow globe principle" apply.
* Mass (an effect like mass) that is not present locally. Gravitationally, it is always associated with red/blue shift.
**Perturbation is the term used in physics for deviation from the conic section.
Ludwig Resch
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