Yes all agree that they are incisive and very helpful to the reader, even the general reader with no mathematical training. I fully agree with this project, I have just started an analysis of a three dimensional hyperbolic orbit in note 270(4) and that is simple to work with. The usual dogma as in Marion and Thornton asserted that a constant angular momentum L = r x p means that both r and p are coplanar, so plane polar coordinates can be used. However, this is obviously wrong from the fundamental analysis of angular momentum in spherical polar coordinates given in UFT269. The usual dogma was simply an assertion that L is in the Z axis. This is only a special case.

To: EMyrone@aol.com

Sent: 01/09/2014 11:02:32 GMT Daylight Time

Subj: Re: Animation of elliptic 3D orbitI am glad that my contributions are received so well.

Concerning the problem that spiral galaxies are mostly planar: A gaseous cloud is 3D, and if the angular momentum is conserved during building of galaxies and stars, so the galaxy structure should also be 3D. There could be a mechanism changing the angular momentum over time. What about assuming a spacetime or ether current that interacts with stars and gases over billions of years? This could be modeled by a simple approach with an inelastic interaction between current and star motion so that the angular component perpendicular to the current is annihilated. Perhaps this is worth some thoughts.Horst

EMyrone@aol.com hat am 31. August 2014 um 17:00 geschrieben:

This is an excellent animation and shows immediately that the 3 -D orbit is a lot more intricate than the 2 – D orbit. The inversion problem is indeed a difficult one, and goes right back to Kepler himself. The computer might be able to find the answer straightforwardly. As Horst writes this should be regarded as a first attempt, but it is already full of originality. Obviously we have opened up a completely new subject area in cosmology upon which all can agree because it is based on the spherical polar coordinates.

To: EMyrone@aol.com

Sent: 31/08/2014 14:44:45 GMT Daylight Time

Subj: Animation of elliptic 3D orbitThis is an animation for the beta ellipse in 3D, parametrized by the theta angle. Since the theta grid has been chosen equidistant, the motion speed is not physical. I am not sure if the orbit is compatible with the first 3D surface r(theta,phi) shown in paper 269,3 (Figs. 3/4). Normally this should be a trace on the surface. This has further to be analysed. It would also not be straightforward to compute the right timing behaviour because the time function has to be inverted which has to be done numerically.

Horst