Very interesting results. Google “largest observed orbital processions” and the seventh or eighth site gives one of 39 degrees per orbit in Quasar OJ287. This is many orders of magnitude greater than precessions in the solar system. There is a large mass orbiting another large mass. These are called “black holes” by the dogmatists but in ECE physics they are just large masses. Agreed about the other points. I will now proceed to writing up UFT374.
Sent: 07/04/2017 11:46:31 GMT Daylight Time
Subj: Re: Precessing Orbits with Cartesian Coordinates
To your comments:
1) setting bold v_f=0 gives the Newtonian equation
bold X dot dot = – MG bold X / r^3
with r = sqrt(X^2 + Y^2) as usual. The orbit is an ellipse as in the case of plane polar coorinates, see Fig. 8. This is well known. The Newtonian frame is a static frame and therefore shows no centrifugal force term, but the result is the same as for a rotating frame since the physics must be independent of the frame chosen.
2) As shown above, a static ellipse is the standard result with no fluid velocity terms. We could add an additional centrifugal or centripetal force by fluid dynamics effects. In such a way we could test a theory supposing that gravitation comes from the fact that heavy masses attract aether particles so that this flow acts like a gravitational centripetal force. We would have to set M=0 in this case and set up a suitable vf.
3) In my earlier example I used for vf:
vf_X = a0*Y
vf_Y = a0*X.
Interestingly the same equations of motion result if X and Y is interchanged:
vf_X = a0*X
vf_Y = a0*Y.
(index dd stands for dot dot).
For a small a0, a small precession comes out, see Fig. 8a. The precession increases for larger a0 (rosette form as I already sent over). Interestingly the angular momentum
L = m bold r x bold v = m ( Y dot * X – X dot * Y)
remains unchanged within numerical precision.
Alternatively I used a quadratic vf:
vf_X = a0*X^2
vf_Y = a0*Y^2.
i.e. we have additional cubic terms. The orbit then is periodic in several periods, see Fig. 8b.
4) We need experimental data from a heavy astronomical object with precession as high as possible. More difficult will be that we have to have the initial conditions for the real orbit. With these data we can apply any of our developed methods to either determine a spin connection, gamma factor or fluid velocity model.
Am 07.04.2017 um 10:45 schrieb EMyrone:
I like this work, it shows clearly that the addition of a velocity field gives a precessing orbit, a remarkable result. I have a few comments.
1) If the field terms v sub fX and v sub fY are zero there is no centrifugal force, in which case there is no orbit. This can be checked with computer algebra.
2) It would be interesting to find under what conditions a static ellipse is obtained. In that case the fields are acting as if they were a centrifugal force.
3) It is interesting to graph the kinds of orbit that are given by different fields.
4) Compare the precessing orbit with experimental data.
The basic idea is that spacetime or ather is a fluid.
Sent: 06/04/2017 09:31:37 GMT Daylight Time
Subj: Re: A direct approach to mass point dynamics in a fluid
I programmed this model, this time in cartesian coordinates so that velocities of the fluid can be defined more easily. I used the Lagrange method with Lagrangian
A general velocity field (vfx, vfy) has been added in the kinetic energy terms. Then the most general Euler-Lagrange equations then are:
For a constant vf there is no change in the equations of a masspoint without fluid velocity, that means such a case is contained in appropriate initial conditions. By defining any form of vf one can obtain various orbit types as I found in the ECE2 fluid dynamics case. For example
gives a rosette which is a precessing ellipse with large precession angle, see Fig. 6. The precession can be minimized by a0 –> 0.
Am 05.04.2017 um 09:11 schrieb Horst Eckardt:
What about the following approach (in cartesian coordinates):
Given: a velocity field bold vf(X,Y,Z,t)
Coordinates of mass point: X,Y,Z
velocity of mass point:
bold v = (v_X + vf_X, v_Y + vf_Y, vZ + vf_Z)
with v_X = X dot, etc.
The Lagrange equations can be obtained from the above equation for bold v. It has to be checked if this is a valid precedure because in Lagrange theory normally the coordinates are transformed and not the velocities. As an alternative, one could certainly solve Newton’s equations directly.
This model does not include viscosity or other additional effects.