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A rotating gravitational ellipse Stefan Boersen 18 march 2015 Berlin
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Objective
A rotating gravitational ellipse
Le Verrier (1811-1877) stated: 'Rotating gravitational ellipses are observed', so lets make a differential equation resulting in a rotating gravitational ellipse in an Euclidean space on the computer. The mathematical tasks is now on the table.
http://www.stefanboersen.nl/RotatingGravitationalEllipse.pdf
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Content 1 Observation: A Rotating gravitational ellipse (Le Verrier)
2 Mathematical work to be done: The third time differentiation of space-by-time
3 The objective: The third-order equation
4 Conclusion
5 Questions
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SlideNumber
The additional rotation is an extra parameter, so the equation will be a three times space-by-time differentiated equation.
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The differentiation of space-by-time
X = R cos(a)
Y = R sin(a)
d(X)/dt
d(Y)/dt
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The differentiation of space-by-time
The first time differentiation of space-by-time
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The second time differentiation of space-by-time
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The differentiation of space-by-time
New 8
X = R cos(a) , Y = R sin(a)
Coriolis 0
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2
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The second time differentiation of space-by-time
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Fcentrifugal
Fcoriolis
Fa
The second time differentiation of space-by-time
Fr Fy
Fx
Fcentrifugal
Fa
Fcoriolis
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Faction = - Freaction
The third time differentiation of space-by-time
New centrifugal third order interactions
New angular Coriolis third order interactions
Gr
Ga
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The third time differentiation of space-by-time
Gr Gy
Gx
Gcentrifugal first term
Ga
Gcoriolis consists of three terms F => G Force = Second order interaction G = Third order interaction
Gcentrifugal second term
ThirdOrder Action = - ThirdOrder Reaction 12
The third time differentiation of space-by-time
Gr Gy
Gx
Ga
The new third order Coriolis terms
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Content 1 Observation: A Rotating gravitational ellipse (Le Verrier)
2 Mathematical work to be done: The third time differentiation of space-by-time
3 The objective: The third-order equation
4 Conclusion
5 Questions
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The third-order equation Trajectories of planets are described using the following two equations.
Differentiate these equations:
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The third-order equation
Rearrange the equations:
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The third-order equation
From the third order space by time relation we have:
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The third-order equation
From the third order space by time relation we have:
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The third-order equation The third order interaction:
We can create this result by doing a rotational transformation. http://www.stefanboersen.nl/RotatingGravitationalEllipse.pdf
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The third-order equation
Ga
Gr
?
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Content 1 Observation: A Rotating gravitational ellipse (Le Verrier)
2 Mathematical work to be done: The third time differentiation of space-by-time
3 The objective: The third-order equation
4 Conclusion
5 Questions
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Conclusion
d(Fr)/dt is not equal Gr d(Fx)/dt
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A rotating gravitational ellipse Stefan Boersen 18 march 2015 Berlin
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Objective
Conclusion We were able to construct an differential equation having a rotating gravitational ellipse as the result.
There are now two differential equations resulting in rotating gravitational ellipses , the relativistic EIH equation and the third order differential equation.
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Questions Any questions?
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http://www.stefanboersen.nl/RotatingGravitationalEllipse.pdf
References 1. Newton, Isaac. "Philosophiæ Naturalis Principia Mathematica (Newton's personally annotated 1st edition)". 2. Tisserand, M.F. (1880). 'Les Travaux de LeVerrier'. Annales de l'Observatoire de Paris, Memoires, XV (in French)., at SAO/NASA ADS 3. G-G Coriolis (1835). 'Sur les equations du mouvement relatif des systemes de corps'. J. De l'Ecole royale polytechnique 15: 144-154.
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Answers What about relativity ?
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.
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The third-order equation
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The third-order equation This results to the following equations:
Original equations:
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Conclusion
Third interaction over a distance 30
