Dear Myron,
I have now resumed graphical/artistic analysis of previous studies, again with focus on the M51 Whirlpool Galaxy and its Hyperbolic Spiral Development.
Please note: I have excluded any notably higher velocity emissions in this part of my studies.
m = any isolated mass emitted from the galactic core area and in hyperbolic spiral orbit as depicted by spiral arms and their extensions.
r = radial distance between M (the Galactic Core or central Mass) and centre of m.
T = Torsion
HS = hyperbolic spiral
In recreating the HS orbit path that best suits the visual data (spiral arm definition and evolution), several points have arisen as related below; bearing in mind that I am presently considering the spinning of Torsion from a fixed frame of reference with fixed x and y axes at present and, would isolate the HS development of m and particularly its orbital velocity in such minimal, fiixed coordinates.
1. After few trials so far, I have produced a decelerating orbital velocity of m which becomes almost constant at some point beyond the outer reaches of the galaxy (in the absence of any forces other than Galactic Torsion; i.e. no spin of m or other inertial forces applied). It may be, that in compliance with the almost straight but never 0 degrees of arc aspect of the HS, the velocity at which m reaches a value of r that is just outside the visible realms of the imagery used, my assumption being that other spacetime systems will begin to affect m after T has faded to some distant r value.
In short, the velocity of m is, or becomes to all intents and purposes, constant after and at whatever value it had on leaving the outer bounds of the galaxy.
I have constructed a constant orbital velocity, acting from the galactic core to its outer bounds, which has given rise to my questioning of what the velocity type should actually be.
The constant velocity scenario would appear to defy the torsion in so far as its Hyperbolic development sends m out into the torsion “field” and progressively outward where, as r logarithmically increases so the torsional orbit velocity decreases, which would result in m travelling faster than its surrounding or “carrier” torsion “field”. That is, m would still be travelling at the speed it left the core area where torsion would not.
Stressing again that I am analysing what would be the motion of just the Torsion alone and treating m almost as flotsam in a liquid analogy of minimal parameters.
2. If the orbital velocity of m were constant, and if the galactic or core Torsional, rotational velocity diminished radially, then a would-be constant velocity of m would still decelerate as r increases; that is, given that torsion is inceptually “carrying” m at emission point from the core, then a constant velocity would have to appear as an addition to the torsional, rotational velocity that although decrementing outwardly (with increasing r), if added to an inherent constant velocity of m in isolation, will still produce a deceleration of m down to any velocity it was given at inception and in addition to torsion. This would not make m follow the general spiral trend in my opinion.
The question this raises in my mind is that to acheive a truly constant velocity, other incrementing forces must be at work where at least one force is incrementally gaining velocity or momentum to counter the deceleration of the torsional field. Are there known forces (in this area) that give increasing velocity after an otherwise peak?
Thus far and unschooled, I have concluded that all velocities must be decelerating as r value increases, up to the point where torsion is reduced to acting minimally – as m and T evolve into the straightest, almost imperceptible arc part of the Hyperbolic Spiral evolution.
3. Am I correct to assume that one suitable, single Hyperbolic Spiral may be used and that it may be scaled up or down, or “fractalised” so that variations in the velocity of m (having been acted upon by explosive emission say) may be reflected by such reduced scale replicas of just the one HS? That the scaling of just one HS can describe all spiral galaxies? I have experimented with this and believe that one HS can describe a range of velocities when scaled up or down, that is if scaled small enough the HS can appear as a straight line with a slightly bending blob at one end and could look like a “sunray”; Other scalings closer to the general spiral of the M51 spiral arms, reflect collision debris orbits being “picked up” from slower velocity to the “average” velocity of the most prominent, visible developments.
I would much appreciate any comments or further guidance,
Best regards,
Robert
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